Engineering Mechanics Dynamics Rc Hibbeler 6th Edition Solution Manual ( Pdfdrive.com ).pdf
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Engineering Mechanics Dynamics Rc Hibbeler 6th Edition Solution Manual ( Pdfdrive.com ).pdf as PDF for free.
More details
- Words: 5,598
- Pages: 148
Loading documents preview...
Engineering Mechanics Dynamics R.C. Hibbeler 6th edition Solution manual; manual & mathcad December 2015. V0.1 March 2018 V0.2
Made by A.J.P. Schalkwijk
12.1 Rectilinear Kinematics: Continuous Motion
Page 7, example 12-1: The car in fig. 12-2 moves in a straight line such that for a short time it's velocity is defined by v=(9t^2 + 2t) ft/s, where t is in seconds. Determine its position and acceleration when t=3s. When t=0, s=0.
Page 8, example 12-2: A small particle is fired vertically downward into a fluid medium with an initial velocity of 60m/s. If the projectile experiences a deceleration which is equal to a=(-0.4v^3) m/s^2, where v is measured in m/s, determine the projectile's velocity and position 4s after it is fired.
Page 9, example 12-3: A boy tosses a ball in the vertical direction of the side of a cliff, as shown in fig. 12-4. If the initial velocity of the ball is 15m/s upward, and the ball is released 40m from the bottom of the cliff, determine the maximum height Sb reached by the ball and the speed of the ball just before it hits the ground. During the entire time the ball is in motion, it is subjected to a constant downward acceleration of 9.81m/s^2 due to gravity. Neglect the effect of air resistance.
Page 10, example 12-4: A metallic particle is subjected to the influence of a magnetic field such that it travels downward through a fluid that extends from plate A to plate B, fig 12-5. If the particle is released from rest at the midpoint C, s=100mm, and the acceleration is measured as a=(4s)m/s^2, where s is in meters, determine the velocity of the particle when it reaches plate B, s=200mm, and the time it needs to travel van C to B.
Page 11, example 12-5: A particle moves along a horizontal line such that it's velocity is given by v=(3t^2-6t)m/ s, where t is the time in seconds. If it is initially located at the origin O, determine the distance traveled by the particle during the time interval t=0 to t=3.5, and the particle's average velocity and average speed during this time interval.
Page12, problem 12-1: If a particle has an initial velocity of V0=12ft/sec to right, determine its position when t=10s, if a=2ft/sec^2 to the left. Originally s0=0.
Page 12, problem 12-2: From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed of 80.7 ft/sec (55 mi/hr) when it hits the ground? Each floor 12ft higher than the one below it.
Page 12, problem 12-3: A particle is moving along a straight line such that its position is given by s=(4t-t^2) ft., where t is in seconds. Determine the distance travelled from t=0 to t=5s, the average velocity, and the average speed of the particle during this time interval.
Page 12, problem 12-5: A particle is moving along a straight line path such that it's position is defined by s=(10t^2+20)mm, where t is in seconds. Determine (a) the displacement of the particle during the time interval from t=1 s to t=5 s, (b) the average velocity of the particle during this time interval, and (c) the acceleration at t=1 s.
Page 12, problem 12-6: A ball is thrown vertically upward from the top of a ledge with an initial velocity of Va=35ft/sec. Determine (a) how high above the top of the cliff the ball will go before its stops at B, (b) the time Ta-b it takes to reach its maximum height, and (c) the total time Ta-c needed for it to reach the ground at C from the instant it is released.
Page 12, problem 12-7: A car, initially at rest, moves along a straight road with constant acceleration such that it attains a velocity of V=60ft/s when s=150ft. Then after being subjected to another constant acceleration, it attains a final velocity of V=100ft/s when s=325ft. Determine the average velocity and average acceleration of the car for the entire 325ft displacement.
Page 12, problem 12-9: When a train is travelling along a straight track at 2m/s, it begins to accelerate at a=(60V^-4)m/s^2, where V is in m/s. Determine the velocity V and the position of the train 3sec. after the acceleration.
Page 12, problem 12-10: A race car uniformly accelerates at 10ft/s^2 from rest, reaches a maximum speed of 60mi/h, and then decelerates uniformly to a stop. Determine the total elapsed time if the distance travelled was 1500ft.
Page 13, problem 12-11: A small metal particle passes through a fluid medium under the influence of magnetic attraction. The position of the particle is defined by s=(0.5t^3+4t)inch., where t is in seconds. Determine the position, velocity, and acceleration of the particle when t=3s.
Page 13, problem 12-13: A particle travels to the right along a straight path with a velocity v=[5/(4+s)]m/s, where s is in meters. Determine its position when t=6s if s=5m when t=0.
Page 13, problem 12-14: The velocity of a particle traveling along a straight line is v=(6t-3t^2)m/s, where t is in seconds. If s=0 when t=0, determine the particle's deceleration and position when t=3s. How far has the particle traveled during the 3-s time interval, and what is the average speed?
Page 13, problem 12-17: At the same instant, two cars A and B start from rest at a stop line. Car A has a constant acceleration of aA=8m/s^2, while car B has an acceleration of aB=(2t(3/2))m/s^2, where t is in seconds. Determine the distance between the cars when A reaches a velocity of Va=120km/h.
Page 13, problem 12-18: A particle moves along a straight path with an acceleration of a=(5/s)m/s^2, where s is in meters. Determine the particle's velocity when s=2m if it is released from rest when s=1m.
Page 13, problem 12-19: A particle moves with accelerated motion such that a=-k*s, where s is the distance from the starting point and k is a proportionality constant which is to be determined. When s=2ft the velocity is 4ft/s, and when s=3.5ft the velocity is 8ft/s. What is s when v=0?
Page 13, problem 12-21: A particle moving along a straight line is subjected to a deceleration a=(-2v^3)m/ s^2, where v is in m/s. If it has a velocity v=8m/s and a position s=10m when t=0, determine its velocity and position when t=4s.
Page 14, problem 12-22: The acceleration of a rocket travelling upward is given by a=(6+0.02s) m/s^2, where s in meters. Determine the rocket's velocity when s=2km and the time needed to reach this elevation. Initially, v=0 and s=0 when t=0.
Page 14, problem 12-23: Two trains are traveling in opposite directions on parallel tracks. Train A is 150m long and has a speed which is twice as fast as train B, which is 250m long. Determine the speed of each train if a passenger in train A observes that train B passes in 4s.
Page 14, problem 12-25: The juggler maintains the motion of three balls, such that each rises to a height of 4ft. If two balls are in the air at any one time, determine the time the third ball must remain in her hand after the first ball is thrown.
Page 14, problem 12-26: The juggler throws a ball into the air 4ft above her hand. How much time will elapse before she must catch it at the same elevation from which she threw it? What would be the elapsed time if she threw it 8 ft into the air?
Page 14, problem 12-27: When two cars A and B are next to one another, they are traveling in the same direction with speeds Va and Vb, respectively. If B maintains its constant speed, while A begins to decelerate at aA, determine the distance between the cars at the instant A stops.
