A ball of mass 0.1kg is dropped from a height of 8m into a hard floor and bounces back to a height of 2m calculate the velocity when the ball hits the ground, the velocity with which the ball leaves the ground,the momentum when the ball hits the ground
To calculate the velocity when the ball hits the ground, you can use the equation for free fall:
v^2 = u^2 + 2as
where:
v = final velocity (which is what we want to find)
u = initial velocity (zero since the ball was dropped)
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = distance fallen (8m)
Plugging the values into the formula:
v^2 = 0^2 + 2 * 9.8 * 8
v^2 = 156.8
Taking the square root of both sides, we get:
v ≈ 12.53 m/s
Therefore, the velocity when the ball hits the ground is approximately 12.53 m/s.
To calculate the velocity with which the ball leaves the ground after bouncing, we can use the principle of conservation of energy. Assuming that there is no energy loss due to air resistance or other factors, the potential energy gained during the fall is equal to the potential energy lost during the bounce.
Potential energy at height of 8m = Potential energy at height of 2m
mgh1 = mgh2
where:
m = mass of the ball (0.1kg)
g = acceleration due to gravity (9.8 m/s^2)
h1 = initial height (8m)
h2 = final height (2m)
Plugging the values into the equation:
0.1 * 9.8 * 8 = 0.1 * 9.8 * 2
7.84 = 1.96
This indicates that the potential energy gained during the fall equals the potential energy lost during the bounce.
Since kinetic energy is directly related to velocity, and the ratio of kinetic energy to potential energy remains constant, we can conclude that the velocity with which the ball leaves the ground is the same as the velocity it had when it hit the ground. Therefore, the velocity with which the ball leaves the ground is approximately 12.53 m/s.
Finally, to calculate the momentum when the ball hits the ground, we use the equation:
momentum = mass * velocity
where:
mass = 0.1kg (given)
velocity = 12.53 m/s (calculated)
Plugging in the values:
momentum = 0.1 * 12.53
momentum ≈ 1.253 kg·m/s
Therefore, the momentum of the ball when it hits the ground is approximately 1.253 kg·m/s.