To determine the loss in potential energy of a body falling from a height of 10 meters to a height of 6 meters, we can follow these steps:
1. Calculate the initial potential energy (PE_initial) when the body is at the initial height of 10 meters.
2. Calculate the final potential energy (PE_final) when the body is at the final height of 6 meters.
3. Determine the loss in potential energy by finding the difference between the initial and final potential energies.
Given:
- Mass of the body, [tex]\( m = 0.2 \)[/tex] kg
- Acceleration due to gravity, [tex]\( g = 10 \, \text{m/s}^2 \)[/tex]
- Initial height, [tex]\( h_{\text{initial}} = 10 \)[/tex] meters
- Final height, [tex]\( h_{\text{final}} = 6 \)[/tex] meters
### Step-by-Step Solution:
1. Calculate the initial potential energy (PE_initial):
Potential energy is given by the formula:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
For the initial height:
[tex]\[
PE_{\text{initial}} = m \cdot g \cdot h_{\text{initial}}
\][/tex]
Substituting the given values:
[tex]\[
PE_{\text{initial}} = 0.2 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 10 \, \text{m} = 20.0 \, \text{J}
\][/tex]
2. Calculate the final potential energy (PE_final):
For the final height:
[tex]\[
PE_{\text{final}} = m \cdot g \cdot h_{\text{final}}
\][/tex]
Substituting the given values:
[tex]\[
PE_{\text{final}} = 0.2 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 6 \, \text{m} = 12.0 \, \text{J}
\][/tex]
3. Determine the loss in potential energy (loss_PE):
The loss in potential energy is the difference between the initial and final potential energies:
[tex]\[
\text{loss\_PE} = PE_{\text{initial}} - PE_{\text{final}}
\][/tex]
Substituting the calculated values:
[tex]\[
\text{loss\_PE} = 20.0 \, \text{J} - 12.0 \, \text{J} = 8.0 \, \text{J}
\][/tex]
Therefore, the loss in potential energy taking place in the body as it falls from a height of 10 meters to a height of 6 meters is [tex]\( 8.0 \, \text{J} \)[/tex].