Page 14, problem 12-29: When a particle falls through the air, it's initial acceleration a=g diminishes until it is zero, and thereafter it falls at a constant velocity Vf. If this variation of the acceleration can expressed as a=(g/Vf^2)(Vf^2-V^2), determine the time needed for the velocity to become V
12.2 Rectilinear Kinematics: Erratic Motion
Page 17, example 12-6: A car moves along a straight line path such that its position is described by the graph shown in fig. 12-9a. Construct the v-t and a-t graphs for the time period 0
Page 19, example 12-7: A rocket sled starts from rest and travels along a straight track such that it accelerates at a constant rate for 10s and then decelerates at a constant rate. Draw the v-t and s-t graphs and determine the time t' needed to stop the sled. How far has the sled traveled?
Page 21, problem 12-8: The v-s graph describing the motion of a motorcycle is shown in fig. 12-15a. Construct the a-s graph of the motion and determine the time needed for the motorcycle to reach the position s=400ft.
Page 22, problem 12-31: If the position of a particle is defined as s=(5t-3t^2) ft, where t is in seconds, construct the s-t, v-t and a-t graph for 0 < t < 10 s.
Page 22, problem 12-33: The speed of a train during the first minute of its motion has been recorded as follows:
Plot the v-t graph, approximating the curve as straight line segments between the given points. Determine the total distance traveled.
Page 22, problem 12-34: The s-t graph for a train has been determined experimentally. From the data, construct the v-t and a-t graphs for the motion.
Page 22, problem 12-35: Two cars start from rest side by side at the same time and position and race along a straight track. Car A accelerates at 4 ft/ s^2 for 35 s and then maintains a constant speed. Car B accelerates at 10 ft/s^2 until reaching a speed of 45mi/h and then maintains a constant speed. Determine the time at which the cars will again be side by side. How far has each car traveled? Construct the v-t graphs for each car.
Page 22, problem 12-37: From experimental data, the motion of a jet plane while traveling along a runway is defined by the v-t graph. Construct the s-t and a-t graphs for the motion.
Page 23, problem12-38: The car travels along a straight road according to the v-t graph. Determine the total distance the car travels until it stops when t=48sec. Also plot the s-t and a-t graphs.
Page 23, problem 12-39: The snowmobile moves along a straight course according to the v-t graph. Construct the s-t and a-t graphs for the same 50 s time interval. When t=0, s=0.
Page 23, problem 12-41: The v-t graph for the motion of a car as it moves along a straight road is shown. Construct the s-t graph and determine the average speed and the distance traveled for the 30 s time interval. The car starts from rest at s=0.
Page 23, problem 12-42: A particle starts from rest and is subjected to the acceleration shown. Construct the v-t graph for the motion, and determine the distance traveled during the time interval 2s < t < 6s.
Page 24, problem 12-43: An airplane lands on the straight runway, originally traveling at 110ft/s when s=0. If it is subjected to the decalerations shown, determine the time t' needed to stop the plane and construct the s-t graph for the motion:
Page 24, problem 12-45: The a-t graph for a car is shown. Construct the vt graph if the car starts from rest at t=0. At what time t' does the car stop?
Page 24, problem 12-46: A race car starting from rest travels along a straight road and for 10s has the acceleration shown. Construct the v-t graph that describes the motion and find the distance traveled in 10s.
Page 25, problem 12-47: The boat is originally traveling at a speed of 8 m/s when it is subjected to the acceleration shown in the graph. Determine the boat's maximum speed and the time t when it stops.
Page 25, problem 12-49: The a-s graph for a race car moving along a straight track has been experimentally determined. If the car starts from rest, determine its speed when s=50 ft, 150ft and 200ft, respectively.
Page 25, problem 12-51: The jet plane starts from rest at s=0 and is subjected to the acceleration shown. Construct the v-t graph and determine the time needed to travel 500ft.
Page 26, problem 12-53: The v-s graph for the car is given for the first 500ft of its motion. Construct the a-s graph for 0<s<500ft. How long does it take to travel the 500ft distance? The car starts at s=0 when t=0.
Page 26, problem 12-54: The a-s graph for a boat moving along a straight path is given. If the boat starts at s=0 when v=0, determine its speed when it is at s=75ft and 125ft respectively. Use Simpson's rule with n=100 to evaluate v at s=125ft.
12.3 General Curvilinear motion
Page 32, example 12-9: At any instant the position of the kite in fig. 12-18a is defined by the coordinates x=30t and y=9t^2 ft, where t is given in seconds. Determine (a) the equation which describes the path and the distance of the kite from the boy when t=2s, (b) the magnitude and direction of the velocity when t=2, and (c) the magnitude and direction of the acceleration when t=2sec.
Page 33, example 12-10: The motion of a bead B sliding down along the spiral path shown in fig. 12-19 is defined by the position vector r={0.5sin(2t)i + 0.5cos(2t)j - 0.2tk}m, where t is given in seconds and the arguments for sine and cosine are given in radians (pi rad = 180deg). Determine the location of the bead when t=0.75s and the magnitude of the bead's velocity and acceleration at this instant.
Page 36, example 12-11: A ball is ejected from the tube, shown in fig 12-21 with a horizontal velocity of 12 m/s. If the height of the tube is 6m, determine the time needed for the ball to strike the floor and the range R.
Page 37, example 12-12: A ball is thrown from a position 5 ft above the ground to the roof of a 40ft high building, as shown in fig 12-22. If the initial velocity of the ball is 70ft/s, inclined at an angle of 60deg from the horizontal, determine the range or horizontal distance R from the point where the ball is thrown to where it strikes the roof.
Page 38, example 12-13: When a ball is kicked from A as shown in fig. 12-23, it just clears the top of the wall at B as it reaches its maximum height. Knowing that the distance from A to the wall is 20m and the wall is 4m heigh, determine the initial speed at which the ball was kicked. Neglect the size of the ball.
Page 39, problem 12-55: If x=1-t and y=t^2, where x and y are in meters and t is in seconds, determine the x and y components of velocity and acceleration and construct the path y=f(x).
Page 39, problem 12-57: If the position of a particle is defined by its coordinates x=4t^2 and y=3t^3, where x and y are in meters and t is in seconds, determine the x and y components of velocity and acceleration and construct the path y=f(x).
Page 39, problem 12-58: The position of a particle is defined by
If , where t is in seconds, determine the particles velocity v and acceleration a at the instant t=1 sec. Express v and a as Cartesian vectors.
Page 39, problem 12-59: If the velocity of a particle is v(t)={0.8t^2i + 12t^0.5j + 5k}m/s, determine the magnitude and coordinate direction angles a,b and c of the particle's acceleration when t=2s.
Page 39, problem 12-61: A particle travels along the curve from A to B in 2s. It takes 4s for it to go from B to C and then 3s to go from C to D. Determine its average velocity when it goes from A to D.
Page 39, problem 12-62: A particle moves with curvilinear motion in the positive x-y plane such that the y component of motion is described by y=7t^3, where y is in feet and t is in seconds. When t=1s, the particle's speed is 60ft/s. If the acceleration of the particle in the x direction is zero, determine the velocity of the particle when t=2s.
