*Be able to use any previous concepts with work & energy, including kinematics & circular motion.

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1 AP Physics 1 Chapter 6 Study Guide Work & Energy Topics: Work o W = Fdcosq, where q is the angle between F & d (only using part of force that makes the object move) o Force must make object move to do work o Scalar quantity o Measured in joules (J) o Can be done on or by an object (+/-) o On F vs d graph, W = area under curve Energy o Total (mechanical) energy is conserved (Law of Conservation of Energy) o Types of energy (Kinetic, Gravitational Potential, Elastic/Spring Potential) o Work-Energy Principle (Wnet = DKE) o If energy is transferred due to nonconservative forces: Einitial = Efinal + Elost (or WNC = DE) Power o Rate at which work is done or rate at which energy is transformed o Measured in watts (W) (1 W = 1 J/s) o Average Power: P = W/t or P = Energy transformed/time or P = Fv *Be able to use any previous concepts with work & energy, including kinematics & circular motion. Practice Problems: 1. An object is dropped from the top of a tall building. Sketch a graph to represent each of the following quantities for the object: a) Kinetic Energy vs. Time b) Potential Energy vs. Time c) Total Energy vs. Time 2. A child throws a ball up into the air. Sketch a graph to represent each of the following quantities for the ball: a) Kinetic Energy vs. Height b) Potential Energy vs. Height c) Total Energy vs. Height

2 3. A 1-kg object travels horizontally in the positive direction due to a horizontal net force being exerted on it. The net force versus displacement graph for the first 4 meters of the object s motion is shown below. a) What is the net work done during the first 2 meters of the object s motion? W = Fd = area under curve W = 5 J b) What is the net work done during the entire 4 meters of the object s motion? W = 5 J 1 J = 4 J c) If the object started from rest, what is its speed after moving 4 meters? W = DKE v = 2.8 m/s 4. A 0.5 kg ball is dropped from a height of 8 m. (Note: Values were calculated using g = 10 m/s 2.) a) What is the ball s initial gravitational potential energy? 40 J b) What is the ball s initial kinetic energy? 0 J c) What is the ball s initial total mechanical energy? 40 J d) What is the ball s gravitational potential the instant before it strikes the ground? 0 J e) What is the ball s kinetic energy the instant before it strikes the ground? 40 J f) What is the ball s total mechanical energy the instant before it strikes the ground? 40 J g) After bouncing, the ball reaches a maximum height of 7 m. What is the ball s potential energy at this point? 35 J h) What is the ball s kinetic energy at this point? 0 J i) What is the ball s total mechanical energy at this point? 35 J j) What was the ball s total mechanical energy the instant after it bounced? 35 J

3 5. A mass swings back and forth on the end of a pendulum, as shown in the diagram below. Points 1 and 5 represent the maximum height of the mass, while point 3 represents the lowest point. List the points 1 through 5 in order from least to greatest for each of the following quantities: 1 = 5, 2 = 4, 3 3, 2 = 4, 1 = 5 1 = 2 = 3 = 4 = 5 6. A mass sitting on a frictionless surface oscillates on the end of a horizontal spring. The diagram below represents the path of the mass as it travels back and forth, with x = 0 representing the equilibrium position and xmin and xmax representing the positions furthest from the equilibrium position to the left and right, respectively. List the positions a through e in order from least to greatest for each of the following quantities: a = e, b = d, c c, b = d, a = e a = b = c = d = e d) If the surface on which the mass is sitting was not frictionless, how would the motion of the block be different? As the mass travels, it would continually lose energy due to friction the mechanical energy would be converted to heat. As a result, the mass displacement from the equilibrium position (x = 0) would get smaller and smaller with each pass. Eventually, the mass would lose all of its energy and it would come to rest at the equilibrium position.

4 7. A mass oscillates up and down on the end of a vertical spring, as shown in the figure below. Points A and E represent the highest position of the mass, while point C represents the lowest. List the points A through E from least to greatest for each of the quantities below. A = C = E, B = D B = D, A = C = E A = B = C = D = E 8. A box of mass m is pushed along a horizontal surface. It is accelerated at a constant rate of a for t seconds. If the box is pushed a total of x meters, at what rate was work done on the box? P = W t = Fd t = max t 9. For an object of mass m traveling along a circular path of radius r at a uniform speed of v, a) What is the kinetic energy of the mass? 1 2 mv2 b) How much work is done on the mass during one revolution? 0 J 10. Eight textbooks, each 4.3 cm thick with mass 1.7 kg, lie flat on a table. How much work is required to stack them one on top of the another? The force required to lift each book is the weight of the book (Fg = mg). The distance each book must be lifted increases by the height of one additional book each time. The first book is already on the table, so it requires no work: W1 = 0 W5 = (17)(0.043)(4) = J W2 = (17)(0.043) = J W6 = (17)(0.043)(5) = J W3 = (17)(0.043)(2) = J W7 = (17)(0.043)(6) = J W4 = (17)(0.043)(3) = J W8 = (17)(0.043)(7) = J The total work required is the sum of these. Work is a scalar, so we just find the sum without regarding direction or components: Wnet = J = 20.5 J

5 11. Bert and Ernie are taking a large box of Oreos to Cookie Monster, whose front door can be reached by either a ramp or a staircase. Bert says it would be easier to slide the box up the ramp (assume it is frictionless), while Ernie insists that they should carry the box up the stairs. If both Bert and Ernie followed their own plan, which one would do more work on the box? Why? Each one would do the same amount of work on the box, since the same force is needed (the weight of the box) to move the box the same distance (the height it reaches). If one person does the job faster than the other, that person would use more power, but the amount of work would still be the same for both. Also, if the ramp was not frictionless, the person would have to work against friction, meaning more work would be required.