Chapter 11, Problem 84A

To determine

For how much distance cart will roll.

Answer to Problem 84A

1.25 m.

Explanation of Solution

Given:

Mass of the cart, $m=0.80\text{ kg}$

Height of hill is $h=0.32\text{ m}$ .

Frictional force, $F=2\text{ N}$

Formula Used:

Potential energy of cart is given by,

  $U=mgh$

Here, m is mass, g is acceleration due to gravity and h is height.

Acceleration due to gravity on earth is $g=9.8{\text{ m/s}}^2$ .

Calculations:

Now, putting the value of m, g and h.

  $\begin{array}{l}U=0.80\times 9.8\times 0.32\\ =2.51\text{ J}\end{array}$

According to work energy theorem potential energy will be equal to work done by frictional force.

  $\begin{array}{l}F\times d=2.51\\ 2\times d=2.51\\ d=1.25\text{ m}\end{array}$

Conclusion:

Therefore, cart will roll by a distance of 1.25 m