To determine how much gravitational potential energy is added to the picture frame when it is lifted to a higher shelf, follow these steps:
1. Understand the problem:
- Mass of the picture frame ([tex]\(m\)[/tex]) = 2 kg
- Initial height ([tex]\(h_i\)[/tex]) = 0.5 meters
- Final height ([tex]\(h_f\)[/tex]) = 1.3 meters
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s[tex]\(^2\)[/tex]
- We need to find the change in gravitational potential energy.
2. Calculate the change in height ([tex]\(\Delta h\)[/tex]):
[tex]\[
\Delta h = h_f - h_i = 1.3 \, \text{m} - 0.5 \, \text{m} = 0.8 \, \text{m}
\][/tex]
3. Determine the change in gravitational potential energy ([tex]\(\Delta U\)[/tex]) using the formula:
[tex]\[
\Delta U = m \cdot g \cdot \Delta h
\][/tex]
Plug in the known values:
[tex]\[
\Delta U = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 0.8 \, \text{m}
\][/tex]
4. Multiply to find the change in potential energy:
[tex]\[
\Delta U = 2 \cdot 9.8 \cdot 0.8 = 15.68 \, \text{J}
\][/tex]
So, the change in gravitational potential energy when the picture frame is lifted to a height of 1.3 meters is [tex]\(15.68\)[/tex] Joules.
Therefore, the correct answer is:
C. [tex]\(15.68 \, \text{J}\)[/tex]
