ism_chapter_06

# ism_chapter_06 - Chapter 6 Work and Energy Conceptual...

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371 Chapter 6 Work and Energy Conceptual Problems *1 Determine the Concept A force does work on an object when its point of application moves through some distance and there is a component of the force along the line of motion. ( a ) False. The net force acting on an object is the vector sum of all the forces acting on the object and is responsible for displacing the object. Any or all of the forces contributing to the net force may do work. ( b ) True. The object could be at rest in one reference frame and moving in another. If we consider only the frame in which the object is at rest, then, because it must undergo a displacement in order for work to be done on it, we would conclude that the statement is true. ( c ) True. A force that is always perpendicular to the velocity of a particle changes neither it’s kinetic nor potential energy and, hence, does no work on the particle. 2 Determine the Concept If we ignore the work that you do in initiating the horizontal motion of the box and the work that you do in bringing it to rest when you reach the second table, then neither the kinetic nor the potential energy of the system changed as you moved the box across the room. Neither did any forces acting on the box produce displacements. Hence, we must conclude that the minimum work you did on the box is zero. 3 False. While it is true that the person’s kinetic energy is not changing due to the fact that she is moving at a constant speed, her gravitational potential energy is continuously changing and so we must conclude that the force exerted by the seat on which she is sitting is doing work on her. *4 Determine the Concept The kinetic energy of any object is proportional to the square of its speed. Because , 2 2 1 mv K = replacing v by 2 v yields () . 4 4 2 2 2 1 2 2 1 K mv v m K' = = = Thus doubling the speed of a car quadruples its kinetic energy.

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Chapter 6 372 5 Determine the Concept No. The work done on any object by any force F r is defined as r F r r d dW = . The direction of net F r is toward the center of the circle in which the object is traveling and r r d is tangent to the circle. No work is done by the net force because net F r and r r d are perpendicular so the dot product is zero. 6 Determine the Concept The kinetic energy of any object is proportional to the square of its speed and is always positive. Because , 2 2 1 mv K = replacing v by 3 v yields () . 9 9 3 2 2 1 2 2 1 K mv v m K' = = = Hence tripling the speed of an object increases its kinetic energy by a factor of 9 and correct. is ) ( d *7 Determine the Concept The work required to stretch or compress a spring a distance x is given by 2 2 1 kx W = where k is the spring’s stiffness constant. Because W x 2 , doubling the distance the spring is stretched will require four times as much work.
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## This note was uploaded on 08/18/2010 for the course IMT 12253 taught by Professor Mikael during the Spring '10 term at École Normale Supérieure.

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ism_chapter_06 - Chapter 6 Work and Energy Conceptual...

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