A ball of mass 80kg falls from rest from a height of 100m.neglecting air resistance, calculate it K.E after falling a distance of 30cm
KE gain = (1/2) M V^2
= Potential energy loss
= M*g*H
= 235 Joules
H is the distance fallen in meters, 0.30 m
To calculate the kinetic energy (K.E.) of the ball after falling a distance of 30 cm, we can use the principle of conservation of energy.
The potential energy (P.E.) of the ball initially is given by the formula: P.E. = m * g * h, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which the ball is dropped.
Given:
m = 80 kg
g = 9.8 m/s^2
h = 100 m
Using these values, we can calculate the initial potential energy of the ball:
P.E. = 80 * 9.8 * 100 = 78400 J
Now, we need to find the potential energy (P.E.') of the ball after it falls a distance of 30 cm.
The potential energy at any given height is given by the formula: P.E.' = m * g * h', where h' is the new height.
Given:
h' = 30 cm = 0.3 m
Using these values, we can calculate the potential energy at the new height:
P.E.' = 80 * 9.8 * 0.3 = 235.2 J
Since the potential energy is converted into kinetic energy as the ball falls, we can find the change in potential energy (ΔP.E.) using the formula: ΔP.E. = P.E. - P.E.'
ΔP.E. = 78400 - 235.2 = 78164.8 J
Finally, the kinetic energy (K.E.) of the ball after falling a distance of 30 cm is equal to the change in potential energy:
K.E. = 78164.8 J
Therefore, the kinetic energy of the ball after falling a distance of 30 cm is approximately 78164.8 J.