Page 39, problem 12-63: A car traveling along the road has the velocities indicated in the figure when it arrives at it points A, B and C. If it takes 10s to go from A to B, and then 15s to go from B to C, determine the average acceleration between points A and B and between points A and C.
Page 40, problem 12-66: The flight path of the helicopter as it takes off from A is defined by the parametric equations x=(2t^2)m and y=(0.04t^3)m, where t is the time in seconds after takeoff. Determine the distance the helicopter is from point A and the magnitude of its velocity and acceleration when t=10s.
Page 40, problem 12-67: A particle is moving along the curve y=x-(x^2/400). If the velocity component in the x direction is Vx=2ft/s, determine the magnitude of the particle's velocity and acceleration when x=20ft.
Page 40, problem 12-69: A particle moves along a hyperbolic path X^2/16 - y^2=28. If the x component of its velocity is always Vx=4m/s, determine the magnitude of its velocity and acceleration when it is at point (32m,6m).
Page 41, problem 12-74: A basketball is tossed from A at angle of 30deg from the horizontal. Determine the speed Va at which the ball is released in order to make the basket B. With what speed does the ball pass through the hoop?. Neglect the size of the ball in the calculation.
Page 41, problem 12-78: The centre of the wheel is traveling at 60ft/s. If it encounters the transitions of two rails, such that there is a drop of 0.25inch. at the joint between the rails, determine the distance s to point A where the wheel strikes the next rail.
Page 42, problem 12-82: A boy at A throw's a ball 45deg from the horizontal such that it strikes the slope at B. Determine the speed at which the ball is thrown and the time of flight.
Page 42, problem 12-83: A frog jumps upward, perpendicular to the incline, with a velocity of Va=10ft/sec. Determine the distance R where it strikes the plate at B.
12.6: Curvilinear motion: normal and tangential components
Page 48, example 12-14: A skier travels with a constant speed of 6m/s along the parabolic path y=(1/20)x^2 shown. Determine his velocity and acceleration at the instant he arrives at A. Neglect the size of the skier in the calculation.
Page 49, example 12-15: A race car C travels around the horizontal circular track that has a radius of 300ft. If the car increases its speed at a constant rate of 7ft/s^2, starting from rest, determine the time needed for it to reach an acceleration of 8ft/s^2. What is it's speed at this instant?
Page 50, example 12-16: A car starts from rest at point A and travels along the horizontal track shown. During the motion, the increase in speed is at=0.2t m/s^2 where t is in seconds. Determine the magnitude of the car's acceleration when it arrives at point B.
Page 51, problem 12-93: A particle is moving along a curved path at a constant speed of 60ft/s. The radii of curvature of the path at points P and P' are 20 and 50 ft, respectively. If it takes the particle 20 sec to go from P to P', determine the acceleration of the particle at P and P'.
Page 51, 12-94: A car travels along a horizontal curved road that has a radius of 600m. If the speed is uniformly increased at a rate of 2000km/ h^2, determine the magnitude of the acceleration at the instant the speed of the car is 60km/h.
Page 51, problem 12-95: A boat is traveling along a circular path having a radius of 20m. Determine the magnitude of the boat's acceleration if at a given instant the boat's speed is v=5 m/s and the rate of increase in the speed is dv/dt =2 m/s^2.
Page 51, problem 12-97: A car moves along a circular track of radius 100ft such that it's speed for a short period of time 0 <= t <= 4s is v=3(t+t^2) ft/s, where t is in seconds. Determine the magnitude of its acceleration when t= 2s. How far has the car traveled in 2s ?
Page 51, problem 12-99: A race car has an initial speed of V0=15m/s when s=0. If it increases its speed along the circular track at the rate of at=(0.4s) m/s^2, where s is in meters, determine the normal and tangential components of the car's acceleration when s=100m.
Page 51, problem 12-101: A particle travels along the path y=a+bx+cx^2, where a, b, c are constants. If the speed of the particle is constant, v=v0, determine the x and y components of velocity and the normal component of acceleration when x=0.
Page 51, problem 12-103: The motorcyclist travels along the curve at a constant speed of 30ft/s. Determine his acceleration when located at point A. Neglect the size of the motorcycle and rider for the calculation.
Page 52, problem 12-105: A bicycle B is traveling down along a curved path which can be approximated by the parabola y=0.01x^2. When it is at A (20,4), the speed of B is measured as v=8m/s and the increase in speed is dv/dt = 4m/s^2. Determine the magnitude of the acceleration of bicycle B at this instant. Neglect the size of the bicycle.
Page 52, problem 12-107: The ferris wheel turns such that the speed of the passengers is increased by v'=(4t)ft/s^2, where t is in seconds. If the wheel starts from rest when alfa=0deg, determine the magnitude of the velocity and acceleration of the passengers when the wheel turns alfa=30deg.
Page 53, problem 12-109: A jet plane is traveling with a constant speed of 220m/s along the curven path. Determine the magnitude of the acceleration of the plane at the instant it reaches point A (y=0).
Page 53, problem 12-110: The ball is thrown horizontally with a speed of 8m/s. Find the equation of the path, y=f(x), and then find the balls velocity and the normal and tangential components of acceleration when t=0.25sec.
Page 53, problem 12-111: The plane travels along the vertical parabolic path at a constant speed of 200m/s. Determine the magnitude of acceleration of the plane when it is at point A.
Page 54, 12-113: A toboggan is traveling down along a curve which can be approximated by the parabola y=0.01x^2. Determine the magnitude of its acceleration when it reaches point A, where its speed is Va=10m/s, and it is increasing at the rate of Va'=3m/s^2.
Page 54, problem 12-114: Two cyclists, A & B, are traveling counterclockwise around a circular track at a constant speed of 8ft/s at the instant shown. If the speed of A is increased at Va'=(Sa)ft/s^2, where Sa is in feet, determine the distance measured counterclockwise along the track from B to A between the cyclists when t=1s. What is the magnitude of the acceleration of each cyclist at this instant?
12.7 Curvilinear Motion: Cylindrical Components
Page 58, example 12-17: The ball B shown is rotating in a horizontal circular path of radius r such that the attached cord has an angular velocity and angular acceleration . Determine the radial and transverse components of velocity and acceleration of the ball.
Page 59, example 12-18: The rod OA shown is rotating in the horizontal plane such that =(t^3) rad. At the same time, the collar B is sliding outward along OA so that r=(100t^2) mm. If in both cases t is in seconds, determine the velocity and acceleration of the collar when t=1s.
Page 60, example 12-19: The searchlight shown casts a spot of light along the face of a wall that is located 100m from the searchlight. Determine the magnitude of the velocity and acceleration at which the spot appears to travel across the wall at the instant = 45deg. The searchlight is rotating at a constant rate of =4 rad/s.
Page 62, problem 12-117: A particle is moving along a circular path having a radius of 4 inch such that its position as a function of time is given by =cos2t, where is in radians and t is in seconds. Determine the magnitude of the acceleration of the particle when =30 .
