Chapter 11, Problem 55A

a.

To determine

Final kinetic energy of P.

Answer to Problem 55A

86490 J

Explanation of Solution

Given:

Mass of P, $m=45\text{ kg}$

Initial velocity of P, $u=0\text{ m/s}$

Final velocity of P, $v=62\text{ m/s}$

Formula Used:

Kinetic energy is given by;

  $KE=\frac{1}{2}m{v}^2$

Here, m is mass and v is velocity.

Calculations:

Therefore, final kinetic energy of P is:

  $\begin{array}{l}K{E}_f=\frac{1}{2}m{v}^2\\ =\frac{1}{2}\times 45\times {62}^2\\ =86490\text{ J}\end{array}$

b.

To determine

Magnitude of force.

Answer to Problem 55A

3931.36 N

Explanation of Solution

Given:

Mass of P $m=45\text{ kg}$

Initial velocity of P, $u=0$

Final velocity of P, $v=62\text{ m/s}$

Distance traveled by applied force, $s=22\text{ m}$

Formula Used:

Kinetic energy is given by:

  $KE=\frac{1}{2}m{v}^2$

Here, m is mass and vis velocity.

Calculations:

Initial kinetic energy of P is:

  $\begin{array}{l}K{E}_i=\frac{1}{2}m{v}^2\\ =\frac{1}{2}\times 45\times 0^2\\ =0\text{ J}\end{array}$

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

Therefore,

  $\begin{array}{l}F\cdot s=K{E}_f-K{E}_i\\ F\times 22=86490-0\\ F=\frac{86490}{22}\\ =3931.36\text{ N}\end{array}$

Conclusion:

So, the magnitude of force is $3931.36\text{ N}$ .