a rubber ball of mass 50g falls from a height of 10 cm and rebounds to a height of 50 cm .determine the change in the linear momentum and average force between the ball and the ground taking time of contact as 0.1 sec
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Unless thrown downward at a high velocity, the ball cannot rebound to a higher height than it started from.
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The answer is 0.225 kg m/sec
To determine the change in linear momentum and average force between the ball and the ground, we need to use the principle of conservation of linear momentum.
Here's how you can calculate the change in linear momentum:
1. Determine the initial and final velocities of the ball. The initial velocity is zero since the ball is falling from rest, and the final velocity can be calculated using the equation:
v_final = √(2gh)
where
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height the ball rebounds to (50 cm or 0.5 m in this case)
Plugging in the values:
v_final = √(2 * 9.8 * 0.5) = √(9.8) ≈ 3.13 m/s
2. Calculate the initial and final momentums. The initial momentum is zero since the initial velocity is zero. The final momentum can be calculated using the equation:
p_final = m * v_final
where
m is the mass of the ball (50 g or 0.05 kg in this case)
Plugging in the values:
p_final = 0.05 * 3.13 ≈ 0.1575 kg m/s
3. Calculate the change in linear momentum by subtracting the initial momentum from the final momentum:
Δp = p_final - p_initial
Since p_initial is zero, we have:
Δp = 0.1575 - 0 = 0.1575 kg m/s
Now, let's calculate the average force:
1. Calculate the impulse, which is equal to the change in linear momentum:
Impulse = Δp = 0.1575 kg m/s
2. Use the equation for impulse:
Impulse = F_avg * Δt
Where
F_avg is the average force
Δt is the time of contact (0.1 sec in this case)
Rearranging the equation to solve for F_avg:
F_avg = Impulse / Δt
Plugging in the values:
F_avg = 0.1575 / 0.1 ≈ 1.575 N
Therefore, the change in linear momentum is 0.1575 kg m/s and the average force between the ball and the ground is approximately 1.575 N.