Chapter 11, Problem 89A

To determine

To find: Whether the cart will reach to the bottom of the hill or not.

Answer to Problem 89A

Cart will not reach to bottom of hill.

Explanation of Solution

Given:

The given figure is shown below.

  

Mass of cart,

Inclination of hill, $m=0.8\text{kg}$

Vertical height, $h=0.5\text{m}$

Friction force, $F=5\text{N}$

Length of inclination, $d=1\text{m}$

Formula Used:

Potential energy of cart is,

  $E=mgh$ …. (1)

Here, $m$ is mass of cart, $g$ is acceleration due to gravity and $h$ is vertical height.

Work done by friction is,

  $W=Fd$ …. (2)

  $F$ is friction force and $d$ is length of track.

Calculation:

From (1)

On putting the value

  $\begin{array}{l}E=0.8\times 9.8\times 0.5\\ =3.92\text{J}\end{array}$

And from (2) on putting the values

  $\begin{array}{l}W=5\times 1\\ =5\text{J}\end{array}$

As work done by friction is greater than potential energy of cart.So, cart will not reach to bottom of hill.

Conclusion:

Therefore, the cart will not reach to the bottom of hill.