AP Physics 1 Lesson 7.a Work, Gravitational Potential, and Kinetic Energy 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 the 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. The teacher is going to show you this video clip (Wile E. Coyote). In the space below, explain what seems to be in error about the video clip. 2. Work as a group to define the following terms based on your prior knowledge. Energy Energy Conservation Energy Transformation Potential Energy Kinetic Energy Elastic Energy Gravitational Potential Energy Explore Energy is a powerful model used in physics to describe the potential of an object to induce change within a system. Energy may be invested in many different forms within a system. For any closed system the total change in energy is zero. In other words, we say that energy is conserved. This is essentially the law of conservation of energy. The teacher will show the Bowling Face video clips. 3. Why is it save to participate in the demonstrations shown in the video clips? 1
Here are strobe photos of a tennis ball bouncing along a floor. 4. Explain why the height of the bounce appears to decrease. 5. Explain where you think energy within the system is going as the ball bounces. The natural tendency for all systems is that high potential energy states are transformed into more distributed energy states. Energy transformations that result in lower potential energy states, with more energy invested in the random motion of small particles are favored. We say that energy transformations of this kind result in an increase in entropy or the relative randomness in the system. 5b. Vocabulary List: conservative, non-conservative, force, open, closed In this course, many of the problems we will address will involve systems in which energy transformations do not include increases in entropy (disorder) as the result of such as friction and vibrations that generate internal heating or sound. In some cases, we will investigate systems where dissipative forces are a factor and energy losses to heat must be considered. 6. Examine the following Energy Well Track video clip. Explain why the ball must be placed in its final release location to escape the well. In conservative systems, we consider energy transformations to be perfect transformations of energy from one form into another. There are many types of energy we will work with in this course. 7. Complete the table shown below. Vocabulary List: kinetic energy, thermal energy, electric energy, elastic potential energy, gravitational potential energy, potential energy, internal energy, heat Term Variable Equation Definition Stored energy. PE or U Energy stored in an object that is the result of the position of an GPE = mgh object relative to the surface of the earth. 2 Energy that is stored in a spring or other elastic material as a result U e U e =1/2 kx of its deformation (usually expansion or compression). U U = Vd Energy that is stored in an electric field. GPE of U g 2 Energy of motion. The energy an object has due to the combination KE KE=1/2 mv of its mass and velocity. The sum of the vibrational, rotational and translational kinetic U U=3/2nKT energies of the particles that make up a material. Q Q=mc T or Q=U±W The amount of molecular kinetic energy transferred between objects or materials. 2
WORK Definition: The process of transforming energy from one form to another is defined to be work. Note that the physics definition of work is significantly different than its common usage. The relationship of work and energy: The work energy theorem is an equation statement of the concept that work is the process of transforming energy from one form into another. We will use the work energy theorem in conservative and non-conservative systems in this course. This means that in some circumstances work is being done and the total energy of the system remains the same and in other cases as work is being done energy is transferred to the environment surrounding our system. The following equation is an applications of the work energy theorem. W Net= KE In physics, when work is done, a force is exerted through a distance and therefore work is calculated as the product of a force times the distance through which the force is applied. The relevant distance is the one in the direction of the motion. Let s consider the following example: A ball is released and allowed to fall without friction. 8. What force is exerted on the ball? 9. Over what distance is the force exerted? 10. What form of energy does the ball have at the release point? 11. What form of energy does the ball have before reaching the horizontal surface? In this example, we say that the gravitational force has done work on the ball, exerting a force through distance. This force has resulted in a decrease in the gravitational potential energy of the ball, and an increase in the kinetic energy of the ball. We can represent this transformation in a number of ways: With pie charts With bar graphs With line gaphs With energy transfer diagrams GPE WORK KE In every case, the core concept is the same: W= KE W= PE 3
