A child pulls a sled across level snow using a rope that makes an angle of above the…

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

Problem

A child pulls a

30\,\text{kg}

sled across level snow using a rope that makes an angle of

30^{\circ}

above the horizontal. The coefficient of kinetic friction between the sled and the snow is

\mu_k=0.10

. The child can sustain a constant power output of

120\,\text{W}

. (a) Derive an expression for the maximum constant speed the sled can achieve in terms of the given quantities

m

g

\mu_k

P

, and the rope angle. (b) Using

m=30\,\text{kg}

g=9.8\,\text{m}\,\text{s}^{-2}

\mu_k=0.10

P=120\,\text{W}

, and a rope angle of

30^{\circ}

, calculate the numerical value of this maximum speed.