Work changes the energy of a system. If the only change resulting from applying a force on an object is change in velocity, then the work done on the object is the change in kinetic energy. The path of the object does not matter; the force on the object does not have to be constant.
W = Ekfinal - Ekinitial = (0.5)m(vfinal)2 - (0.5)m(vinitial)2
W = Fdcosø
Work-Energy Theorem
The work done on a rigid body by a net force changes the energy of the body.
W = Ekfinal - Ekinitial = (0.5)m(vfinal)2 - (0.5)m(vinitial)2
W = Fdcosø
When the energy of the body increases, work is positive.
WORK and KINETIC ENERGY PROBLEMS
1. A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and accelerating to 3.00 m/s. How much work was done on the cart?
2. A 30.0 kg box sliding at 5.00 m/s on a rough surface is brought to rest by 20.0 N of friction. What distance does the box slide?
3. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m. What is the average net force on the truck?
4. A space ship of mass 5.00 ×104 kg is traveling at a speed 1.15 × 104 m/s in outer space. Except for the
force generated by its own engine, no other force acts on the ship. As the engine exerts a constant force of
4.00 × 105 N, the ship moves a distance of 2.50 × 106 m in the direction of the force of the engine.
a. Determine the final speed of the ship using the work-energy theorem.
b. Determine the final speed of the ship using the kinematics equations.
5. A force of 6.0 N is used to accelerate a mass of 1.0 kg from rest for a distance of 12m. The force is applied along the direction of travel. The coefficient of kinetic friction is 0.30. What is the
a. work done by the applied force?
b. work done by friction?
c. kinetic energy at the 12-m mark?
6. A 0.600-kg particle has speed of 2.00 m/s at point A and kinetic energy of 7.50 J at point B. What is
a. its kinetic energy at A?
b. its speed at B?
c. the total work done on the particle as it moves from A to B?
7. Two carts, one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?
8. A weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What propulsive force was necessary to attain the muzzle speed within the 6.00-m barrel? (Assume constant acceleration and neglect the Earth's gravitational effect.
9. A catcher stops a 91 mi/h pitch in his glove, bringing it to rest in 0.00179 m. If force exerted by the catcher is 785 N, what is the mass of the ball?
10. A baggage handler drops your 7.80 kg suitcase onto a conveyor belt running at 1.60 m/s. The materials are such that µs= 0.470 and µk = 0.150 . How far is your suitcase dragged before it is riding smoothly on the belt?
11. A 12.4 g bullet is fired horizontally into a 96 g wooden block initially at rest on a horizontal surface. After impact, the block slides 7.5 m before coming to rest. If the coefficient of kinetic friction between block and surface is 0.650, what was the speed of the bullet immediately before impact?
12. A toy cart moves with a kinetic energy of 30 J. If its speed is doubled, what will its kinetic energy be?
13. A car traveling 59 miles/hour locks up its brakes. The brakes are released when the car reaches 42 miles/hour. The mass of the car is 79.2 slugs. Calculate the Energy lost to Friction in Joules.
14. A 70 kg diver steps off a 10 m tower and drops from rest straight down into the water. If he comes to rest 5 m beneath the surface, determine the average resistive force exerted on him by the water.
15. The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about 98 m, 74 m, and 23 m, respectively. Neglecting air resistance, calculate the minimum initial kinetic energies that would produce these throws and estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2 m.
16. A 1300-kg car coasts on a horizontal road with a speed of 18 m/s. After crossing an unpaved, sandy stretch of road 30.0 m long its speed decreases to 15 m/s. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section.
ANSWER to WORK and KINETIC ENERGY PROBLEMS
1. W = Ekfinal - Ekinitial = (0.5)m(vfinal)2 - (0.5)m(vinitial)2
= (0.5)(5.00)(3.00)2 - (0.5)(5.00)(0.500)2
= 21.9 J
For solutions to all the problems on this page click here.
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