Question

fill in the blank 1 point a box is placed on a shelf at a height h above the ground. a second box with three times the mass of the first box is placed on the same shelf. the gravitational potential energy of the second box is answer as much as the first box. a rock is on a ledge at a height h. another rock with ten times the mass is on a ledge at the same height. the gravitational potential energy of the second rock is answer as much as the first rock. a book is on a shelf at a height h. another book with four times the mass is placed on a shelf at three times the height. the gravitational potential energy of the second book is answer as much as the first book. a ball is held at a height h. a second ball with the same mass is held at four times the height. the gravitational potential energy of the second ball is answer as much as the first ball.

Explanation:

Step1: Recall gravitational potential energy formula

Gravitational potential energy is given by $PE = mgh$, where $m$ = mass, $g$ = gravitational acceleration, $h$ = height.

Step2: Solve for the box comparison

Let first box: $m_1=m$, $h_1=h$. Second box: $m_2=3m$, $h_2=h$.
$\frac{PE_2}{PE_1}=\frac{3m \times g \times h}{m \times g \times h}=3$

Step3: Solve for the rock comparison

Let first rock: $m_1=m$, $h_1=h$. Second rock: $m_2=10m$, $h_2=h$.
$\frac{PE_2}{PE_1}=\frac{10m \times g \times h}{m \times g \times h}=10$

Step4: Solve for the book comparison

Let first book: $m_1=m$, $h_1=h$. Second book: $m_2=4m$, $h_2=3h$.
$\frac{PE_2}{PE_1}=\frac{4m \times g \times 3h}{m \times g \times h}=12$

Step5: Solve for the ball comparison

Let first ball: $m_1=m$, $h_1=h$. Second ball: $m_2=m$, $h_2=4h$.
$\frac{PE_2}{PE_1}=\frac{m \times g \times 4h}{m \times g \times h}=4$

Answer:

1. three times
2. ten times
3. twelve times
4. four times