Page 62, problem 12-118: A train is traveling along the circular curve of radius r = 600ft. At the instant shown, it's angular rate of rotation is =0.02 rad/s, which is decreasing at =-0.001 rad/s^2. Determine the magnitude of the train's velocity and acceleration at this instant.
Page 62, problem 12-119: If a particle moves along a path such that r =(2sin t^2)m and =t^2 rad, where t is in seconds, plot the path r=f( ), and determine the particle's radial and transverse components of velocity and acceleration as function of time.
Page 62, problem 12-122: The motion of the pin P is controlled by the rotation of the grooved link OA. If the link is rotating at a constant angular rate of = 6 rad/s, determine the magnitude of the velocity and acceleration of P at the instant = /2 rad. The spiral path is defined by the equation r = (40 )mm, where is measured in radians.
Page 63, problem 12-125: A ship is traveling along the circular curve of radius r=1500m with a constant speed of v=1.5m/s. Determine the angular rate of rotation and the acceleration of the ship.
Page 63, problem 12-126: Starting from rest, the boy runs outward in the radial direction from the center of the platform with a constant acceleration of 0.5 m/s^2. If the platform is rotating at a constant rate =0.2rad/s, determine the radial and transverse components of the velocity and acceleration of the boy when t=3s. Neglect his size.
Page 63, problem 12-127: A particle moves along an Archimedian spiral --r=(8 )ft, where is given in radians. If = 4 rad/s (constant), determine the radial and transverse components of the particle's velocity and acceleration at the instant = /2 rad. Sketch the curve and show the components on the curve.
Page 63, problem 12-129: The slotted arm AB drives the pin C through the spiral groove described by the equation r = a . If the angular rate of rotation is constant at , determine the radial and transverse components of velocity and acceleration of the pin.
Page 63, problem 12-130: Solve problem 12-129 if the spiral path is logarithmic, i.e., .
Page 63, problem 12-131:
Page 65, problem 12-137: The rod OA rotates counterclockwise with a constant angular rate of 5 rad/s. A double collar B is pin connected together such that one collar slides over the straight rod OA and the other over the curved rod whose shape is a limaçon described by the equation r = (2-cos ) ft, where is given in radians. Determine the magnitude of the velocity and acceleration of the double collar when = 120deg.
Page 65, problem 12-139: The car travels along a road which is defined by r = (200/ ) ft, where is in radians. If it maintains a constant speed of v=35ft/s, determine the radial and transverse components of its velocity when = /3 rad.
Page 66, problem 12-41: The motion of a particle along a path is defined by the parametric equations r=1.5m, =2t rad, and z=t^2 m, where t is in seconds. Determine the unit vector that specifies the direction of the binormal axis to the osculating plane with respect to a set of fixed x, y, z coordinate axis when t=0.25s. Hint: formulate the particles velocity Vp and acceleration Ap in terms of their i, j, k components. The binormal is parallel to Ap x Vp. Why?
Page 66, problem 12-142:
Page 66, problem 12-143: For a short time the jet plane moves along a path in the shape of a lemniscate, r^2=2500cos2 km^2. At the instant =30deg, the radar tracking device is rotating at =5(10^-3)rad/s with =2(10^-3)rad/s^2. Determine the radial and transverse components of velocity and acceleration of the plane at this instant.
12.8 Absolute dependent motion analysis of two particles
12.9 Relative motion analysis of two particles using translating axes
Page 69, example 12-21: Determine the speed of block A in figure if block B has an upward speed of 6ft/s.
Page 70, example 12-22: Determine the speed of block A if block B has an upward speed of 6 ft/s.
Page 71, example 12-23: Determine the speed with which block B rises if the end of the cord at A is pulled down with a speed of 2 m/s.
Page 72, example 12-24: A man at A is hoisting a safe by walking to the right with a constant velocity Va=0.5m/s. Determine the velocity and acceleration of the safe when it reaches the window elevation at E. The rope is 30m long and passes over a small pulley at D.
Page 75, example 12-25: Water drips from a faucet at the rate of 5 drops per second as shown. Determine the vertical separation between two consecutive drops after the lower drop has attained a velocity of 3 m/s.
Page 76, example 12-26: A train traveling at a constant speed of 60mi/h, crosses over a road as shown. If auto A is traveling at 45mi/h along the road, determine the relative velocity of the train with respect to the auto.
Page 78, problem 12-145: The crate is being lifted up the inclined plane using the motor M and the rope and pulley arrangement shown. Determine the speed at which the cable must be taken up by the motor in order to move the crate up the plane with a constant speed of 4ft/s.
Page 78, problem 12-146: Determine the speed vp at which point P on the cable must be traveling toward the motor M to lift platform A at va=2 m/s.
Page 78, problem 12-147: In each case, if the end of the cable at A is pulled down with a speed of 2m/s, determine the speed at which block B rises.
Page 79, problem 12-149: The crane is used to hoist the load. If the motors at A and B are drawing in the cable at a speed of 2 ft/s, and 4ft/s respectively, determine the speed of the load.
Page 79, problem 12-150: If blocks A and B and C all move downward with velocities of 1ft/s, 2ft/s and 3ft/s, respectively, at the instant shown, determine the velocity of block D.
Problem 12-151, page 79: The hook B on the oil rig is supported by a cable which is connected to the drum A, passes over a pulley at E, down around the hooks pulley at B, up and around another pulley at E, and is then attached to the drum at C. Determine the time needed to hoist the hook from h=0 to h=120ft if (a) drum A draws the cable in at a speed of 4ft/s and drum C is stationary, and (b) drum A draws in the cable at 3ft/s and drum C draws in the cable at 2ft/s.
Problem 12-153, page 80: The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when Xd is zero, and moves forward with a constant acceleration of ad=0.5m/s^2, determine the speed of the block at the instant Xd=2m. Neglect the size of the pulleys in the calculation. When Xd=0, Yc=5m, so that points C and D are at the same elevation.
Problem 12-154, page 80: The crate C is being lifted by moving the roller at A downward with a constant speed of Va=4m/s along the guide. Determine the velocity and acceleration of the crate at the instant s=1m. When the roller is at B, the crate rests on the ground. Neglect the size of the pulleys in the calculation.
Problem 12-158, page 81: Three blocks A, B and C move in a straight line with constant velocities. If the relative velocity of block A with respect to block B is 10ft/s (moving to the right), and the relative velocity of block B with respect to block C is -5ft/s (moving to the left), determine the velocities of block A and B. The velocity of block C is 6ft/s to the right.
Problem 12-159, page 81: At the instant shown, the car at A is traveling at 10m/s around the curve while increasing its speed at 5m/s^2. The car at B is traveling at 18.5 m/s along the straightaway and increasing its speed at 2m/s^2. Determine the relative velocity and relative acceleration of A with respect to B at this instant.
Problem 12-163, page 82: A passenger in the automobile B observes the motion of the train car A. At the instant shown, the train has a speed of 18m/s and is reducing its speed at a rate of 1.5m/s^2. The automobile is accelerating at 2m/s^2 and has a speed of 25m/s. Determine the velocity and acceleration of A with respect to B. The train is moving along a curve of radius r=300m.
