A ball of mass 8kg falls from rest from a height of 100m. Neglecting air resistance,calculate it's total energy after falling a distance of 40m
To calculate the total energy of the ball after falling a certain distance, we need to consider both its potential energy and its kinetic energy.
1. First, let's calculate the potential energy (PE) of the ball initially at a height of 100m. The formula for potential energy is given by:
PE = m * g * h
Where:
m = mass of the ball (8kg)
g = acceleration due to gravity (approx. 9.8 m/s^2)
h = height (100m)
Substituting the values into the formula:
PE = 8kg * 9.8 m/s^2 * 100m
PE = 7840 Joules
2. Next, we need to calculate the potential energy of the ball after falling a distance of 40m. The formula remains the same, but we use the new height:
PE' = m * g * h'
Where:
m = mass of the ball (8kg)
g = acceleration due to gravity (approx. 9.8 m/s^2)
h' = new height (40m)
Substituting the values into the formula:
PE' = 8kg * 9.8 m/s^2 * 40m
PE' = 3136 Joules
3. Finally, to calculate the total energy (TE) of the ball after falling 40m, we need to add the kinetic energy (KE) to the potential energy (PE'):
TE = PE' + KE
Since the ball fell from rest, its initial kinetic energy is zero. Therefore, the total energy after falling 40m is equal to the potential energy alone:
TE = PE'
TE = 3136 Joules
Therefore, the total energy of the ball after falling a distance of 40m is 3136 Joules.