Consider the following situations: 12. Prepare pie charts, bar graphs, line graphs and energy transfer diagrams for each of these situations in the space below. This should look similar to the example following question 11 on the previous page. Use the start, half way up the hill, and top of the hill as the three points of interest. Use the start, half way up the hill, and top of the hill as the three points of interest. With this apparatus, the Salford-based physicist James Joule (1845) discovered the 'mechanical equivalent of heat', quantifying how heat can be converted into mechanical work and vice versa. The apparatus used a system of paddles to stir water vigorously in the vessel. The resulting rise in water temperature was related to the mechanical work expended in moving the paddles, which was provided by falling weights. This led ultimately to the formulation of the first law of thermodynamics, concerning the conservation of energy. The standard unit of energy is now called the Joule (1 Joule = 1 N m) Elaborate Now that we have a basic understanding of the concepts of energy, potential energy, kinetic energy, energy conservation, the work energy theorem and entropy, we will investigate the quantitative aspects of these ideas. Consider the set up below. A mass is connected to a cart by a low friction pulley. A motion detector is set up to monitor the position of the cart. The mass is permitted to fall through a distance d. 13. Predict what will happen to the gravitational potential energy of the mass as it falls through the distance d. 14. Predict what will happen to the kinetic energy of the cart as the mass falls through a distance d. Assume this is a frictionless set up. 15. Prepare a free body diagram for the mass as it falls. 16. Prepare a free body diagram for the cart as it accelerates. 4
17. What energy transformation occurs for the mass? What is the starting energy and what is the final energy? 18. Does all of the initial gravitational potential energy invested in the mass get transformed into the final kinetic energy of the mass? 19. Where does the rest of the initial gravitational potential energy of the mass get transferred? 20. How could you determine the kinetic energy of the system once the mass is released? Measure the peak velocity attained by the system for several different distance d values. Conduct 3 trials for each distance d. Calculate the initial GPE, the work done W, and the change in KE experienced by the system. Mass (kg) Distance mass dropped (m) GPE of Mass GPE=mgh (Joules) (h refers to the change in position, therefore a change in GPE) Work done (W=F d) (Joules) (gravity is the force doing the work here) 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 the System (hanging mass+cart) (kg) KE of System 1/2mv 2 (Joules) 21. Compare the GPE to the KE for each of the trials. 22. What could account for differences between the predicted (calculated GPE) and the actual (measured KE) change in energy? 23. On the grid below, plot GPE values (x) vs. KE values (y). 24. What is the apparent relationship between the change gravitational potential energy and kinetic energy for the system? 5
Explain 25. Practice I. II. Ball released at A. Bar Graphs Bar Graphs I II III A B C III. IV. Ball released at A. I II III IV V I II III IV V 6
Practice Calculations A 3 kg brick is lifted to a height of 4 m. 26. What is the gravitational potential energy of the brick at that height? 27. If the brick falls to a new height of 2m, what is the new gravitational potential energy of the brick? 28. Suppose the brick comes to rest on the floor (height = 0m). What is the gravitational potential energy of the brick at this final height? A 2kg ball rolls down a ramp. 29. After rolling a small distance down the ramp, the ball achieves a speed of 3 m/s. What is the kinetic energy of the ball when moving at this speed? 30. After rolling halfway down the ramp, the ball achieves a speed of 6m/s. What is the kinetic energy of the ball when moving at this speed? 31. Upon reaching the bottom of the ramp, the ball achieves a speed of 9m/s. What is the kinetic energy of the ball when moving at this speed? 32. If the initial velocity of the ball was 0m/s, what was the initial height of the ball? 7
The LAW OF CONSERVATION OF ENERGY applies to the calculation of energy at different points in an event. In this example, a diver starts with a certain amount of GPE. As the diver falls, this energy is transformed into KE. 33. Calculate the KE values using the LAW OF CONSERVATION OF ENERGY. 34. The 2kg ball shown above rolls down the ramp. Prepare the table below. Calculate the GPE at each height, and the KE at each height. Height (m) 5 4 3 2 1 0 Gravitational Potential Energy GPE (joules) Kinetic Energy KE (joules) 35. Look back at your definitions for question 2. Make any changes necessary if you have a different understanding of these terms than before. 8