1. What must be stored in the bow?

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1 AP Physics 1 Lesson 7.b Work and Elastic Potential Energy in Springs Outcomes 1. Define work. 2. Define energy. 3. Determine the work done by a constant force. 4. Determine the work done by a force exerted on or by a spring. 5. Determine he kinetic energy of a moving object. 6. Apply the work energy theorem to solve problems. 7. Determine gravitational potential energy and elastic potential energy. 8. Apply the Law of Conservation of energy to solve problems. Name Date Period Engage 1. What must be stored in the bow? 2. When the coyote releases his grip, what will be exerted on the coyote? 3. Prepare a free-body diagram for the coyote once his grip is released and while is still touching the string. 4. What will happen to the elastic potential energy of the coyote once his grip is released? 5. Compare the energy stored in the bow before he releases his grip and the kinetic energy of the coyote at the instant he leaves the bow. 6. If the coyote has a mass of 20 kg, the bow has a maximum potential energy of 2000 J, and the roadrunner has a velocity of 15 m/s, will the coyote catch the roadrunner? Show your work. The teacher will show you the Sling Shot Girl.mov video. 7. What does the tractor exert on the slingshot? 8. If a force is exerted through a distance then what is done on the slingshot? 9. What does this work result in an increase of? (Yes, I ended a sentence with a preposition if you don t like it, change it.) 10. What happens to this elastic potential energy (Ue)? 11. The string will vibrate for a while. The vibrations are called oscillations. Over time, the oscillations decrease in amplitude. Explain why this occurs. 1

2 Explore I. Let s see what you remember from the last lesson. There isn t a vocabulary list, since there are no new terms. Notes I. : The potential to produce change within a system. The ability to do work within a system. II. of energy. Type of Energy Variable Equation Definition Stored energy. III. The Nature of Systems Energy stored in an object that is the result of the position of an object relative to the surface of the earth. Energy that is stored in a spring or other elastic material as a result of its deformation (usually expansion or compression). Energy that is stored in an electric field. Energy of motion. The energy an object has due to the combination of its mass and velocity. The sum of the vibrational, rotational and translational kinetic energies of the particles that make up a material. The amount of molecular kinetic energy transferred between objects or materials. A. 1. A measure of the randomness or disorder in a system. B. The natural tendency of systems is to high potential energy states into more distributed forms of energy. C. D.. IV. The Law of 1. Systems where losses due to dissipative forces (such as friction) are not a factor in making predictions or solving problems. 1. Systems where losses due to dissipative forces are a factor in solving problems. of Energy. A. For conservative systems, the total energy of a system remains unchanged and therefore the change in energy U is =. V. A. The process of transforming energy from one form into another. It is also the force exerted through a distance. 1. W=. 2. Units B. did pioneering work to demonstrate the equivalency of mechanical energy with thermal energy. VI. Theorem 2

3 A. Consider this example. 1. What force is exerted on the ball once it is released? 2. Over what distance is the force exerted? 3. What does this work result in? 4. With respect to the KE of the ball, is this work considered positive, negative or zero? (positive work results in an increase in kinetic energy or in other words the force is in the direction of the motion) VI. Graphical Analysis of Work. Clue: Look at the equation to calculate work and what is recorded on the x and y axis in the graphs below. Think back when you analyzed kinematic graphs. A. Examine the graph below. This force was exerted on a 2kg object in a conservative system. B. Examine the graph below. This force was exerted on a 2kg object in a conservative system. a) How much work was performed by this force over the distance of 3m? a) How much work was performed by this force over the distance of 3m? b) What is the final velocity of the object? b) What is the final velocity of the object? Elaborate The cart can be pulled to the right, stretching the spring. If the cart is released, it will accelerate to the left The can be stretched a small amount (A) or a large amount (B). 3

