Chapter 9, Problem 7A

(a)

To determine

The gravitational potential energy relative to its starting position.

Answer to Problem 7A

The gravitational potential energy relative to its starting position is $100\text{ J}$ .

Explanation of Solution

Given info:

The work to elevate the bucket of water is $W=100\text{ J}$ .

Formula used:

The expression for potential energy as follows:

  $PE=mg\Delta h=W$

Here, $m$ is the mass, $g$ is the acceleration due to gravity, $\Delta h$ is the change in position, and $W$ is the work.

Calculation:

Consider the required energy to raise the bucket would be transferred into potential energy.

Find the gravitational potential energy as follows:

  $\begin{array}{l}PE=mg\Delta h\\ PE=W\\ PE=100\text{ J}\end{array}$

Hence, the gravitational potential energy relative to its starting position is $100\text{ J}$ .

Conclusion:

Thus, the gravitational potential energy relative to its starting position is $100\text{ J}$ .

(b)

To determine

The gravitational potential energy if the bucket were raised twice as high.

Answer to Problem 7A

The gravitational potential energy if the bucket were raised twice as high is $200\text{ J}$ .

Explanation of Solution

Given info:

The work to elevate the bucket of water is $W=100\text{ J}$ .

Formula used:

The expression for potential energy as follows:

  $PE=mg\Delta h$

Here, $m$ is the mass, $g$ is the acceleration due to gravity, and $\Delta h$ is the change in position.

Refer part (a).

The gravitational potential energy relative to its starting position is $100\text{ J}$ .

Find the gravitational potential energy if the bucket were raised twice as high as follows:

  $\begin{array}{l}P{E}^{\prime }=mg\Delta h\\ P{E}^{\prime }=mg\left(2\Delta h\right)\\ P{E}^{\prime }=2PE\\ P{E}^{\prime }=2\times 100\text{ J}\\ P{E}^{\prime }=200\text{ J}\end{array}$

Conclusion:

Thus, the gravitational potential energy if the bucket were raised twice as high is $200\text{ J}$ .