Chapter 4, Problem 49P

To determine

The average retarding force on the sled which reaches the bottom of a hill and travels a horizontal straightaway to a stop.

Answer to Problem 49P

Solution:

The average retarding force on the sled was found to be 1.20 × 10²N and it acts opposite to the direction of the velocity of the sled.

Explanation of Solution

The sled reaches the bottom of the hill with a velocity $v_0$ and travels a distance s horizontally, and comes to rest. The force of friction acting between the sled and the surface on which it skids exerts a retarding force on the sled, which brings it to rest.

Given:

The initial velocity of the sled $v_0=10.0\text{ m/s}$

The final velocity of the sled $v=0\text{ m/s}$

The distance traveled by the sled before coming to rest $s=25.0\text{ m}$

Mass of the child and the sled $m=60.0\text{ kg}$.

Formula used:

      $v^2=v_0^2+2as$

      $F_{\text{avg}}=ma$

Here, the acceleration of the sled is a and the average force is $F_{\text{avg}}$.

Calculation:

Calculate the average acceleration of the sled as it comes to rest.

Substitute the given values in the equation of motion,

$\begin{array}{c}{v}^2=v_0^2+2as\\ {\left(0\text{ m/s}\right)}^2=\left(10.0\text{ m/s}\right)+2a\left(25.0\text{ m}\right)\\ a=-2.00{\text{ m/s}}^2\end{array}$

Calculate the value of the average retarding force acting on the sled using Newton’s second law.

$\begin{array}{l}{F}_{\text{avg}}=ma\\ =\left(60.0\text{ kg}\right)\left(-2.00{\text{ m/s}}^2\right)\\ =-1.20\times {10}^2\text{N}\end{array}$

The negative sign shows that the force acts opposite to the direction of motion of the sled.