Question

1. a 2-kg book is moved from a shelf that is 2 m off the ground to a shelf that is 1.5 m off the ground. what is the change in gpe?
2. what is the gravitational potential energy of a diver with a mass of 60 kg who is 10 m above the water?

Explanation:

Problem 4:

Step1: Recall GPE change formula

$\Delta GPE = mg\Delta h$ where $g=9.8\ \text{m/s}^2$

Step2: Calculate height change

$\Delta h = 1.5\ \text{m} - 2\ \text{m} = -0.5\ \text{m}$

Step3: Substitute values into formula

$\Delta GPE = 2\ \text{kg} \times 9.8\ \text{m/s}^2 \times (-0.5\ \text{m})$

Step4: Compute the result

$\Delta GPE = -9.8\ \text{J}$

Problem 5:

Step1: Recall GPE formula

$GPE = mgh$ where $g=9.8\ \text{m/s}^2$

Step2: Substitute values into formula

$GPE = 60\ \text{kg} \times 9.8\ \text{m/s}^2 \times 10\ \text{m}$

Step3: Compute the result

$GPE = 5880\ \text{J}$

Answer:

1. The change in gravitational potential energy is $\boldsymbol{-9.8\ \text{J}}$
2. The gravitational potential energy of the diver is $\boldsymbol{5880\ \text{J}}$