A ball of mass 0.2kg falls a height of 45m on striking the ground it rebounds in 0.1s two third of velocity with which it struck the ground calculate A. the momentum changed on hitting the ground B. the force on the ball due to impact
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To calculate the momentum change and the force on the ball due to impact, we'll need to use the principles of physics.
A. Calculating the momentum change:
The momentum change of an object can be calculated using the formula:
Δp = m * (v2 - v1)
where:
Δp = momentum change
m = mass of the ball
v2 = final velocity of the ball after impact
v1 = initial velocity of the ball before impact
In this case, the mass of the ball is given as 0.2 kg. The final velocity after impact is two-thirds of the initial velocity. So, v2 = (2/3) * v1.
Substituting these values into the formula, we get:
Δp = 0.2 kg * [(2/3) * v1 - v1]
Simplifying further:
Δp = 0.2 kg * [(-1/3) * v1]
Therefore, the momentum change on hitting the ground is equal to -0.0667 kg * v1, where v1 is the initial velocity.
B. Calculating the force on the ball due to impact:
To calculate the force, we can use Newton's second law of motion:
F = Δp / Δt
where:
F = force on the ball
Δp = momentum change
Δt = duration of the impact
In this case, the duration of the impact is given as 0.1 seconds. Substituting the value of Δp calculated above, we get:
F = (-0.0667 kg * v1) / 0.1 s
Simplifying further:
F = -0.667 kg * v1 / s
Therefore, the force on the ball due to impact is equal to -0.667 kg * v1 / s, where v1 is the initial velocity. Please note that the negative sign indicates that the force is in the opposite direction of motion, as the ball rebounds.