Chapter 15, Problem 96A

(a)

To determine

To calculate:The energy absorbed by the cushion if the person weighs $\text{480 N}$ .

Answer to Problem 96A

The energy absorbed by the cushion is $\text{10}\text{.560 kJ}$ .

Explanation of Solution

Given:

Height of the building = $\text{22 m}$

Acceleration = $3.0{\text{ m/s}}^2$

Weight of the body = $\text{480 N}$

Formula used:

Potential energy $U$ of a body is given by the formula

  $U=mgh$

Where, $m$ is the mass of the body, $g$ is the acceleration due to gravity and $h$ is the height of the body from the ground.

Calculation:

As per problem,

Weight of the body ( $mg$ ) = $\text{480 N}$

Height of the building ( $h$ ) = $\text{22 m}$

The energy absorbed by the cushion is the mechanical energy of the stunt person, which is equal to her potential energy (at height kinetic energy is zero)

Calculate her potential energy using the formula

  $U=mgh$

Substitute $mg=\text{480 N}$ and $h=\text{22 m}$

  $\begin{array}{l}U=(480\text{ N)(22 m)}\\ U=10560\text{ J =10}\text{.560 kJ}\end{array}$

Conclusion:

The energy absorbed by the cushion is $\text{10}\text{.560 kJ}$ .

(b)

To determine

To calculate:The force exerted by the pillow on the stunt person.

Answer to Problem 96A

The force exerted by the pillow on the stunt person is $146.7\text{ N}$ .

Explanation of Solution

Given:

Acceleration ( $a$ ) = $3.0{\text{ m/s}}^2$

Weight of the body ( $mg$ ) = $\text{480 N}$

Formula used:

Force on a body is given by

  $F=ma$

Where $m$ is the mass of the body and $a$ is the acceleration of the body.

Calculation:

As per Newton’s third law of motion,

The force exerted by the pillow on the stunt person is equal to the force exerted by her on the pillow.

So, force exerted by the pillow

  $F=ma$

Using weight $mg=\text{480 N}$ calculate $m$ taking $g=9.8{\text{ m/s}}^2$

  $\begin{array}{l}m=\frac{mg}{g}=\frac{480\text{ N}}{9.8{\text{ m/s}}^2}\\ m=48.9\text{ kg}\end{array}$

Use the above calculated value of mass and $a=3.0{\text{ m/s}}^2$ to calculate force

  $\begin{array}{l}F=(48.9\text{ kg})(3.0{\text{ m/s}}^2)\\ F=146.7\text{ N}\end{array}$

Conclusion:

The force exerted by the pillow on the stunt person is $146.7\text{ N}$ .