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Answer :
The increase in gravitational potential energy of the man-earth system is: [tex]\[ {1.118 \text{ kJ}} \][/tex].
The increase in gravitational potential energy (PE) of the man-earth system when the man climbs up a flight of stairs is given by the formula:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Given:
[tex]- \( m = 114 \) kg, - \( g = 9.81 \) m/s\( ^2 \), - \( h = 1 \) m.[/tex]
Plugging in the values, we get:
[tex]\[ PE = 114 \text{ kg} \cdot 9.81 \text{ m/s}^2 \cdot 1 \text{ m} \] \[ PE = 114 \cdot 9.81 \text{ kg} \cdot \text{m/s}^2 \cdot \text{m} \] \[ PE = 1117.74 \text{ kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
Since [tex]1 kg\( \cdot \)m\( ^2 \)/s\( ^2 \)[/tex] is equivalent to 1 joule (J), and we want the answer in kilojoules (kJ), we convert joules to kilojoules by dividing by 1000:
[tex]\[ PE = \frac{1117.74}{1000} \text{ kJ} \] \[ PE = 1.11774 \text{ kJ} \][/tex]
Rounding to the appropriate number of significant figures, the increase in gravitational potential energy of the man-earth system is: [tex]\[ {1.118 \text{ kJ}} \][/tex].
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Answer:
1.118KJ
Explanation:
Potential energy is the energy possessed by a body by virtue of its position.
If the body has a mass (m), and climbs through height (h), the potential energy will be mass×acceleration due to gravity×height
P.E = mgh
Given m = 114kg, g = 9.81m/s² h = 1m
P.E = 114×9.81×1
P.E = 1,118.34Joules
P.E = 1.118KJ
This shows that increase in the gravitational potential energy of the man-earth system is 1.118KJ
