Chapter 11.1, Problem 12SSC

a.

To determine

The gravitational potential energy of the shell-Earth system when the shell’s height is $425\text{m}$ .

Answer to Problem 12SSC

  $1.04\times {10}^5\text{J}$

Explanation of Solution

Given:

The mass of the shell is, $m=25\text{kg}$

Height of the shell, $h=425\text{}\text{m}$

Formula used:

The gravitational potential energy of an object which is at a height $h$ from the surface is given by,

  $PE=mgh$

Calculation:

Using the given values in above, the gravitational potential energy of shell-Earth’s system is,

  $\begin{array}{c}PE=mgh\\ =\left(25\right)\left(9.8\right)\left(425\right)\\ =1.04\times {10}^5\text{J}\end{array}$

Conclusion:

Thus, the gravitational potential energy of the given shell-Earth’s system is $1.04\times {10}^5\text{J}$ .

b.

To determine

The change in the system’s potential energy of if the shell falls to a height of $225\text{m}$ from a height of $425\text{m}$ .

Answer to Problem 12SSC

  $4.9\times {10}^4\text{J}$

Explanation of Solution

Given:

The mass of the shell is, $m=25\text{kg}$

Initial height of the shell, $h=425\text{}\text{m}$

Initial height of the shell, $h=225\text{}\text{m}$

Formula used:

The gravitational potential energy of an object which is at a height $h$ from the surface is given by,

  $PE=mgh$

Calculation:

Using the given values in above, the change in the potential energy of shell-Earth’s system is,

  $\begin{array}{c}PE=mg{h}_f-mg{h}_i\\ =\left(25\right)\left(9.8\right)\left(425-225\right)\\ =4.9\times {10}^4\text{J}\end{array}$

Conclusion:

Thus, the change in the system’s potential energy of if the shell falls to a height of $225\text{m}$ is $4.9\times {10}^4\text{J}$ .