1. In the diagram below, calculate the work done if:
   (a) F = 15.0 N, θ = 15°, and Δx = 2.50 m,
   (b) F = 25.0 N, θ = 75°, and Δx = 12.0 m,
   (c) F = 10.0 N, θ = 135°, and Δx = 5.50 m,
   

   

2. In the diagram below, a rope with tension T = 150 N pulls a 15.0-kg block 3.0 m up an incline (θ = 25.0°). The coefficient of kinetic friction is μ_k = 0.20. Find the work done by each force acting on the block.

   

3. What is the work done by friction in slowing a 10.5-kg block traveling at 5.85 m/s to a complete stop in a distance of 9.65 m? What is the kinetic coefficient of friction?
   

4. A 50.0-N force is applied horizontally to a 12.0-kg block which is initially at rest. After traveling 6.45 m, the speed of the block is 5.90 m/s. What is the coefficient of kinetic friction?

5. Determine the work done by the following. Determine the angles between the forces and the displacements. The forces are in Newtons and the displacements are in metres:
   (a) F = <1, 2, 3> and Δr = <4, 5, 6>
   (b) F = <1, 2, 3> and Δr = <4, 5, -6>
   (c) F = <4, 2, 4> and Δr = <2, -8, 2>
   

6. In the diagram below, a 5.00-kg block slides from rest at a height of h₁ = 1.75 m down to a horizontal surface where it passes over a 2.00 m rough patch. The rough patch has a coefficient of kinetic friction μ_k = 0.25. What height, h₂, does the block reach on the incline?

   

7. In the diagram below, a 5.00-kg block slides from rest at a height of h₁ = 1.75 m down to a smooth horizontal surface until it encounters a rough incline. The incline has a coefficient of kinetic friction μ_k = 0.25. What height, h₂, does the block reach on the θ = 30.0° incline?

   

8. In the diagram below, the spring has a force constant of 5000 N/m, the block has a mass of 6.20 kg, and the height h of the hill is 5.25 m. Determine the compression of the spring such that the block just makes it to the top of the hill. Assume that there are no non-conservative forces involved.

   

9. Suppose that there is friction in the previous problem and that the compression must in fact be 0.425 m for the block to just reach the top of the hill. What work is done by the frictional force?

10. At point A in the figure shown below, a spring (spring constant k = 1000 N/m) is compressed 50.0 cm by a 2.00 kg block. When released the block travels over the frictionless track until it is launched into the air at point B. It lands at point C. The inclined part of the track makes an angle of θ = 55.0° with the horizontal and point B is a height h = 4.50 m above the ground. How far horizontally is point C from point B?
    
    

11. A block of mass m₁ is hanging over a massless pulley via a string connected to a second block of mass m₂ sitting on a tabletop. The coefficient of kinetic is μ_k for the block on the table. Find an expression for the speed of the hanging block when it is released and allowed to drop a distance h.
    

12. A block of mass m₁ is hanging over a massless pulley via a string connected to a second block of mass m₂ sitting on a tabletop. The tabletop is frictionless block the second block is connected to a wall by an unstretched spring with spring constant K. Find an expression for the speed of the hanging block when it is released and allowed to drop a distance h.
    

13. A block of mass m is a height h above an uncompressed vertical spring of spring constant K. When the block is released, what will be the maximum compression of the vertical spring?
    

14. What power is required to pull a 5.0 kg block at a steady speed of 1.25 m/s? The coefficient of friction is 0.30.

15. A 7500 W engine is propelling a boat at 12 km/h. What force is the engine exerting on the boat? What force and how much power is water resistance exerting on the speedboat?

16. A 3.0 hp engine is 35% efficient as it pulls a block at constant speed up a 12.0 m 30.0° incline. How long does this take? Ignore friction. The mass of the block is 245 kg. Note 1 hp = 746 Watts.

17. If a typical 70-kg person consumes energy at a rate of 100 W, and a typical candy bar has a food energy of 450 KJ, how many candy bars perday must the person consume if that is all he eats?

18. If the 70-kg person consumes an extra two 450 KJ candy bars a day, how far must he walk to “burn off” the extra calories? Assume the person requires 60 kcal to walk one kilometre. If he were to climb stairs, what height would he reach? Assume that the person is 25% efficient in converting food energy into mechanical energy.

19. The same person consumes an extra two 450 KJ candy bars a day without exercising for a year and the excess energy is stored as body fat. The energy content of body fat is 9.3 kcal/g. How much mass will the person gain?

20. A typical 70-kg person has a basic metabolic rate of 100 W. He is planning a weeklong biking trip and wants to know how much food to pack in the form of 450 KJ candy bars. He expects to ride 8 hours per day for that week. He uses Google and finds the metabolic rate of a person while biking is 1.0 cal/(s-kg). How many bars does he pack?

Questions? mikec@kwantlen.bc.ca