Made by A.J.P. Schalkwijk
12.1 Rectilinear Kinematics: Continuous Motion
Page 7, example 12-1: The car in fig. 12-2 moves in a straight line such that for a short time it's velocity is defined by v=(9t^2 + 2t) ft/s, where t is in seconds. Determine its position and acceleration when t=3s. When t=0, s=0.
Page 8, example 12-2: A small particle is fired vertically downward into a fluid medium with an initial velocity of 60m/s. If the projectile experiences a deceleration which is equal to a=(-0.4v^3) m/s^2, where v is measured in m/s, determine the projectile's velocity and position 4s after it is fired.
Page 9, example 12-3: A boy tosses a ball in the vertical direction of the side of a cliff, as shown in fig. 12-4. If the initial velocity of the ball is 15m/s upward, and the ball is released 40m from the bottom of the cliff, determine the maximum height Sb reached by the ball and the speed of the ball just before it hits the ground. During the entire time the ball is in motion, it is subjected to a constant downward acceleration of 9.81m/s^2 due to gravity. Neglect the effect of air resistance.
Page 10, example 12-4: A metallic particle is subjected to the influence of a magnetic field such that it travels downward through a fluid that extends from plate A to plate B, fig 12-5. If the particle is released from rest at the midpoint C, s=100mm, and the acceleration is measured as a=(4s)m/s^2, where s is in meters, determine the velocity of the particle when it reaches plate B, s=200mm, and the time it needs to travel van C to B.
Page 11, example 12-5: A particle moves along a horizontal line such that it's velocity is given by v=(3t^2-6t)m/ s, where t is the time in seconds. If it is initially located at the origin O, determine the distance traveled by the particle during the time interval t=0 to t=3.5, and the particle's average velocity and average speed during this time interval.
Page12, problem 12-1: If a particle has an initial velocity of V0=12ft/sec to right, determine its position when t=10s, if a=2ft/sec^2 to the left. Originally s0=0.
Page 12, problem 12-2: From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed of 80.7 ft/sec (55 mi/hr) when it hits the ground? Each floor 12ft higher than the one below it.
Page 12, problem 12-3: A particle is moving along a straight line such that its position is given by s=(4t-t^2) ft., where t is in seconds. Determine the distance travelled from t=0 to t=5s, the average velocity, and the average speed of the particle during this time interval.
Page 12, problem 12-5: A particle is moving along a straight line path such that it's position is defined by s=(10t^2+20)mm, where t is in seconds. Determine (a) the displacement of the particle during the time interval from t=1 s to t=5 s, (b) the average velocity of the particle during this time interval, and (c) the acceleration at t=1 s.
Page 12, problem 12-6: A ball is thrown vertically upward from the top of a ledge with an initial velocity of Va=35ft/sec. Determine (a) how high above the top of the cliff the ball will go before its stops at B, (b) the time Ta-b it takes to reach its maximum height, and (c) the total time Ta-c needed for it to reach the ground at C from the instant it is released.
Page 12, problem 12-7: A car, initially at rest, moves along a straight road with constant acceleration such that it attains a velocity of V=60ft/s when s=150ft. Then after being subjected to another constant acceleration, it attains a final velocity of V=100ft/s when s=325ft. Determine the average velocity and average acceleration of the car for the entire 325ft displacement.
Page 12, problem 12-9: When a train is travelling along a straight track at 2m/s, it begins to accelerate at a=(60V^-4)m/s^2, where V is in m/s. Determine the velocity V and the position of the train 3sec. after the acceleration.
Page 12, problem 12-10: A race car uniformly accelerates at 10ft/s^2 from rest, reaches a maximum speed of 60mi/h, and then decelerates uniformly to a stop. Determine the total elapsed time if the distance travelled was 1500ft.
Page 13, problem 12-11: A small metal particle passes through a fluid medium under the influence of magnetic attraction. The position of the particle is defined by s=(0.5t^3+4t)inch., where t is in seconds. Determine the position, velocity, and acceleration of the particle when t=3s.
Page 13, problem 12-13: A particle travels to the right along a straight path with a velocity v=[5/(4+s)]m/s, where s is in meters. Determine its position when t=6s if s=5m when t=0.
Page 13, problem 12-14: The velocity of a particle traveling along a straight line is v=(6t-3t^2)m/s, where t is in seconds. If s=0 when t=0, determine the particle's deceleration and position when t=3s. How far has the particle traveled during the 3-s time interval, and what is the average speed?
Page 13, problem 12-17: At the same instant, two cars A and B start from rest at a stop line. Car A has a constant acceleration of aA=8m/s^2, while car B has an acceleration of aB=(2t(3/2))m/s^2, where t is in seconds. Determine the distance between the cars when A reaches a velocity of Va=120km/h.
Page 13, problem 12-18: A particle moves along a straight path with an acceleration of a=(5/s)m/s^2, where s is in meters. Determine the particle's velocity when s=2m if it is released from rest when s=1m.
Page 13, problem 12-19: A particle moves with accelerated motion such that a=-k*s, where s is the distance from the starting point and k is a proportionality constant which is to be determined. When s=2ft the velocity is 4ft/s, and when s=3.5ft the velocity is 8ft/s. What is s when v=0?
Page 13, problem 12-21: A particle moving along a straight line is subjected to a deceleration a=(-2v^3)m/ s^2, where v is in m/s. If it has a velocity v=8m/s and a position s=10m when t=0, determine its velocity and position when t=4s.
Page 14, problem 12-22: The acceleration of a rocket travelling upward is given by a=(6+0.02s) m/s^2, where s in meters. Determine the rocket's velocity when s=2km and the time needed to reach this elevation. Initially, v=0 and s=0 when t=0.
Page 14, problem 12-23: Two trains are traveling in opposite directions on parallel tracks. Train A is 150m long and has a speed which is twice as fast as train B, which is 250m long. Determine the speed of each train if a passenger in train A observes that train B passes in 4s.
Page 14, problem 12-25: The juggler maintains the motion of three balls, such that each rises to a height of 4ft. If two balls are in the air at any one time, determine the time the third ball must remain in her hand after the first ball is thrown.
Page 14, problem 12-26: The juggler throws a ball into the air 4ft above her hand. How much time will elapse before she must catch it at the same elevation from which she threw it? What would be the elapsed time if she threw it 8 ft into the air?
Page 14, problem 12-27: When two cars A and B are next to one another, they are traveling in the same direction with speeds Va and Vb, respectively. If B maintains its constant speed, while A begins to decelerate at aA, determine the distance between the cars at the instant A stops.
