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ch06-work-and-kinetic-energy

ch06-work-and-kinetic-energy - MasteringPhysics 12:30 AM...

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10/13/08 12:30 AM MasteringPhysics Page 1 of 11 http://session.masteringphysics.com/myct [ Print View ] Introductory mechanics Chapter 06 - Work And Kinetic Energy Due at 11:59pm on Tuesday, October 14, 2008 View Grading Details The Work-Energy Theorem Learning Goal: To understand the meaning and possible applications of the work-energy theorem. In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work- energy theorem. We will start with a special case: a particle of mass moving in the x direction at constant acceleration . During a certain interval of time, the particle accelerates from to , undergoing displacement given by . Part A Find the acceleration of the particle. Hint A.1 Some helpful relationships from kinematics By definition, . Furthermore, the average speed is , and the displacement is . Combine these relationships to eliminate . Express the acceleration in terms of , , and . ANSWER: = Part B Find the net force acting on the particle. Hint B.1 Using Newton's laws Hint not displayed Express your answer in terms of and . ANSWER: = Part C Find the net work done on the particle by the external forces during the particle's motion. Express your answer in terms of and . ANSWER: = Part D Substitute for from Part B in the expression for work from Part C. Then substitute for from the relation in Part A. This will yield an expression for the net work done on the particle by the external forces during the particle's motion in terms of mass and the initial and final velocities. Give an expression for the work in terms of those quantities. [ Print ]
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10/13/08 12:30 AM MasteringPhysics Page 2 of 11 http://session.masteringphysics.com/myct Express your answer in terms of , , and . ANSWER: = The expression that you obtained can be rearranged as The quantity has the same units as work. It is called the kinetic energy of the moving particle and is denoted by . Therefore, we can write and . Note that like momentum, kinetic energy depends on both the mass and the velocity of the moving object. However, the mathematical expressions for momentum and kinetic energy are different. Also, unlike momentum, kinetic energy is a scalar. That is, it does not depend on the sign (therefore direction) of the velocities. Part E Find the net work done on the particle by the external forces during the motion of the particle in terms of the initial and final kinetic energies. Express your answer in terms of and . ANSWER: = This result is called the work-energy theorem. It states that the net work done on a particle equals the change in kinetic energy of that particle. Also notice that if is zero, then the work-energy theorem reduces to . In other words, kinetic energy can be understood as the amount of work that is done to accelerate the particle from rest to its final velocity.
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