Chapter 7. Work and Kinetic Energy

I. Work Done by a Constant Force

1.  Work is measured in units of:

a.  N

b.  N-m

c.  N/m

d.  N-m2/s

e.  N-s2/m

2.  A truck pulls a trailer exerting a constant force F = 1000 N. What is the amount of work done by the truck if it moves the trailer 200 m? Assume that the angle between F and the displacement vector of the trailer is 0o. The trailer moves without friction.

3.  A 2-kg block (box, body) is pulled by a force F = 50 N for 100 m. What is the total work done on the block if the coefficient of kinetic friction between the block and the floor is 0.3 and a = 30o.

4.  The picture below shows an overhead view of a box that is put in motion by four forces acting in the xy plane. Knowing that F1 = 7 N, F2 = 35 N, F3 =15 N, F4 = 20 N, a = 30o, and b = 45o, find the net work done on the box if the box moves 7 m. Friction is not involved.

5.  A 1500-kg car starts moving from a stoplight with an acceleration of 2 m/s2. Find the work done by the engine during the first 5 m. The coefficient of friction between the tires and the road is 0.3.

6.  A 5-kg wooden block placed on an inclined surface is allowed to slide in the direction of the x axis (see picture). Find the measure of a in degrees, deg, if the block travels 2 m along the incline and if the work done by the gravitational force is 500 J. Assume there is no friction.

7.  A 50-kg sled is pulled 30 m over the ice at a constant speed. The coefficient of friction between sled and ice is 0.13. How much work is done in pulling the sled the 30 m?

8.  A constant horizontal force of 2.29 N is applied to a 1.82 kg block initially at rest on a friction-free surface. How much work is done on the block in the first 1.85 s after the force is applied?

II. Kinetic Energy and The Work-Energy Theorem

  1. What are the units of energy?

a.  Joules

b.  Newtons

c.  Kilograms

d.  Amperes

e.  Radians

  1. Energy is measured in units of:
  2. kg-m-s
  3. kg-m/s
  4. kg-m2/s2
  5. kg-m2/s
  6. kg-m/s2
  7. Find the kinetic energy of a 1-kg rock moving with a speed of 45 km/h.
  8. The kinetic energy of an 10-kg object is equal 4000 J. What is its speed?
  9. A car has a speed of 60 mi/h. Find its mass if its kinetic energy is 8 x 105 J.
  10. An engine does 1.5 x 105 J of work while accelerating a 1200-kg car from rest. Find the change in speed of the car.
  11. A box is pulled along a rough surface as shown in the picture. It starts with an initial speed of 1 m/s. Eventually it is accelerated up to 5 m/s. Find the coefficient of kinetic friction between the box and the surface if the mass of the box is 2 kg, F = 15 N, a = 20o, and the distance the box moves is 2 m.
  1. A 900-kg car is traveling at 50 mi/h. At some point the driver puts on the breaks and the car comes to a stop 9 s later. Find the force exerted on the car by the breaks using the Work-Energy Theorem.

III. Work Done by a Variable Force

  1. A 2-kg box sliding without friction reaches a spring that is firmly attached to a wall on the opposite side. The box compresses the spring by 10 cm. Find the initial speed of the box if originally the spring was in its equilibrium position. Assume the force constant of the spring to be 100 N/m.
  1. A 2-kg box sliding without friction reaches a spring that is firmly attached to a wall on the opposite side. The box has an initial speed of 5 m/s. Find the maximum compression of the spring caused by the box if the force constant of the spring is 300 N/m.
  1. A spring has a force constant of 300 N/m. How much work is required to compress this spring 10 cm?
  2. According to the graph, how much work is required to stretch the spring from x1 = 1 cm to x2 = 2 cm?


  1. A spring that has a block firmly attached to it on one end is stretched a length Dx. At some point the block is released. What is its speed as it passes through the equilibrium position of the spring (x0) if the mass of the block is 2 kg. Assume that the points x0 and x1 are 6 cm and 10 cm away from the wall respectively, and the force constant of the spring is 300 N/m. The block moves without friction.

IV. Power

  1. A 900-kg car accelerates from a stop reaching a speed of 60 mi/h in 9 s. Calculate the power supplied by the engine during these 9 s. Give the answer in watts, W.
  2. How much power is produced by an engine of a car at 50 mi/h if the pulling force exerted by the engine is 105 N. Give your answer in watts, W.
  3. What is the power required to accelerate a 4-kg block from rest up to 5 m/s if the block travels 2 m and a = 30o? Assume there is no friction.
  1. You lift a box off the ground with a speed of 1 m/s. What is the mass of the box if the power output of your body is 110 W?
  2. A spring that was initially in its equilibrium state is compressed 15 cm. What is the force constant k of the spring if the compression required 40 W of power and was done over 1 s?