A BALL OF MASS 2KG FALLS FROM REST FROM A HEIGHT OF 200M.CALCULATE ITS KINETIC ENERGY AFTER FALLING A DISTANCE OF 50M?
KE gained = PE lost
To calculate the kinetic energy of the ball after falling a distance of 50m, we can use the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the ball (m) = 2kg
Height from which the ball falls (h) = 200m
Distance fallen (d) = 50m
First, let's calculate the velocity of the ball when it falls from a height of 200m.
Potential Energy at height h = mgh
Potential Energy at height h = 2kg * 9.8m/s^2 * 200m = 3,920 J
The total energy at height h is equal to the sum of potential energy and kinetic energy:
Total Energy at height h = Potential Energy at height h
When the ball falls a distance of 50m, the potential energy is converted into kinetic energy.
Potential Energy at height d = mgh
Potential Energy at height d = 2kg * 9.8m/s^2 * 50m = 980 J
Thus, the kinetic energy after falling a distance of 50m is equal to the change in potential energy (ΔPE) between heights h and d:
ΔPE = Potential Energy at height h - Potential Energy at height d
ΔPE = 3,920 J - 980 J = 2,940 J
Therefore, the kinetic energy of the ball after falling a distance of 50m is 2,940 Joules.