A ball of mass 100g falls from a height of 5m onto a concrete floor and rebounds to a height of 3m. Calculate the energy lost. (g = 10ms-2)
To calculate the energy lost when a ball falls from a height of \(5 \, \text{m}\) and rebounds to a height of \(3 \, \text{m}\):
Given: Mass of the ball, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \), Initial height, \( h_1 = 5 \, \text{m} \),
Rebound height, \( h_2 = 3 \, \text{m} \), Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
Calculating the potential energy at height \( h_1 \):
\(\text{PE}_1 = mgh_1 = 0.1 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 5 \, \text{m} = 5 \, \text{J}\)
Calculating the potential energy at height \( h_2 \):
\(\text{PE}_2 = mgh_2 = 0.1 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 3 \, \text{m} = 3 \, \text{J}\)
The energy lost is:
\(\text{Energy lost} = \text{PE}_1 - \text{PE}_2 = 5 \, \text{J} - 3 \, \text{J} = 2 \, \text{J}\)
Thus, the energy lost is: \({2 \, \text{J}}\)
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