Physics20 Work Energy Power

Work/Energy/Pow er Work Definition: Work is done when a force acts through a distance. When energy is transferred to an object work has been done on the object.

Formulas:

W W F F

= = = =

Fd mgd mag ma

units kg m s2 kg m2 s2 Nm

=

N

=

J

=

J

Problem 1: Three men attempt to push a car out of a ditch using a force of 275 N. How much work is done on the car? Solution 1: Since the car has not moved, a force has NOT acted through a distance, therefore, no work is done.

Problem 2: Sally pushes a box 20.0 m across the floor with a force of 25.0 N. How much work is done on the box? Solution 2:

W = Fd W = (25.0 N)(20.0 m) W=500 J

Problem 3: A 70.0 kg man climbs a 3.5 m ladder. Calculate the amount of work done

climbing up the ladder. Solution:

W = mgh W = (70.0 kg) (9.81 m/s2) (3.5 m)

Problem 4: How much work is done in lifting a 5.0 kg package from a 1.0 m high table to 2.5 m above the floor? Solution 4:

W = mgh W = (5.0 kg) (9.81 m/s2) (1.5 m) W = 74 J

Problem 5: Tom pulls his sled for a distance of 180 m by exerting a force of 7.0 N at an angle of 350 with the horizontal.

Problem 6: A 16.0 kg package is pushed up an inclined plane which is 3.00 m long onto a loading dock 1.50 m high. How much work is done on the package?

Energy Definitions: Energy - the ability to do work Potential energy - stored energy by way of position Kinetic energy - is energy associated with motion Formulae: Ep = mgh

Ep = Fd = W

EK = 1 mv2 2 Problem 1: A 12.0 kg box is picked up from the ground and placed on the tailgate of a truck 1.20 m above the ground. Calculate the gravitational potential energy of the box on the tailgate with respect to the ground.

Problem 2: A 5.00 kg package is carried a distance of 20.0 m. What is the gain in gravitational potential energy?

Problem 3: A 50.0 kg window falls from an office building, 23.0 m above the ground. What is the gravitational potential energy of the window with respect to the ground?

Problem 6: Calculate the velocity of an alpha particle which has a kinetic energy of 3.50 x 1017J The mass of an alpha particle is 6.65 x 10-27 kg.

Problem 8: Joey drops a 50.0 g toy from his window which is 6.00 m from the ground. What is the kinetic energy of his toy as it hits the ground?

A roller-coaster and its passengers have a mass of 2.0 x 103 kg. At the bottom of the first hill they go through a 360o loop. What will be their velocity at point B, the top of the loop?

Problem 12: Drawing back the string of a bow 0.75 m, an archer uses a force of 16 N. If the arrow has a mass of 42 g, at what speed does the arrow leave the bow?

Problem A 12 kg child swings on a swing which is 0.30 m above the ground. If she 14: reaches a maximum height of 1.5 m what is her potential energy at the highest point in her swing? What is her speed when she reaches this point?

Power Definition: Power is the rate at which work is done.

Problem 1: How much power does a machine develop doing 5.5 x 103J of work in 2.3 min.?

Problem 2: How much power can a cyclist devleop if he expends 7.5 x 104J of energy in 5.0 min.?

Problem 3: What rate of work is developed by a 50.0 kg jogger who runs around a 1.00 km track three times in 18.0 minutes?

Problem 5: Calculate the amount of energy consumed by a 1500W hair dryer that is used for 5.0 minutes.

Problem 6: A 0.50 kW food processor is capable of doing how much work in 3.0 minutes?

Problem 7: An engine rated at 6000. watts lifts a load 20. m in 15 seconds. What is the

maximum mass that could be lifted at this rate?

Problem 8: A freight elevator and its contents have a mass of 750 kg. The elevator, powered by a 55 kW motor, must lift this load a distance of 25 m. If the efficiency of the motor is 72%, how long will it take to move the load?

Problem 9: Calculate the input power of a pump which produces output power of 35 kW and is 45% efficient.

Problem A small vessel of mass 12 tonne pulls out of the harbour 10: accelerating uniformly from rest to 12 . If the distance to a nearby island is 5.0 km and the force of friction between the vessel and the water is 4.5 N, calculate the output power.