How Do You Calculate the Impulse of a Ball During a Collision with the Floor?

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AI Thread Summary
To calculate the impulse of a ball during its collision with the floor, the initial and final velocities must be determined using the height from which the ball is dropped and the height it rebounds to. The ball's final velocity before impact is calculated to be 4.64 m/s, while the initial velocity after rebounding is 4.15 m/s. Applying the Impulse-Momentum Theorem, the impulse is computed as J = mvf - mvo, resulting in an impulse of 4.22 kg*m/s. The calculations and approach used appear to be correct based on the provided values and equations. This method effectively demonstrates how to analyze the impulse during a collision.
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Homework Statement



A 0.480-kg ball is dropped from rest at a point 1.10 m above the floor. The ball rebounds straight upward to a height of 0.880 m. Taking the negative direction to be downward, what is the impulse of the net force applied to the ball during the collision with the floor?

m = 0.480 kg

h0 = 1.10 m

hf = 0.880 m

vo = ?

vf = ?

a = 9.80 m/s2

Homework Equations



Impulse-Momentum Theorem

J = mvf - mvo

vf2 = vo2 + 2ay

The Attempt at a Solution



As we need the velocity of the ball before and after the collision, we can use vf2 = vo2 + 2ay. But I'm wondering, would we solve it once for the vf using ho = 1.10 m? As that would determine the final velocity of the ball just before it hits the floor. And then solve it again, but this time for vo using hf = 0.880 m? The would determine the initial velocity of the ball as soon as it rebounds up? Right...?

Doing it this way, I came up with:

vf = 4.64 m/s

vo = 4.15 m/s

Putting these into the Impulse-Momentum Theorem, vf from above would now be the vo as it is the velocity right before impact. This velocity would also be negative as it is pointing downwards. Then vo from above would be the new vf as it is the velocity right after impact. Did that make sense?


J = mvf - mvo

J = 0.480 kg (4.15 m/s) - [ - 0.480 kg (4.64 m/s)]

J = 1.992 kg*m/s - (- 2.227 kg*m/s)

J = 4.22 kg*m/s

Ummm...Does that look right? I've tried this question a few different ways but haven't been successful yet.

Thanks!
 
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