# A father pulls his daughter on a sled

#### 2 mechanics problems

A father pulls his young daughter on a sled with a constant velocity on a level surface a distance of 10 M, as illustrated in the figure . If the total mass of the sled and the girl is 33 KG and the coefficient of kinetic friction between the sled runners and the snow is 0.21, how much work does the father do?

A crate is dragged 4.0 m along a rough floor with a constant velocity by a worker applying a force of 450 N to a rope at an angle of 30 degrees to the horizontal. A) How much work does each of these forces do?B)What is the total work done on the crate?

The work done when the father pulls his daughter is simply the dot product between the force applied and the distance traveled (d) (BY DEFINITION OF THE WORK). Therefore

$W = F*d*cos(\alpha) = F_f*d$ where $F_f$ is the friction force

Hence if $\mu$ is the coefficient of the friction we write

$W = m*g*\mu *d =33*9.81*0.21 *10 =679.833 J$

The work is again by DEFINITION the dot product between the force applied and the distance traveled

$W =F*d*cos(\alpha) =450*4*cos(30) =1558.85 J$

The problem can be regarded as the work done by the horizontal component of the force which is

$W= 1558.85 J$ and the work done by the normal component of the force which is null (0).

The total work is again $W =1558.85 J$