Page 14, problem 12-29: When a particle falls through the air, it's initial acceleration a=g diminishes until it is zero, and thereafter it falls at a constant velocity Vf. If this variation of the acceleration can expressed as a=(g/Vf^2)(Vf^2-V^2), determine the time needed for the velocity to become V
12.2 Rectilinear Kinematics: Erratic Motion
Page 17, example 12-6: A car moves along a straight line path such that its position is described by the graph shown in fig. 12-9a. Construct the v-t and a-t graphs for the time period 0
Page 19, example 12-7: A rocket sled starts from rest and travels along a straight track such that it accelerates at a constant rate for 10s and then decelerates at a constant rate. Draw the v-t and s-t graphs and determine the time t' needed to stop the sled. How far has the sled traveled?
Page 21, problem 12-8: The v-s graph describing the motion of a motorcycle is shown in fig. 12-15a. Construct the a-s graph of the motion and determine the time needed for the motorcycle to reach the position s=400ft.
Page 22, problem 12-31: If the position of a particle is defined as s=(5t-3t^2) ft, where t is in seconds, construct the s-t, v-t and a-t graph for 0 < t < 10 s.
Page 22, problem 12-33: The speed of a train during the first minute of its motion has been recorded as follows:
Plot the v-t graph, approximating the curve as straight line segments between the given points. Determine the total distance traveled.
Page 22, problem 12-34: The s-t graph for a train has been determined experimentally. From the data, construct the v-t and a-t graphs for the motion.
Page 22, problem 12-35: Two cars start from rest side by side at the same time and position and race along a straight track. Car A accelerates at 4 ft/ s^2 for 35 s and then maintains a constant speed. Car B accelerates at 10 ft/s^2 until reaching a speed of 45mi/h and then maintains a constant speed. Determine the time at which the cars will again be side by side. How far has each car traveled? Construct the v-t graphs for each car.
Page 22, problem 12-37: From experimental data, the motion of a jet plane while traveling along a runway is defined by the v-t graph. Construct the s-t and a-t graphs for the motion.
Page 23, problem12-38: The car travels along a straight road according to the v-t graph. Determine the total distance the car travels until it stops when t=48sec. Also plot the s-t and a-t graphs.
Page 23, problem 12-39: The snowmobile moves along a straight course according to the v-t graph. Construct the s-t and a-t graphs for the same 50 s time interval. When t=0, s=0.
Page 23, problem 12-41: The v-t graph for the motion of a car as it moves along a straight road is shown. Construct the s-t graph and determine the average speed and the distance traveled for the 30 s time interval. The car starts from rest at s=0.
Page 23, problem 12-42: A particle starts from rest and is subjected to the acceleration shown. Construct the v-t graph for the motion, and determine the distance traveled during the time interval 2s < t < 6s.
Page 24, problem 12-43: An airplane lands on the straight runway, originally traveling at 110ft/s when s=0. If it is subjected to the decalerations shown, determine the time t' needed to stop the plane and construct the s-t graph for the motion:
Page 24, problem 12-45: The a-t graph for a car is shown. Construct the vt graph if the car starts from rest at t=0. At what time t' does the car stop?
Page 24, problem 12-46: A race car starting from rest travels along a straight road and for 10s has the acceleration shown. Construct the v-t graph that describes the motion and find the distance traveled in 10s.
Page 25, problem 12-47: The boat is originally traveling at a speed of 8 m/s when it is subjected to the acceleration shown in the graph. Determine the boat's maximum speed and the time t when it stops.
Page 25, problem 12-49: The a-s graph for a race car moving along a straight track has been experimentally determined. If the car starts from rest, determine its speed when s=50 ft, 150ft and 200ft, respectively.
Page 25, problem 12-51: The jet plane starts from rest at s=0 and is subjected to the acceleration shown. Construct the v-t graph and determine the time needed to travel 500ft.
Page 26, problem 12-53: The v-s graph for the car is given for the first 500ft of its motion. Construct the a-s graph for 0<s<500ft. How long does it take to travel the 500ft distance? The car starts at s=0 when t=0.
Page 26, problem 12-54: The a-s graph for a boat moving along a straight path is given. If the boat starts at s=0 when v=0, determine its speed when it is at s=75ft and 125ft respectively. Use Simpson's rule with n=100 to evaluate v at s=125ft.
12.3 General Curvilinear motion
Page 32, example 12-9: At any instant the position of the kite in fig. 12-18a is defined by the coordinates x=30t and y=9t^2 ft, where t is given in seconds. Determine (a) the equation which describes the path and the distance of the kite from the boy when t=2s, (b) the magnitude and direction of the velocity when t=2, and (c) the magnitude and direction of the acceleration when t=2sec.
Page 33, example 12-10: The motion of a bead B sliding down along the spiral path shown in fig. 12-19 is defined by the position vector r={0.5sin(2t)i + 0.5cos(2t)j - 0.2tk}m, where t is given in seconds and the arguments for sine and cosine are given in radians (pi rad = 180deg). Determine the location of the bead when t=0.75s and the magnitude of the bead's velocity and acceleration at this instant.
Page 36, example 12-11: A ball is ejected from the tube, shown in fig 12-21 with a horizontal velocity of 12 m/s. If the height of the tube is 6m, determine the time needed for the ball to strike the floor and the range R.
Page 37, example 12-12: A ball is thrown from a position 5 ft above the ground to the roof of a 40ft high building, as shown in fig 12-22. If the initial velocity of the ball is 70ft/s, inclined at an angle of 60deg from the horizontal, determine the range or horizontal distance R from the point where the ball is thrown to where it strikes the roof.
Page 38, example 12-13: When a ball is kicked from A as shown in fig. 12-23, it just clears the top of the wall at B as it reaches its maximum height. Knowing that the distance from A to the wall is 20m and the wall is 4m heigh, determine the initial speed at which the ball was kicked. Neglect the size of the ball.
Page 39, problem 12-55: If x=1-t and y=t^2, where x and y are in meters and t is in seconds, determine the x and y components of velocity and acceleration and construct the path y=f(x).
Page 39, problem 12-57: If the position of a particle is defined by its coordinates x=4t^2 and y=3t^3, where x and y are in meters and t is in seconds, determine the x and y components of velocity and acceleration and construct the path y=f(x).
Page 39, problem 12-58: The position of a particle is defined by
If , where t is in seconds, determine the particles velocity v and acceleration a at the instant t=1 sec. Express v and a as Cartesian vectors.
Page 39, problem 12-59: If the velocity of a particle is v(t)={0.8t^2i + 12t^0.5j + 5k}m/s, determine the magnitude and coordinate direction angles a,b and c of the particle's acceleration when t=2s.
Page 39, problem 12-61: A particle travels along the curve from A to B in 2s. It takes 4s for it to go from B to C and then 3s to go from C to D. Determine its average velocity when it goes from A to D.
Page 39, problem 12-62: A particle moves with curvilinear motion in the positive x-y plane such that the y component of motion is described by y=7t^3, where y is in feet and t is in seconds. When t=1s, the particle's speed is 60ft/s. If the acceleration of the particle in the x direction is zero, determine the velocity of the particle when t=2s.
Page 39, problem 12-63: A car traveling along the road has the velocities indicated in the figure when it arrives at it points A, B and C. If it takes 10s to go from A to B, and then 15s to go from B to C, determine the average acceleration between points A and B and between points A and C.
