Question

read each scenario and then answer the question.
scenario a: a 6-kg bucket is raised a distance of 6 m.
scenario b: a 9-kg bucket is raised a distance of 5 m.
scenario c: a 12-kg bucket is raised a distance of 4 m.
scenario d: a 15-kg bucket is raised a distance of 3 m.
which scenario generates the most gravitational potential energy?
a
b
c
d

Explanation:

Step1: Recall GPE formula

Gravitational Potential Energy (GPE) is calculated using the formula \( GPE = mgh \), where \( m \) is mass (kg), \( g \) is acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \), constant for all scenarios), and \( h \) is height (m). Since \( g \) is constant, we can compare \( m \times h \) for each scenario.

Step2: Calculate \( m \times h \) for Scenario A

For Scenario A: \( m = 6 \, \text{kg} \), \( h = 6 \, \text{m} \).
\( m \times h = 6 \times 6 = 36 \, \text{kg·m} \).

Step3: Calculate \( m \times h \) for Scenario B

For Scenario B: \( m = 9 \, \text{kg} \), \( h = 5 \, \text{m} \).
\( m \times h = 9 \times 5 = 45 \, \text{kg·m} \).

Step4: Calculate \( m \times h \) for Scenario C

For Scenario C: \( m = 12 \, \text{kg} \), \( h = 4 \, \text{m} \).
\( m \times h = 12 \times 4 = 48 \, \text{kg·m} \).

Step5: Calculate \( m \times h \) for Scenario D

For Scenario D: \( m = 15 \, \text{kg} \), \( h = 3 \, \text{m} \).
\( m \times h = 15 \times 3 = 45 \, \text{kg·m} \).

Step6: Compare the values

Compare \( 36 \), \( 45 \), \( 48 \), and \( 45 \). The largest value is \( 48 \), which corresponds to Scenario C.

Answer:

C. Scenario C: A 12-kg bucket is raised a distance of 4 m.