2. What would happen to his acceleration if his speed were half? Energy The ability to do work

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1 1. A 40 kilogram boy is traveling around a carousel with radius 0.5 meters at a constant speed of 1.7 meters per second. Calculate his centripetal acceleration. 2. What would happen to his acceleration if his speed were half? Energy The ability to do work Kinetic Energy Units Potential Energy Gravitational Potential Energy if not specified, potential energy is gravitational potential energy Elastic (or Spring) Potential Energy Mechanical Energy 1

2 1. What is the kinetic energy for a 2 kg toy car traveling at 3 m/s? 2. What is the potential energy of the same toy car if it is atop a 1.2 m table? 3. Calculate the total mechanical energy of the car from # A spring with spring constant 220 N/m is compressed 0.05 m. What is the energy stored in the spring? 5. A 1200 kg car has kinetic energy of 240,000 J. How fast is it moving? 2

3 Work Energy Theorem Joules of work are done to a Joey s 100 kg motorcycle. What is its change in total energy? 7. Monica pulls on a 6 kg toy wagon with a force of 20 N for 2 meters. What is the change in energy of the wagon? 8. Ross does 800 Joules of work pushing a 100 N box up a hill with constant speed. a. What type of energy is Ross giving the box? How much? b. How high up the hill did he push the box? 9. Phoebe does 500 Joules of work pushing a 20 kg box on a horizontal, frictionless surface. a. What type of energy is Phoebe giving the box? How much? b. How fast is the box moving when she is done? 3

4 10. What happens to KE when speed doubles? When speed is half as much? 11. What happens to PE when height doubles? When height is half as much? 12. What happens to PE s when x doubles? When x is half as much? Conservation of Energy Ideal Systems skate park 4

5 A 1 kg ball released from rest rolls down a hill a. What type of energy does the ball have initially? b. When it reaches the bottom of the hill, what will the potential energy be? c. What type of energy then will the ball have at the bottom of the hill? 5

6 20. A marble launcher uses a spring to launch a marble. The spring has spring constant k = 6000 N/m, and a 0.1 kg marble is sitting on the spring compressed to 0.02 m. (a) What type of energy does the marble initially have? How much? (b) Immediately after it is released, what type of energy does the marble have? How much? (c) At its maximum height, what type of energy does the marble have? How much? (d) Find the speed of the marble from part (b) (e) Find the maximum height the marble reaches in part (c) (f) At half the maximum height, what will the potential energy be? What will the kinetic energy be? 6

7 21. A 3.0 kilogram object is placed on a frictionless track at point A and released from rest. (Assume the gravitational potential energy of the system to be zero at point C.) a. Calculate the gravitational potential energy of the object at point A. b. Calculate the kinetic energy of the object at point B c. Which letter represents the farthest point on the track the object will reach? 22. A 0.15 kg marble rolls on a frictionless track starting fro a height h = 0.39 m. The ball is released from rest at point a. Calculate the KE and PE at point A b. Calculate the KE and PE at point B Calculate the KE and PE at point C. How fast is the marble moving at point C? 7

8 Ideal Conservation of Energy Non ideal Systems Non ideal Total Energy Internal Energy skate park 8

9 27. A 1 kg ball released from rest rolls down a 20 m tall hill. Mechanical energy is not conserved a. What type of energy does the ball initially have? How much? b. The ball s speed at the bottom is 10 m/s. Calculate the KE at the bottom. c. How much energy was lost to heat/friction/internal energy? 28. A 70 kg cliff diver stands atop a 10 m cliff. a. What is his potential energy? b. His speed when he hits the ground is 10 m/s. What is his KE at the bottom? c. How much energy was lost to air resistance? 9

10 29. A 100 kg motorcycle and rider are traveling at 10 m/s atop a 20 m hill. a. What is the total mechanical energy at top of the hill (KE + PE)? b. If 10,000 J are lost to heat, how fast is the motorcycle moving when it reaches the bottom? Energy Conversions 1. A car is moving along a flat surface with an increasing speed. What type(s) of energy are changing? 2. A car is moving up an incline with constant speed. 3. A car is applying its brakes and slowing down as it moves down a slope. 4. A cart is moving on a flat surface toward a wall and is stopped by a spring on its front. 5. A rocket flies upward with an increasing velocity 10

11 30. A student pulls a box 5.0 meters across a horizontal surface at a constant speed of 4.0 meters per second using a force of 60 newtons. a. Calculate the amount of work done by the student. b. What type of energy is being produced by this work? 31. A 5.0 kilogram object is dropped from a height of 3.0 meters and hits the ground with a speed of 4.5 meters per second. Determine the amount of work done by friction as the object falls to the ground. 32. A 0.10 newton spring toy with a spring constant of 160 newtons per meter is compressed 0.05 meter before it is launched. When released the spring toy pops up and reaches a maximum height of 1.5 meters. a. How much elastic potential energy is initially stored in the spring? b. How much internal energy is produced as the toy springs up to its maximum height? Momentum and energy in collisions In a collision Momentum is Total energy is Mechanical energy is 11

12 33. A constant force is used to speed up a block sliding along a rough, horizontal track. As the block slides there could be an increase in its (1) gravitational potential energy only (2) internal energy only (3) gravitational potential energy and kinetic energy (4) kinetic energy and internal energy 34. As shown in the diagram, a student exerts an average force of 600 newtons on a rope to lift a 50 kilogram crate a vertical distance of 3 meters. Compared to the work done by the student, the gravitational potential energy gained by the crate is (1) exactly the same (2) 330 J less (3) 330 J more (4) 150 J more 35. A 155 N box pushed up a 5.6 meter ramp. Neglect friction a. What is the increase in potential energy of the box? b. What is the work done on the box? 36. The diagram to the right shows points A, B, and C at or near Earth s surface. As a mass is moved from A to B, 100 joules of work are done against gravity. What is the amount of work done against gravity as an identical mass is moved from A to C? 37. A 55 kilogram diver falls freely from a diving platform that is 3.00 meters above the surface of the water in a pool. When she is 1.00 meter above the water, what are her gravitational potential energy and kinetic energy with respect to the water s surface? 38. As an ideal pendulum swings from point A to point B: What happens to total mechanical energy? What happens to kinetic energy? What happens to potential energy? 12