Tutorial-2.pdf

University of Bahrain Department of Mechanical Engineering MENG 263 TUTORIAL # 2 (Chapter 1)

Q1. Sand is discharged at A from a conveyor belt and falls onto the top of a stockpile at B. Knowing that the conveyor belt forms an angle α = 20° with the horizontal, determine the speed v0 of the belt. ( Ans. 7.59 m/s ) Q2. The ball at A is kicked with a speed VA = 24 m/s and at an angle θA = 30°. Determine the point (x , y) where it strikes the ground. Assume the ground has the shape of a parabola as shown. ( Ans. x = 11.244, y = -5.06 )

Q3. A projectile is fired from the vertical tube mounted on the vehicle which is traveling at the constant speed u = 30 km/h. The projectile leaves the tube with a velocity vr = 20 m/s relative to the tube. If air resistance is neglected, show that the projectile will land on the vehicle at the tube location and calculate the distances traveled by the vehicle during the flight of the projectile. (Ans. s = 34.0 m) Q4. The pilot of an airplane carrying a package of mail to a remote outpost wishes to release the package at the right moment to hit the recovery location A. What angle θ with the horizontal should the pilot’s line of sight to the target make at the instant of release? The airplane is flying horizontally at an altitude of 100 m with a velocity of 200 km/h. ( Ans. θ = 21.7°)

Q5. The balloon A is ascending at the rate vA = 12 km/h and is being carried horizontally by the wind at vw = 20 km/h. If a ballast bag is dropped from the balloon at the instant h = 50 m, determine the time needed for it to strike the ground. Assume that the bag was released from the balloon with the same velocity as the balloon. Also, with what speed does the bag strike the ground? ( Ans. t = 3.556 sec, v = 32.0 m/s )

Q6. The truck travels along a circular road that has a radius of 50 m at a speed of 4 m/s. For a short distance when t = 0, its speed is then increased by rate = (0.4t) m/s2. where t is in seconds. Determine the speed and the magnitude of the truck’s acceleration when t=4s. ( Ans. v = 7.20 m/s, a = 1.91 m/s2 )

Q7. The automobile is originally at rest at s = 0. If it then starts to increase its speed at rate = (0.02t2) m/s2, where t is in seconds, determine the magnitudes of its velocity and acceleration at s = 180 m. ( Ans. v = 39.86 m/s, a = 20.92 m/s2 )

Q8. The car travels at a constant speed from the bottom A of the dip to the top B of the hump. If the radius of curvature of the road at A is ρA = 120 m and the car acceleration at A is 0.4g, determine the ear speed v. If the acceleration at B must be limited to 0.25g, determine the minimum radius of curvature ρB of the road at B. (Ans. ρB = 190 m)

Q9. The speed of a car increases uniformly with time from 50 km/h at A to 100 km/h at B during 10 seconds. The radius of curvature of the hump at A is 40 m. If the magnitude of the total acceleration of the car’s mass center is the same at B as at A, compute the radius of curvature ρ of the dip in the road at B. The mass center of the car is 0.6 m from the road. (Ans. ρB = 163.0 m ) Q10. What is the smallest radius which should be used for a highway curve if the normal component of the acceleration of a car traveling at 72 km/h is not to exceed 0.72 m/s2? ( Ans. ρ = 556 m )

Q11. Race car A follows path a-a while race car B follows path b-b on the unbanked track. If each car has a constant speed limited to that corresponding to a lateral (normal) acceleration of 0.8g, determine the times tA and tE for both cars to negotiate the turn as delimited by the line C-C. ( Ans. tA = 10.52 s, tB = 10.86 s)

Q12. At the instant shown, the watersprinkler is rotating with an angular speed ω = 2 rad/s and an angular acceleration α = 3 rad/s2. If the nozzle lies in the vertical plane and water is flowing through it at a constant rate of 3 m/s, determine the magnitudes of the velocity and acceleration of a water particle as it exits the open end, r = 0.2 m. ( Ans. v = 3.03 m/s, a =12.6 m/s2 )

Q13. The ladder of a fire truck is designed to be extended at the constant rate 1 = 6 in/sec and to be elevated at the constant rate 0 = 2 deg/see. As the position 0 = 50° and 1 = 15 ft is reached, determine the magnitudes of the velocity v and the acceleration a of the fireman at A. (Ans. v = 1.320 ft/sec, a = 0.0551 ft/sec2)

Q14. At the instant shown, cars A and B are traveling at speeds of 30 km/h and 20 km/h, respectively. If A is increasing its speed at 400 km/h2 whereas the speed of B is decreasing at 800 km/h2, determine the velocity and acceleration of B with respect to . ( Ans. v B/A =26.449 km/h @ 40.9º, a B/A = 1955 km/h2 @ 0.767º )

Q15. At the instant shown, the bicyclist at A is traveling at 7 m/s around the curve on the race track while increasing his speed at 0.5 rn/s2. The bicyclist at B is traveling at 8.5 m/s along the straight-a-way and increasing his speed at 0.7 rn/s2. Determine the relative velocity and relative acceleration of A with respect to Bat this instant. ( Ans. vA/B = 6.69m/s @ 53.3º, a A/B = 1.52 m/s2 @ 41.9º )

Q16. At the instant shown, cars A and B are traveling at speeds of 55 km/h and 40 km/h, respectively. If B is decreasing its speed at 1500 km/h while A is increasing its speed at 800 km/h2. determine the acceleration of B with respect to A. Car B moves along a curve having a radius of curvature of 0.75 km. ( Ans. a B/A = 3351 km/h2 @ 19.1º ) Q17. At the instant shown, car A has a speed of 20 km/h, which is being increased at the rate of 300 km/h2 as the car enters an expressway. At the same instant, car B is decelerating at 250 km/h2 while traveling forward at 100 km/h. Determine the velocity and acceleration of car A with respect to car B. ( v A/B = 120 km/h down , a A/B = 4000 km/h2 @ 0.716º)

Q18. a) To study the performance of a race car, a high-speed motion - picture camera is positioned at point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car travels on straightaway BC. Determine the speed of the car in terms of b, θ, and θ. b) Determine the magnitude of the acceleration of the race car in terms of b, θ, θ, and θ.