A sled on a friction-free frozen lake is to receive of useful mechanical energy from…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A sled on a friction-free frozen lake is to receive

500\,\text{J}

of useful mechanical energy from a student who pulls it with a constant force

F

making an angle

\theta

above the horizontal. (a) Starting from the definition of work for a constant force, derive an expression for the horizontal displacement

s

required to deliver a specified amount of work

W

in terms of

F

and

\theta

. (b) Using your expression, calculate the displacement needed when

F = 40\,\text{N}

W = 500\,\text{J}

and

\theta = 60^{\circ}

. (c) If the angle is increased to

75^{\circ}

while the magnitude of the force remains

40\,\text{N}

, determine the percentage increase in displacement required to supply the same

500\,\text{J}

of work.