Question

A 3.4 kg object is lifted from the floor and placed on a shelf that is 2.3 m above the floor. What is the gravitational potential energy of the object sitting on the shelf?

Group of answer choices

7.9 J

0.2 J

14.5 J

76.6 J

Answer 1

The gravitational potential energy (GPE) of an object can be calculated using the formula:

\[
\text{GPE} = m \cdot g \cdot h
\]

Where:
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height above the reference point (in meters).

For the given object:
- Mass \( m = 3.4 \, \text{kg} \)
- Height \( h = 2.3 \, \text{m} \)
- Acceleration due to gravity \( g \approx 9.81 \, \text{m/s}^2 \)

Now, substituting the values into the formula:

\[
\text{GPE} = 3.4 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 2.3 \, \text{m}
\]

Calculating this step-by-step:

1. Calculate \( 3.4 \times 9.81 \):

\[
3.4 \times 9.81 \approx 33.434
\]

2. Now multiply by the height \( 2.3 \):

\[
33.434 \times 2.3 \approx 76.9 \, \text{J}
\]

Therefore, the gravitational potential energy of the object sitting on the shelf is approximately \( 76.9 \, \text{J} \).

Among the options given, the closest value is:

**76.6 J**