A small plastic block of mass is dragged across level ice by a horizontal force of…

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

Problem

A small plastic block of mass

2.5\,\text{kg}

is dragged across level ice by a horizontal force of constant magnitude

50\,\text{N}

. In addition to kinetic friction, the block experiences an air-drag force whose magnitude is given by

F_{\text{drag}} = c v^{2}

, where

v

is the block’s speed and

c = 0.30\,\text{N\,s}^{2}\!\big/\!\text{m}^{2}

. The coefficient of kinetic friction between the block and the ice is

\mu_{k}=0.10

. (a) Derive an expression for the block’s speed

v_{c}

when it moves at constant velocity on the ice in terms of the given parameters

F_{p}

\mu_{k}

m

g

, and

c

. (b) Using the numerical values provided, calculate

v_{c}

for the block on Earth where

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

. (c) The same experiment is repeated on the Moon, where

g = 1.6\,\text{m/s}^{2}

, using the same pulling force

50\,\text{N}

. Determine the new constant speed and explain briefly why it differs from the value on Earth.