Page 40, problem 12-66: The flight path of the helicopter as it takes off from A is defined by the parametric equations x=(2t^2)m and y=(0.04t^3)m, where t is the time in seconds after takeoff. Determine the distance the helicopter is from point A and the magnitude of its velocity and acceleration when t=10s.
Page 40, problem 12-67: A particle is moving along the curve y=x-(x^2/400). If the velocity component in the x direction is Vx=2ft/s, determine the magnitude of the particle's velocity and acceleration when x=20ft.
Page 40, problem 12-69: A particle moves along a hyperbolic path X^2/16 - y^2=28. If the x component of its velocity is always Vx=4m/s, determine the magnitude of its velocity and acceleration when it is at point (32m,6m).
Page 41, problem 12-74: A basketball is tossed from A at angle of 30deg from the horizontal. Determine the speed Va at which the ball is released in order to make the basket B. With what speed does the ball pass through the hoop?. Neglect the size of the ball in the calculation.
Page 41, problem 12-78: The centre of the wheel is traveling at 60ft/s. If it encounters the transitions of two rails, such that there is a drop of 0.25inch. at the joint between the rails, determine the distance s to point A where the wheel strikes the next rail.
Page 42, problem 12-82: A boy at A throw's a ball 45deg from the horizontal such that it strikes the slope at B. Determine the speed at which the ball is thrown and the time of flight.
Page 42, problem 12-83: A frog jumps upward, perpendicular to the incline, with a velocity of Va=10ft/sec. Determine the distance R where it strikes the plate at B.
12.6: Curvilinear motion: normal and tangential components
Page 48, example 12-14: A skier travels with a constant speed of 6m/s along the parabolic path y=(1/20)x^2 shown. Determine his velocity and acceleration at the instant he arrives at A. Neglect the size of the skier in the calculation.
Page 49, example 12-15: A race car C travels around the horizontal circular track that has a radius of 300ft. If the car increases its speed at a constant rate of 7ft/s^2, starting from rest, determine the time needed for it to reach an acceleration of 8ft/s^2. What is it's speed at this instant?
Page 50, example 12-16: A car starts from rest at point A and travels along the horizontal track shown. During the motion, the increase in speed is at=0.2t m/s^2 where t is in seconds. Determine the magnitude of the car's acceleration when it arrives at point B.
Page 51, problem 12-93: A particle is moving along a curved path at a constant speed of 60ft/s. The radii of curvature of the path at points P and P' are 20 and 50 ft, respectively. If it takes the particle 20 sec to go from P to P', determine the acceleration of the particle at P and P'.
Page 51, 12-94: A car travels along a horizontal curved road that has a radius of 600m. If the speed is uniformly increased at a rate of 2000km/ h^2, determine the magnitude of the acceleration at the instant the speed of the car is 60km/h.
Page 51, problem 12-95: A boat is traveling along a circular path having a radius of 20m. Determine the magnitude of the boat's acceleration if at a given instant the boat's speed is v=5 m/s and the rate of increase in the speed is dv/dt =2 m/s^2.
Page 51, problem 12-97: A car moves along a circular track of radius 100ft such that it's speed for a short period of time 0 <= t <= 4s is v=3(t+t^2) ft/s, where t is in seconds. Determine the magnitude of its acceleration when t= 2s. How far has the car traveled in 2s ?
Page 51, problem 12-99: A race car has an initial speed of V0=15m/s when s=0. If it increases its speed along the circular track at the rate of at=(0.4s) m/s^2, where s is in meters, determine the normal and tangential components of the car's acceleration when s=100m.
Page 51, problem 12-101: A particle travels along the path y=a+bx+cx^2, where a, b, c are constants. If the speed of the particle is constant, v=v0, determine the x and y components of velocity and the normal component of acceleration when x=0.
Page 51, problem 12-103: The motorcyclist travels along the curve at a constant speed of 30ft/s. Determine his acceleration when located at point A. Neglect the size of the motorcycle and rider for the calculation.
Page 52, problem 12-105: A bicycle B is traveling down along a curved path which can be approximated by the parabola y=0.01x^2. When it is at A (20,4), the speed of B is measured as v=8m/s and the increase in speed is dv/dt = 4m/s^2. Determine the magnitude of the acceleration of bicycle B at this instant. Neglect the size of the bicycle.
Page 52, problem 12-107: The ferris wheel turns such that the speed of the passengers is increased by v'=(4t)ft/s^2, where t is in seconds. If the wheel starts from rest when alfa=0deg, determine the magnitude of the velocity and acceleration of the passengers when the wheel turns alfa=30deg.
Page 53, problem 12-109: A jet plane is traveling with a constant speed of 220m/s along the curven path. Determine the magnitude of the acceleration of the plane at the instant it reaches point A (y=0).
Page 53, problem 12-110: The ball is thrown horizontally with a speed of 8m/s. Find the equation of the path, y=f(x), and then find the balls velocity and the normal and tangential components of acceleration when t=0.25sec.
Page 53, problem 12-111: The plane travels along the vertical parabolic path at a constant speed of 200m/s. Determine the magnitude of acceleration of the plane when it is at point A.
Page 54, 12-113: A toboggan is traveling down along a curve which can be approximated by the parabola y=0.01x^2. Determine the magnitude of its acceleration when it reaches point A, where its speed is Va=10m/s, and it is increasing at the rate of Va'=3m/s^2.
Page 54, problem 12-114: Two cyclists, A & B, are traveling counterclockwise around a circular track at a constant speed of 8ft/s at the instant shown. If the speed of A is increased at Va'=(Sa)ft/s^2, where Sa is in feet, determine the distance measured counterclockwise along the track from B to A between the cyclists when t=1s. What is the magnitude of the acceleration of each cyclist at this instant?
12.7 Curvilinear Motion: Cylindrical Components
Page 58, example 12-17: The ball B shown is rotating in a horizontal circular path of radius r such that the attached cord has an angular velocity and angular acceleration . Determine the radial and transverse components of velocity and acceleration of the ball.
Page 59, example 12-18: The rod OA shown is rotating in the horizontal plane such that =(t^3) rad. At the same time, the collar B is sliding outward along OA so that r=(100t^2) mm. If in both cases t is in seconds, determine the velocity and acceleration of the collar when t=1s.
Page 60, example 12-19: The searchlight shown casts a spot of light along the face of a wall that is located 100m from the searchlight. Determine the magnitude of the velocity and acceleration at which the spot appears to travel across the wall at the instant = 45deg. The searchlight is rotating at a constant rate of =4 rad/s.
Page 62, problem 12-117: A particle is moving along a circular path having a radius of 4 inch such that its position as a function of time is given by =cos2t, where is in radians and t is in seconds. Determine the magnitude of the acceleration of the particle when =30 .
Page 62, problem 12-118: A train is traveling along the circular curve of radius r = 600ft. At the instant shown, it's angular rate of rotation is =0.02 rad/s, which is decreasing at =-0.001 rad/s^2. Determine the magnitude of the train's velocity and acceleration at this instant.
