A crate is pulled up a straight ramp that is inclined at above the horizontal

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

160\,\text{kg}

crate is pulled up a straight ramp that is inclined at

15^{\circ}

above the horizontal. The coefficient of kinetic friction between the crate and the ramp surface is

\mu_k=0.25

. The crate is to be moved up the ramp at a constant speed of

0.60\,\text{m}\,\text{s}^{-1}

. A worker uses a rope to pull the crate at an angle

\phi

above the surface of the ramp. The worker’s maximum sustainable power output is

450\,\text{W}

. (a) If the worker pulls parallel to the ramp surface (

\phi=0^{\circ}

), calculate the power required to move the crate at the stated speed. State whether this power is within the worker’s limit. (b) The worker instead pulls at an angle

\phi

above the ramp surface so that the vertical component of the rope’s tension reduces the normal force on the crate. Derive an equation that can be solved for

\phi

when the power required equals the worker’s

450\,\text{W}

limit, and determine the value of

\phi

that satisfies this condition.

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