Work & Power
Problem Set
A> Work: Assume motion is constant unless otherwise stated.
1)Two students apply a total force of 800. N to push a car 40.0 m across a road. How much work is done?
2)How much work is done lifting a 60.0 kg crate from the ground to a height of 10.0 m.
3)Using a pulley system, a dockworker does 1920 J of work to lift a crate from one floor to the next (40.0 m) in a warehouse. What was the tension in the rope?
4)A person pushes a lawnmower with a force of 50.0 N at an angle of 35.0 below the horizontal. If the mower moves through a distance of 25.0 m, how much work is done by the person?
5)In order to change a tire, a force of 80.0 N is exerted on the handle of a screw type jack. The handle to which the steel shaft is attached has a radius of 0.50 m. The handle is turned through 30 revolutions. How much work is done?
6)A person uses a rope to pull a 1000. kg boat 50.0 m along the wharf at constant speed. The rope makes an angle of 45 with the wharf. If a force of 40.0 N is used to move the boat, how much work is done on the boat by the water?
7)Calculate the work done in pushing a 4.00 kg block up a frictionless inclined plane 10.0 m long that makes an angle of 30 with the floor. You may assume that the block moves at constant speed.
8)Calculate the work done lifting the 4.00 kg block in question #7 from the ground to the top of the inclined plane. (Hint: First find the height of the incline.)
9)How does the work in problem 7 compare to the work in problem 8. Explain.
10)It takes 12.0 kJ of work to pull a loaded sled weighing 800 N a distance of 200. m. To do this, a force of 120 N is exerted on the rope that makes an angle with the horizontal. At what angle is the rope held?
11)The hammer of a pile driver has a mass of 100.0 kg. The machine’s engine lifts it to a height of 5.0 m every 10.0 s.
a) How much work does the machine do to lift the hammer?
b) How much work does the machine do in one minute?
c) How much work is done by gravity as the machine lifts the hammer?
d) How much work is done by gravity as the hammer is dropped?
1) 32 kJ / 2) 5880 J / 3) 48 N / 4) 1020 J / 5) 7540 J6) -1414 J / 7) 196 J / 8) 196 J / 10) 60
12) (a) 4900 J (b) 2.94 x 104 J (c) –4900 J (d) 4900 J
B> Power:
1)A box that weighs 575 N is lifted a distance of 20.0 m straight up by a rope. The job is done in 10.0 s. What power is delivered in watts and kilowatts?
2)An electric motor uses 65 kW as it lifts a loaded elevator 17.5 m in 35.0 s. What force does the motor exert?
3)A boat’s engine pushes it through water at a steady rate of 15 m/s. The force of friction that acts against the boat is 6000. N. What is the power of the engine?
4)A 300. kg piano is being lifted at a steady speed from ground level straight up to an apartment 10.0 m above the ground. The crane that is lifting produces a steady power of 400. W. How much time does it take to lift the piano?
5)A 1000. kg car accelerates at 1.25 m/s2 as it goes from 20.0 m/s to 30.0 m/s.
(a)What force is applied to the car by its engine?
(b)How far does the car travel during this period of acceleration?
(c)How much work is done to accelerate the car?
(d)How much time elapsed while the car was accelerating?
(e)What is the power of the car’s engine?
1) 1150 W; 1.15 kW / 2) 1.3 x 105 N / 3) 90 kW / 4) 73.5 s5) (a) 1250 N (b) 200. m (c) 250. kJ (d) 8.00 s (e) 31.3 kW
C> Kinetic Energy:
1)How much work is done to slow an 875 kg compact car from 44.0 m/s to 22.0 m/s?
2)If the car from problem # 1 was moving at 44.0 m/s, how much work would be done to stop the car?
3)A rifle can shoot a 4.20 g bullet at a speed of 965 m/s.
(a)Find the kinetic energy of the bullet as it leaves the rifle.
(b)What work is done on the bullet if it starts from rest?
(c)If the work is done over a distance of 75 cm, what is the average force on the bullet?
(d)If the bullet comes to rest by penetrating 1.5 cm into metal, what is the magnitude and direction of the force the metal exerts on the bullet?
4)A comet with a mass of 7.85 x 1011 kg strikes the earth with a speed of 25.0 km/s. Find the kinetic energy of the comet in joules.
5)Accelerating a 5700 kg trailer truck from rest to 100 km/h requires 2.2 x 106 J.
(a)What would be the truck’s speed if half as much work were done on it?
(b)What would be the truck’s speed if twice as much work were done on it?
6)A 1600 kg car travels at a speed of 12.5 m/s. What is its kinetic energy?
7)A racing car has a mass of 1525 kg. What is its kinetic energy of it has a speed of 108 km/h?
8)Toni has a mass of 45 kg and is moving with a speed of 10.0 m/s
(a)What is Toni’s kinetic energy?
(b)Toni’s speed is reduced to half as much (5.0 m/s). What is her kinetic energy now?
(c)What is the ratio of the kinetic energies in parts a and b? Why isn’t it 2 to 1?
