A) For that interval, determine the sign of the work done on the person by: the

Question

A) For that interval, determine the sign of the work done on the person by:

the earth

the trampoline

Explain your reasoning.

B) Is the magnitude of the work done on the person by the trampoline greater than, less than, or equal to the magnitude of the work done on the person by the earth? Explain.

C) For each of the following systems, state wether each of the quantities below is positive, negative, or zero for the interval in question. In each case, briefly explain.

System A (consisting of the person and the trampoline, but not the earth)

1) Change in potential energy

2) Change in total energy of system A

System B (consisting of the person, the trampoline, and the earth)

3) Change in potential energy

4) Change in total energy of system B

Explanation / Answer

a) work done by the gravitational field (earth) displacement and force both in the same direction - downwards so , positive work work done by force due to trampoline displacement (down) and force (up) in opposite direction so, negative work b) for the given time interval, the final kinetic energy is 0 so by work energy theorem initial KE + work done by gravity = -1 * work done by trampoline as net work done = work by gravity + work by trampoline = KEfinal - KEinitial so if the initial KE is greater than 0, magnitude of work done by trampoline is greater than work done by gravity above analysis was for system consisting of person only now for system consisting of both person and trampoline for the given time interval 1) by work energy theorem as above work done by gravity + initial KE = potential energy stored in trampoline= -1 * work done by trampoline so change in PE = positive 2) from the above eqn change in total energy = Energy final - Energy initial = PE of trampoline - KE initial of person = work done by gravity so positive now for (earth + trampoline + person) system work done by external forces is zero so energy is conserved energy initial = energy final KE man + PE (of earth-person system) = PE of trampoline so change in potential energy of system = KE man initial = positive change in total energy = 0 NOTE gravitational energy is always for earth - body system. talking about potential energy of a body doesn't make sense so we didn't include gravitational potential energy in the first case

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