Math  /  Algebra

QuestionNote: Figure not drawn to scale.\text{Note: Figure not drawn to scale.}
A fan is attached to the top of a block, as shown. The block is released from rest at the top of a ramp and the fan exerts a constant force on the block opposite the block's direction of motion. The block slides a distance D1D_{1} along the ramp and then transitions to a horizontal surface, eventually coming to rest momentarily after traveling a distance D2D_{2}. Frictional forces are negligible. Which of the following correctly describes the relationship between D2D_{2} and D1D_{1}?
(A) D2D_{2} must be less than D1D_{1}.

Studdy Solution
The work done by the fan on the ramp and on the horizontal surface is equal to the kinetic energy the block had at the bottom of the ramp.
Since the fan exerts a constant force, the distance D2D_2 on the horizontal surface, where the block comes to rest, must be less than D1D_1, because the block starts with less kinetic energy on the horizontal surface than it had at the bottom of the ramp.
The correct relationship is:
(A) D2D_{2} must be less than D1D_{1}.

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