You are pulling with a constant force F on a stringg that is attached to a box o

Question

You are pulling with a constant force F on a stringg that is attached to a box over a massless frictionless pulley. The box has a mass m, and slides with a constant speed up along a constant frictionless incline that makes an angle theta from horizontal. In time t, the box slides a distance of d along the incline from point A to point B. You can consider the box as a point particle.

Which of the following can be the gravitational potential energy of the box-earth system when the box is at point B. (Point B is at the top of the incline).

A) mgdcos(theta)

B) mgdsin(theta)

C) 0

D) -mgd

E) All of the above can be.

Please show how you arrived at your answer.

Explanation / Answer

considering point A as the zero potential energy referrence,

height of point B as compared to point A=d*sin(theta)

so potential energy at point B with the assumption that potential energy at point A is zero =m*g*height from A to B

=m*g*d*sin(theta)

but as we are free to chose any point as out zero potential energy, choosing suitable referrence for zero potential energy, we can

obtain potential energy at B as any of the values given in the option.

so the correct answer will be option E.

hence always remember:

1. potential energy of a system does not have a meaning until some zero reference point is specified.

2. in energy calculations, we are more interested in change in potential energy because change in potential energy gets transferred to some other form of energy (thermal, kinetic etc) from which we can derive the other aspects of the system (temperature, speed etc.)

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