4 14. In which situation would the kinetic energy of the car be the greatest? Support your answer with graphs of force and displacement. Consider if the force remains constant when the spring is being stretched or if it changes. In the last question you made predictions about the work performed in a conservative system, the maximum Ue developed in the system, and the maximum KE of the motion of the system, assuming perfect energy transformations. In this investigation, we will determine whether or not your predictions are supported by the evidence. The following investigation has two parts. Since the force applied by the spring depends on how far the spring is stretched as well as how stiff or how springy the spring is, we need to find a way to determine this second factor, spring stiffness, first. We are applying Hooke s law to do that. Hooke discovered the relationship between the force applied to a spring either stretching or compressing it and the change in the length of the spring. F = -kx The negative sign indicates that since this force is the restoring force (getting the spring back to its original position) it is exerted in the opposite direction to the force stretching or compressing the spring. x refers to the amount the spring has been stretched or compressed from its resting (equilibrium) position. First, we will examine the relationship between the force required to displace the spring and the distance the spring is being stretched. Prepare the following set up. Measure the extension (change in length) of the spring for increasing amounts of mass. You can also use a meter stick to measure the extension instead of the motion sensor. Force (N) (F=m g) The force stretching the spring is gravity acting on the mass suspended from the spring. Extension (m) How much the spring length changed from its original unstretched length. Plot the data 15. How would you determine the work done stretching this spring? Think graphical analysis and check the variables appearing on the y-axis and x-axis. Would the slope make sense or possibly the area? 4

5 16. Determine the slope of your graph. This slope represents the relationship between the force and the distance the spring is stretched. It is an unique value indicating the stiffness of the spring. This value is called the k value of the spring. Different springs have different k values. Stiffer springs have higher k values and store more energy for a given displacement. 17. The equation for determining elastic potential energy is Ue=1/2kx 2. How is this equation derived? (Not an easy question - look back at question 15 and remind yourself that work equals the change in energy) Examine the set up below Consider the set up below. A spring is connected to a cart by a low friction pulley. A motion detector is set up to monitor the position of the cart. The cart will be pulled back different distances d. 18. Predict what will happen to the elastic potential energy of the spring as it is stretched through the distance d. Assume this is a frictionless set up. 19. Predict what will happen to the kinetic energy of the cart as the spring contracts back through a distance d. 20. Prepare a free body diagram for the cart as the spring contracts back through the distance d. 21. What energy transformations occur for the system? 22. How do you determine the Ue for the system once the cart has been pulled back? 23. How do you determine the final KE of the car once it is released? 5

6 Measure the peak velocity attained by the car for several different distance d values. Conduct 3 trials for each distance d. Calculate the initial Ue, the work done W, and the change in KE experienced by the car. Spring Constant (N/m) Make sure you use the same type of spring for which you found k already. Distance cart is displaced (m) Ue of Spring Ue=1/2kx 2 (Joules) x is the stretch of the spring and equals the displacement of the cart. Work done (W=1/2F d) (Joules) Hint: What is the relationship of work and change of energy? Trial 1 peak velocity (m/s) Trial 2 peak velocity (m/s) Trial 3 peak velocity (m/s) Average Peak Velocity (m/s) Mass of Car (kg) KE of Car 1/2mv 2 (Joules) 24. Compare the Ue to the KE for each of the trials. 25. What could account for differences between the two values for each distance d? 26. On the grid below, plot Ue values (x) vs. KE values (y). 27. What is the apparent relationship between the change gravitational potential energy and kinetic energy for the system? 6

7 Explain 28. Practice I. Total Energy II. I II III Ball released at A. Total Energy. I II III IV V 29. What is the final KE of the skier? 30. What is the initial GPE of the skier? 31. Is this a conservative or non-conservative system? How do you know? The skier has a mass of 75 kg. For the conservative system on the left: 32. What is the K o of the mass? 33. Once the mass is in contact with the spring, what will be the maximum U e of the spring? Think energy transformation and conservation. m= 2.0 kg v= 1.5 m/s k= 20N/m 34. What is the maximum displacement of the spring? 7

8 A block gliding on a smooth surface encounters a rough section. 35. What is the initial K of the block? 36. What is the friction force exerted on the block? 37. What is the friction force exerted on the block? 38. What is the work done by friction on the block over the 0.5 m? m=2.0kg v o=2m/s 39. What is the K of the block at the end of the 0.5 m? 40. What is the final velocity of the block? A 2kg block experiences the forces described by the graph below. Assume the initial velocity of the block = 3.0 m/s 41. What is the work done on the block in the first meter? 42. What is the velocity of the block at the end of 1 meter? 43. What is the work done on the block in the first 2 meters? 43. What is the velocity of the block at the end of 2 meters? 44. What is the total work done on the block after 5 meters? 45. What is the final velocity of the block after 5 meters? A 250 kg roller coaster car travels the track illustrated below. 46. What is the K of the car at A? 47. What is the U g of the car at A? 48. What is the total energy of the car at A? 49. What is the velocity of the car at B? 50. What is the velocity of the car at C? 8