Chapter 11, Problem 47A

a.

To determine

Change in cart’s kinetic energy.

Answer to Problem 47A

345.07 J

Explanation of Solution

Given:

Mass of kart, $m=15\text{ kg}$

Initial velocity of cart, $u=7.50\text{ m/s}$

Final velocity of cart, $v=3.20\text{ m/s}$

Formula used:

  $KE=\frac{1}{2}m{v}^2$

Here, m is mass and vis velocity.

Calculation:

Change in kinetic energy is:

  $\begin{array}{c}\Delta KE=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2\\ =\frac{1}{2}m\left({3.2}^2-{7.5}^2\right)\\ =\frac{1}{2}\times 15\times \left({3.2}^2-{7.5}^2\right)\\ =\frac{1}{2}\times 15\times -46.01\\ =-345.07\text{ J}\end{array}$

Conclusion:

Therefore, change in kinetic energy of cart is -345.07 J.

b.

To determine

Work done on the cart

Answer to Problem 47A

-345.07 J

Explanation of Solution

Given:

Mass of kart, $m=15\text{ kg}$

Initial velocity of cart, $u=7.50\text{ m/s}$

Final velocity of cart, $v=3.20\text{ m/s}$

Formula used:

Kinetic energy is given by,

  $KE=\frac{1}{2}m{v}^2$

Here, m is mass and vis velocity.

Work done is given by;

  $W=F\cdot s$

According to work energy theorem,

  $W=\Delta KE$

Calculation:

According to work energy theorem work done is equal to change in kinetic energy.

Change in kinetic energy is:

  $\begin{array}{c}\Delta KE=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2\\ =\frac{1}{2}m\left({3.2}^2-{7.5}^2\right)\\ =\frac{1}{2}\times 15\times \left({3.2}^2-{7.5}^2\right)\\ =\frac{1}{2}\times 15\times -46.01\\ =-345.07\text{ J}\end{array}$

Conclusion:

Therefore, work done $W=-345.07\text{ J}$

c.

To determine

Distance covered by cart.

Answer to Problem 47A

34.51 m

Explanation of Solution

Given:

Mass of kart, $m=15\text{ kg}$

Initial velocity of cart, $u=7.50\text{ m/s}$

Final velocity of cart, $v=3.20\text{ m/s}$

Magnitude of force, $F=10\text{ N}$

Formula used:

Work done can be obtained by:

  $W=F\cdot s$

Calculation:

From previous part, work done $W=345.07\text{ J}$

Therefore,

  $\begin{array}{c}345.07=10\times s\\ s=\frac{345.07}{10}\\ =34.51\text{ m}\end{array}$

Conclusion:

So, distance moved by cart is 34.51 m.