To determine how much gravitational potential energy is added to the picture frame when it is lifted from a height of [tex]$0.5 \text{ meters}$[/tex] to a height of [tex]$1.3 \text{ meters}$[/tex], we need to follow these steps:
1. Calculate the initial gravitational potential energy:
The formula for gravitational potential energy (GPE) is:
[tex]\[
GPE = m \cdot g \cdot h
\][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms)
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared)
- [tex]\( h \)[/tex] is the height above the reference point (in meters)
For the initial height ([tex]\( h = 0.5 \text{ meters} \)[/tex]):
[tex]\[
GPE_{\text{initial}} = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 0.5 \, \text{m} = 9.8 \, \text{J}
\][/tex]
2. Calculate the final gravitational potential energy:
For the final height ([tex]\( h = 1.3 \text{ meters} \)[/tex]):
[tex]\[
GPE_{\text{final}} = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 1.3 \, \text{m} = 25.48 \, \text{J}
\][/tex]
3. Determine the change in gravitational potential energy:
The change in gravitational potential energy ([tex]\( \Delta GPE \)[/tex]) is the difference between the final and initial GPE:
[tex]\[
\Delta GPE = GPE_{\text{final}} - GPE_{\text{initial}} = 25.48 \, \text{J} - 9.8 \, \text{J} = 15.68 \, \text{J}
\][/tex]
Therefore, the amount of gravitational potential energy added to the picture frame when it is lifted to a shelf of height 1.3 meters is:
A. [tex]\( 15.68 \, \text{J} \)[/tex]
