To calculate the gravitational potential energy (GPE) of the shot put when it is at a height of 4.17 meters, we can use 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 \( 9.81 , \text{m/s}^2 \) on the surface of the Earth),
- \( h \) is the height above the ground (in meters).
Given:
- The weight of the shot is 87 kg (assuming the "shot weight 87" refers to its mass).
- The height \( h \) is 4.17 m.
- \( g \) is approximately \( 9.81 , \text{m/s}^2 \).
First, we need to ensure that we express the weight correctly. If the weight is meant to be in newtons, we should convert mass into weight. However, if we're directly using the mass of the shot as 87 kg, we can proceed with the calculation as follows:
-
Using \( m = 87 , \text{kg} \): \[ \text{GPE} = 87 \cdot 9.81 \cdot 4.17 \]
-
Performing the calculation: \[ \text{GPE} = 87 \cdot 9.81 \cdot 4.17 \approx 87 \cdot 40.9327 \approx 3566.24 , \text{J} \]
Therefore, the gravitational potential energy of the shot is approximately 3566.24 joules.