Physics 1100 In-Class Problems: Work & Energy

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. A winch lifts a 150 kg crate 3.0 m upwards with an acceleration of 0.50 m/s². How much work is done by the winch? How much work is done by gravity?




4. What work does a baseball bat do on a baseball of mass 0.325 kg which has an initial speed forward of 36 m/s and a final speed of 27 m/s backwards. Assume motion is linear and horizontal. The work done by the bat is a non-conservative force.
5. How much work must be done to stop a 2000-kg car travelling at 60 km/h in 15.0 m? What was the average breaking force?
6. In the diagram below, determine the speed of the block at each point. Assume no friction. The mass of the block is 10.0 kg.




7. A 2.0-kg rock is thrown with initial speed of 9.8 m/s at an unknown angle. The speed of the rock at the top of the parabola is 2.1 m/s. How high does it go? Assume no air resistance.

8. 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?

   

9. 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?




10. In the figure below, a block of mass 5.0 kg starts at point A with a speed of 15.0 m/s on a flat frictionless surface. At point B, it encounters an incline with coefficient of kinetic friction μ_k = 0.15. The block makes it up the incline to a second flat frictionless surface. What is the work done by friction? What is the velocity of the block at point C? The incline is 2.2 m long at an angle θ = 15°.




11. Two blocks are connected by a string hung over a frictionless massless pulley. Block A has mass M_A and block B has mass M_B. Initially the blocks are held at rest before being allowed to move. How fast will block B be moving when it has risen a distance h?

    

12. Two blocks are connected by a string hung over a frictionless massless pulley. Block A has mass M_A and is on a table top. Block B has mass M_B and is hanging in the air. Initially the blocks are held at rest. The coefficients of friction between block A and the tabletop are μ_S and μ_K.
    (a) B is allowed to fall. How fast will block B be moving when it has fallen distance h?
    (b) Block A is pulled to the left by a horizontal force F for a distance L. How fast will block B be moving?

    

13. Two blocks are connected by a sting slung over a pulley as shown in the diagram below. The hanging block is allowed to drop. How fast will it be moving when it hits the ground? The block on the incline has mass M_A = 2.50 kg.  The hanging block has mass M_B = 1.50 kg. The incline makes and angle θ = 30° with horizontal.  Ignore friction. 
    

    

14. In the diagram, below what is the minimum height that the skier must start from to successfully make it around the loop. Assume (a) no friction, and (b) that friction does -3.0 × 10³ J of work on the skier. The radius is 5.00 m and the skier has mass 65.0 kg.

    
    

15. Tarzan, Lord of Apes, is swinging through the jungle. In the diagram below, Tarzan is standing at point A on a tree branch h₁ = 22.0 m above the floor of the jungle. Tarzan is holding one end of a vine which is attached to a branch on a second tree. The vine is L = 21.0 m long. When Tarzan swings on the vine, his path is in an arc of a circle. At the bottom of his swing he is at point B, 13.0 m above the ground . Ignore Tarzan's height. Tarzan has a mass of 90.0 kg. The vine does not stretch and has negligible mass.
    (a) Why does the tension in the vine do no work?
    (b) What will be his speed at point B? 
    (c) What will be the tension in the rope at point B?

    

16. A 0.200-kg block slides down the track and horizontally off a table as show in the diagram below.
    
(a)   Assumingthat friction is negligible, how far from the table does the block land?
(b)   The block only land 1.20 m away.  How much work was done by friction and other non-conservative forces?



17. A 50-hp engine is used to lift heavy loads at a worksite. It is used to lift a load of bricks weighing 2000 N to the top of a new building 35.0 m above ground. How long does it take for the load to get to the top?
18. A 5.0 MW generating station is situated at a 22-m high dam. The energy used to generate the electricity comes from the loss in potential energy of the water as it falls the height of the dam. What is the minimum amount of water going through the dam every day?
19. 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.
20. A 7000 W engine is propelling a speedboat at 30 km/h. What force is the engine exerting on the speedboat? What force and how much power is water resistance exerting on the speedboat?

Questions?mike.coombes@kwantlen.ca