Page 62, problem 12-119: If a particle moves along a path such that r =(2sin t^2)m and =t^2 rad, where t is in seconds, plot the path r=f( ), and determine the particle's radial and transverse components of velocity and acceleration as function of time.
Page 62, problem 12-122: The motion of the pin P is controlled by the rotation of the grooved link OA. If the link is rotating at a constant angular rate of = 6 rad/s, determine the magnitude of the velocity and acceleration of P at the instant = /2 rad. The spiral path is defined by the equation r = (40 )mm, where is measured in radians.
Page 63, problem 12-125: A ship is traveling along the circular curve of radius r=1500m with a constant speed of v=1.5m/s. Determine the angular rate of rotation and the acceleration of the ship.
Page 63, problem 12-126: Starting from rest, the boy runs outward in the radial direction from the center of the platform with a constant acceleration of 0.5 m/s^2. If the platform is rotating at a constant rate =0.2rad/s, determine the radial and transverse components of the velocity and acceleration of the boy when t=3s. Neglect his size.
Page 63, problem 12-127: A particle moves along an Archimedian spiral --r=(8 )ft, where is given in radians. If = 4 rad/s (constant), determine the radial and transverse components of the particle's velocity and acceleration at the instant = /2 rad. Sketch the curve and show the components on the curve.
Page 63, problem 12-129: The slotted arm AB drives the pin C through the spiral groove described by the equation r = a . If the angular rate of rotation is constant at , determine the radial and transverse components of velocity and acceleration of the pin.
Page 63, problem 12-130: Solve problem 12-129 if the spiral path is logarithmic, i.e., .
Page 63, problem 12-131:
Page 65, problem 12-137: The rod OA rotates counterclockwise with a constant angular rate of 5 rad/s. A double collar B is pin connected together such that one collar slides over the straight rod OA and the other over the curved rod whose shape is a limaçon described by the equation r = (2-cos ) ft, where is given in radians. Determine the magnitude of the velocity and acceleration of the double collar when = 120deg.
Page 65, problem 12-139: The car travels along a road which is defined by r = (200/ ) ft, where is in radians. If it maintains a constant speed of v=35ft/s, determine the radial and transverse components of its velocity when = /3 rad.
Page 66, problem 12-41: The motion of a particle along a path is defined by the parametric equations r=1.5m, =2t rad, and z=t^2 m, where t is in seconds. Determine the unit vector that specifies the direction of the binormal axis to the osculating plane with respect to a set of fixed x, y, z coordinate axis when t=0.25s. Hint: formulate the particles velocity Vp and acceleration Ap in terms of their i, j, k components. The binormal is parallel to Ap x Vp. Why?
Page 66, problem 12-142:
Page 66, problem 12-143: For a short time the jet plane moves along a path in the shape of a lemniscate, r^2=2500cos2 km^2. At the instant =30deg, the radar tracking device is rotating at =5(10^-3)rad/s with =2(10^-3)rad/s^2. Determine the radial and transverse components of velocity and acceleration of the plane at this instant.
12.8 Absolute dependent motion analysis of two particles
12.9 Relative motion analysis of two particles using translating axes
Page 69, example 12-21: Determine the speed of block A in figure if block B has an upward speed of 6ft/s.
Page 70, example 12-22: Determine the speed of block A if block B has an upward speed of 6 ft/s.
Page 71, example 12-23: Determine the speed with which block B rises if the end of the cord at A is pulled down with a speed of 2 m/s.
Page 72, example 12-24: A man at A is hoisting a safe by walking to the right with a constant velocity Va=0.5m/s. Determine the velocity and acceleration of the safe when it reaches the window elevation at E. The rope is 30m long and passes over a small pulley at D.
Page 75, example 12-25: Water drips from a faucet at the rate of 5 drops per second as shown. Determine the vertical separation between two consecutive drops after the lower drop has attained a velocity of 3 m/s.
Page 76, example 12-26: A train traveling at a constant speed of 60mi/h, crosses over a road as shown. If auto A is traveling at 45mi/h along the road, determine the relative velocity of the train with respect to the auto.
Page 78, problem 12-145: The crate is being lifted up the inclined plane using the motor M and the rope and pulley arrangement shown. Determine the speed at which the cable must be taken up by the motor in order to move the crate up the plane with a constant speed of 4ft/s.
Page 78, problem 12-146: Determine the speed vp at which point P on the cable must be traveling toward the motor M to lift platform A at va=2 m/s.
Page 78, problem 12-147: In each case, if the end of the cable at A is pulled down with a speed of 2m/s, determine the speed at which block B rises.
Page 79, problem 12-149: The crane is used to hoist the load. If the motors at A and B are drawing in the cable at a speed of 2 ft/s, and 4ft/s respectively, determine the speed of the load.
Page 79, problem 12-150: If blocks A and B and C all move downward with velocities of 1ft/s, 2ft/s and 3ft/s, respectively, at the instant shown, determine the velocity of block D.
Problem 12-151, page 79: The hook B on the oil rig is supported by a cable which is connected to the drum A, passes over a pulley at E, down around the hooks pulley at B, up and around another pulley at E, and is then attached to the drum at C. Determine the time needed to hoist the hook from h=0 to h=120ft if (a) drum A draws the cable in at a speed of 4ft/s and drum C is stationary, and (b) drum A draws in the cable at 3ft/s and drum C draws in the cable at 2ft/s.
Problem 12-153, page 80: The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when Xd is zero, and moves forward with a constant acceleration of ad=0.5m/s^2, determine the speed of the block at the instant Xd=2m. Neglect the size of the pulleys in the calculation. When Xd=0, Yc=5m, so that points C and D are at the same elevation.
Problem 12-154, page 80: The crate C is being lifted by moving the roller at A downward with a constant speed of Va=4m/s along the guide. Determine the velocity and acceleration of the crate at the instant s=1m. When the roller is at B, the crate rests on the ground. Neglect the size of the pulleys in the calculation.
Problem 12-158, page 81: Three blocks A, B and C move in a straight line with constant velocities. If the relative velocity of block A with respect to block B is 10ft/s (moving to the right), and the relative velocity of block B with respect to block C is -5ft/s (moving to the left), determine the velocities of block A and B. The velocity of block C is 6ft/s to the right.
Problem 12-159, page 81: At the instant shown, the car at A is traveling at 10m/s around the curve while increasing its speed at 5m/s^2. The car at B is traveling at 18.5 m/s along the straightaway and increasing its speed at 2m/s^2. Determine the relative velocity and relative acceleration of A with respect to B at this instant.
Problem 12-163, page 82: A passenger in the automobile B observes the motion of the train car A. At the instant shown, the train has a speed of 18m/s and is reducing its speed at a rate of 1.5m/s^2. The automobile is accelerating at 2m/s^2 and has a speed of 25m/s. Determine the velocity and acceleration of A with respect to B. The train is moving along a curve of radius r=300m.
Related Documents
Engineering Mechanics Dynamics Solution Manual 6th Pdf
January 2021 1
Fluid Mechanics Solution Manual
January 2021 1