9)Shawn and his bike have a total mass of 45.0 kg. Shawn rides his bike 1.80 km in 10.0 minutes at a constant velocity. What is Shawn’s kinetic energy?
10)In the 1950’s, an experimental train that had a mass of 2.5 x 104 kg was powered across a level track by a jet engine that produced a thrust of 5.00 x 105 N for a distance of 509 m. Find the final speed of the train if it started from rest and friction was negligible.
11)A 14,700 N car is traveling at 25 m/s. The brakes are applied suddenly, and the car slides to a stop. The average braking force between the tires and the road is 7100 N. How far will the car slide once the brakes are applied?
1)-6.35 x 105 J / 2)-8.47 x 105 J / 3)(a) 1960 J (b) 1960 J (c) 2600 N (d) 1.3 x 105 N backward4)2.45 x 1020 J / 5)(a) 71 km/h (b) 140 km/h / 6)1.3 x 105 J / 7)686 kJ
8)(a) 2300 J (b) 560 J (c) 4 to 1 / 9)203 J / 10)143 m/s / 11)66 m
D> Potential Energy:
1)A 90 kg rock climber climbs 45 m up to the top of a quarry then descends 85 m from the top to the bottom of the quarry. If the initial height is the reference level, find the potential energy at the top and at the bottom.
2)A 50.0 kg shell is shot from a cannon at the Earth’s surface to a height of 425 m. What is the gravitational potential energy of the shell at this height?
3)A 7.26 kg bowling ball hangs from the end of a 2.5 m rope. The ball is pulled back until the rope makes an angle of 45 with the vertical. What is the increase in the ball’s potential energy when it is lifted?
4)How much potential energy does Tim, with a mass of 60.0 kg, gain when he climbs a gymnasium rope a distance of 3.5 m?
5)A 6.5 kg bowling ball is lifted 2.1 m into a storage rack. Calculate the increase in the ball’s potential energy.
6)Mary weighs 505 N. She walks down a flight of stairs to a level 5.50 m below her starting position. What is the change in Mary’s potential energy?
7)A weightlifter raises a 180 kg barbell to a height of 1.95 m. How much work is done on the barbell?
8)Amy raised a 12.0 N physics book from a table 75 cm above the floor to a shelf 2.15 m above the floor. What was the change in potential energy of the book?
9)If 1.00 J of work is done to lift a block 1.00 m, what is the mass of the block?
1)top: 4 x 104J; bottom: -4 x 104 J / 2)2.08 x 105 J / 3)52 J / 4)2.1 kJ5)130 J / 6)–2780 J / 7)3400 J / 8)16.8 J / 9)0.10 kg
E> Conservation of Energy:
1)A 15.0 kg model airplane flies horizontally at 12.5 m/s.
a)Determine the kinetic energy of the plane.
b)The plane goes into a dive and levels off 20.4 m closer to the ground. How much potential energy did the plane lose during the dive?
c)What was the change in kinetic energy of the plane during the dive?
d)What is the plane kinetic energy at this lower altitude?
e)What is the plane’s speed at this lower altitude?
2)A partially filled bag of cement having a mass of 16.0 kg falls 40.0 m from a bridge.
a)What was the kinetic energy of the bag just as it strikes the ground?
b)With what speed will the bag of cement impact the ground?
3)A 98.0 N block falls 64.0 m.
a)What is the potential energy of the block before it begins to fall?
b)What is the kinetic energy of the block just as it strikes the ground?
c)What is the speed of the block upon impact?
4)During a hammer throw at a track meet, an 8.0 kg hammer is accidentally thrown straight up into the air. If the release speed of the hammer is 14.0 m/s, how high will the hammer rise above its release position?
5)A 98.0 N test rocket is fired from KennedySpaceCenter. Its fuel provides 1960 J before it leaves the launch pad. How high will the rocket rise?
6)In an electronics factory, small cabinets slide down a 30 incline for a distance of 16.0 m to reach the next assembly stage. The cabinets each have a mass of 10.0 kg.
a)What is the speed of the cabinets as they reach the bottom of the incline?
b)How much kinetic energy do the cabinets have at this point?
7)A biker approaches a hill with a speed of 8.5 m/s.
a)Write an expression for representing the kinetic energy of the biker at the bottom of the hill.
b)Write an expression for the potential energy of the biker at the top of the hill.
c)Using these two expressions, how high up the hill will the biker be when he stops?
8)A motorcyclist is trying to leap across a canyon by driving horizontally off the cliff at a speed of 38.0 m/s. Find the speed with which the cyclist strikes the ground on the other side.
1) (a) 1170 J (b) 3000 J (c) 3000 J (d) 4170 J (e) 23.6 m/s / 2) (a) 6270 J (b) 28.0 m/s3) (a) 6270 J (b) 6270 J (c) 35.4 m/s / 4) 10. m / 5) 20. m
6) (a) 12.5 m/s (b) 784 J / 7) 3.69 m / 8) 46.2 m/s