Question 1191955: Gavin and Andrew are keen rollerbladers. Gavin approaches his stationary brother at a speed of 2.0m/s and bumps into him. As a result of the collision, Gavin, who has a mass of 60 kg, stops moving, and Andrew, who has a mass of 70 kg, moves off in a straight line. The surface on which they are 'blading' is smooth enough that friction can be ignored.
a) With what speed does Andrew move off?
b) Calculate the magnitude of the impulse on Gavin as a result of the bump.
c) Calculate the magnitude of Gavin's change in momentum.
d) Calculate the magnitude of Andrew's change in momentum.
e) How would the motion of each of the brothers after their interaction be different if they pushed each other instead of just bumping?
f) If Gavin held onto Andrew so that they moved off together, what would be their final velocity?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this collision problem using the principle of conservation of momentum:
**a) Andrew's speed:**
* **Initial momentum:** Only Gavin is moving initially. Momentum = mass * velocity
Initial momentum = 60 kg * 2.0 m/s = 120 kg m/s
* **Final momentum:** Only Andrew is moving finally.
Final momentum = 70 kg * v (where v is Andrew's velocity)
* **Conservation of momentum:** Initial momentum = Final momentum
120 kg m/s = 70 kg * v
v = 120 kg m/s / 70 kg
v ≈ 1.71 m/s
Andrew moves off at approximately 1.71 m/s.
**b) Impulse on Gavin:**
Impulse is the change in momentum. Gavin's initial momentum was 120 kg m/s, and his final momentum is 0.
Impulse = Change in momentum = Final momentum - Initial momentum
Impulse = 0 - 120 kg m/s = -120 kg m/s
The magnitude of the impulse is 120 kg m/s.
**c) Gavin's change in momentum:**
Gavin's change in momentum is the same as the impulse on him.
Change in momentum = -120 kg m/s
The magnitude of Gavin's change in momentum is 120 kg m/s.
**d) Andrew's change in momentum:**
Andrew's initial momentum was 0, and his final momentum is 70 kg * 1.71 m/s ≈ 120 kg m/s.
Change in momentum = 120 kg m/s - 0 = 120 kg m/s
The magnitude of Andrew's change in momentum is 120 kg m/s. Notice that the magnitudes of the changes in momentum are equal and opposite, as required by the law of conservation of momentum.
**e) Pushing instead of bumping:**
If they pushed each other, both Gavin and Andrew would have a final velocity. The total momentum would still be conserved. The exact velocities would depend on how hard they pushed and for how long. They would both be moving after the interaction. If they pushed each other in opposite directions, they would move in opposite directions.
**f) Holding on and moving together:**
* **Combined mass:** 60 kg + 70 kg = 130 kg
* **Initial momentum:** 120 kg m/s (only Gavin is moving)
* **Final momentum:** (130 kg) * v (where v is their final velocity)
* **Conservation of momentum:**
120 kg m/s = 130 kg * v
v = 120 kg m/s / 130 kg
v ≈ 0.92 m/s
Their final velocity would be approximately 0.92 m/s.
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