A ball of mass 1 kg is dropped from 20m height on ground and it reboun...
Velocity of the ball when it hit the ground can be calculated as
on striking the ground let the ball rebound with the velocity u in upward direction. it can be calculated as
Change in momentum of the ball = final momentum of the ball −initial momentum of the ball
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A ball of mass 1 kg is dropped from 20m height on ground and it reboun...
Given:
- Mass of the ball (m) = 1 kg
- Initial height (h1) = 20 m
- Final height (h2) = 5 m
To find:
- Magnitude of change in momentum during the collision with the ground
Assumptions:
- We assume that there is no air resistance or any other external forces acting on the ball during its motion.
Explanation:
Step 1: Calculate the initial potential energy:
The initial potential energy (U1) of the ball is given by the formula:
U1 = m * g * h1
where m is the mass of the ball, g is the acceleration due to gravity, and h1 is the initial height.
Substituting the given values, we have:
U1 = 1 kg * 9.8 m/s^2 * 20 m
U1 = 196 J
Step 2: Calculate the final potential energy:
The final potential energy (U2) of the ball is given by the formula:
U2 = m * g * h2
where m is the mass of the ball, g is the acceleration due to gravity, and h2 is the final height.
Substituting the given values, we have:
U2 = 1 kg * 9.8 m/s^2 * 5 m
U2 = 49 J
Step 3: Calculate the change in potential energy:
The change in potential energy (ΔU) is given by the formula:
ΔU = U2 - U1
Substituting the calculated values, we have:
ΔU = 49 J - 196 J
ΔU = -147 J
Step 4: Calculate the change in momentum:
The change in momentum (Δp) is equal to the negative change in potential energy, according to the law of conservation of energy. Thus:
Δp = -ΔU
Substituting the calculated values, we have:
Δp = -( -147 J )
Δp = 147 J
Step 5: Calculate the magnitude of change in momentum:
The magnitude of the change in momentum is given by the absolute value of the change in momentum. Thus:
|Δp| = |147 J|
|Δp| = 147 J
Conclusion:
The magnitude of the change in momentum during the collision with the ground is 147 J.
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