A ball of mass 8kg falls from rest from a hight 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 distance of 40m, we need to consider both its potential energy and kinetic energy.

Given:
Mass (m) = 8kg
Initial height (h1) = 100m
Final height (h2) = 40m

1. Calculate the potential energy at the initial height:
Potential energy (PE1) = mgh1
PE1 = 8kg * 9.81m/s^2 * 100m
PE1 = 7848 J

2. Calculate the potential energy at the final height:
Potential energy (PE2) = mgh2
PE2 = 8kg * 9.81m/s^2 * 40m
PE2 = 3139.2 J

3. Calculate the kinetic energy at the final height:
Since the ball falls from rest, the initial kinetic energy is 0.
Therefore, the total energy at the final height is the sum of the potential and kinetic energies:
Total energy = PE2 + KE2
Total energy = 3139.2 J

Therefore, the total energy of the ball after falling a distance of 40m is 3139.2 Joules.

The total energy of the ball is the sum of its kinetic energy and potential energy.

At the beginning of the fall, the ball has only potential energy:

Potential energy (PE) = mgh
PE = 8 kg - 9.8 m/s² - 100 m
PE = 7840 J

As the ball falls, its potential energy is converted into kinetic energy:

Kinetic energy (KE) = 1/2 mv²

After falling a distance of 40m, the ball's potential energy has decreased by:

ΔPE = mgh
ΔPE = 8 kg - 9.8 m/s² - 40 m
ΔPE = 3136 J

Therefore, the ball's kinetic energy has increased by:

ΔKE = ΔPE
ΔKE = 3136 J

So, the ball's total energy after falling a distance of 40m is:

Total energy = KE + PE
Total energy = 3136 J + (7840 J - 3136 J)
Total energy = 7840 J