A sled of mass is pulled across a level

PHYSICS · Multi-part · AP · Physics C: Mechanics · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A sled of mass

4.0\,\text{kg}

is pulled across a level, snow-covered field by a rope that exerts a constant horizontal force of

18\,\text N

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

\mu_k=0.050

. In addition, a wind blowing opposite to the motion exerts a speed-dependent drag force of magnitude

F_d = kv

, where

k = 1.2\,\text{N}\,\text{s}\,\text{m}^{-1}

and

v

is the sled’s instantaneous speed. Neglect any other forces. Answer the following questions. Use

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

. (a) Write an expression for the net horizontal force on the sled as a function of its speed

v

. (b) Determine the sled’s acceleration at the instant its speed is

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

. (c) Calculate the terminal speed (if any) that the sled can approach under the given conditions and justify your calculation. (d) Explain, using the expression from part (a), whether the sled will ever accelerate in the direction opposite to the applied pulling force.

Related theory

Browse the problem library