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.

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Work and Energy: W_external = ΔE_system

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5. Consider a 0.50-kg block travelling at 2.0 m/s on a horizontal surface. At the instant shown, there is a rope with a tension of 1.0 N attached while the block travels 1.0 m to the right. In each case:
   a. Determine what object(s) make(s) up the system.
   b. Determine if the system is isolated or if there are external forces are acting on the system.
   c. Determine if there are internal forces to the system.
   d. Find the final speed of the block.

6. Consider the blocks travelling at 5.0 m/s on a horizontal surface in the diagrams below. The blocks travels 2.0 m to the right. In each case:
   a. Determine what object(s) make(s) up the system.
   b. Determine if the system is isolated or if there are external forces are acting on the system.
   c. Determine if there are internal forces to the system.
   d. Find the final speed of the block(s)

7. Consider the two blocks travelling at 5.0 m/s on a horizontal surface in the diagrams below. The blocks will one by one slide down the 3.0 m-long, 40° incline to the lower side. The string between the blocks is long enough so that the first block will be down on the lower level before the second block hits the incline. In each case:
   a. Determine what object(s) make(s) up the system.
   b. Determine if the system is isolated or if there are external forces are acting on the system.
   c. Determine if there are internal forces to the system.
   d. Find the final speed of the blocks when just the first block reaches the lower level.
   e. Find the final speed of the blocks when both blocks reach the lower level.

8. 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?
9. 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.




10. 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.

11. 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?

    

12. 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?




13. 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°.




14. 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?

    

15. 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?

    

16. 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. 
    

    

17. 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.

    
    

18. 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?

    

19. 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?



20. 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 frictional forces involved.

    

21. A block of mass m is connected by a string of negligible mass to a spring with spring constant K which is in turn fixed to a wall. The spring is horizontal and the string is hung over a pulley such that the mass hangs vertically. The pulley is massless.As shown in the diagram below, the spring is initially in its equilibrium position and the system is not moving.
    (a) Use energy methods, to determine the speed v of the block after it has fallen a distance h. Express your answer in terms of g, m, K, and h.
    (b) The block will oscillate between its initial height and its lowest point. At its lowest point, it turns around. Use your answer to part (a) to find where it turns around.
    

    

22. 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?

    

23. A block of mass M on a flat table is connected by a string of negligible mass to a vertical spring with spring constant K which is fixed to the floor. The string goes over a pulley that is a solid disk of mass M and radius R. As shown in the diagram below, the spring is initially in its equilibrium position and the system is not moving. A person pulls the block with force F through a distance L. Determine the speed v of the block after it has moved distance L. The tabletop is frictionless.

    
24. 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?
25. 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?
26. 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.
27. 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@kpu.ca