Which has greater momentum?

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In summary, momentum is a measure of an object's motion that takes into account both its mass and velocity. A heavy object moving slowly will have greater momentum than a light object moving quickly because momentum is directly proportional to mass. In collisions, momentum is conserved and the object with greater momentum exerts a greater force on the other object. An object with a smaller mass can have greater momentum than an object with a larger mass if it is moving at a higher velocity. Velocity is a measure of an object's speed and direction, while momentum also considers its mass.
  • #1
blackout85
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Please check over my work

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by an equal horizontal forces for equal times. Just after the forces are removed, the body of greater mass will have:
The body of greater mass will have the the greater speed, the greater acceleration, the smaller momentum, the greater momentum, or the same amount as the other body.

Would the answer be the larger body would have the same amount amount of momentum as the other body because P(before)=P(after). The momentum would have to come out the same in order for that to be right.

second question:

A 0.2kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30m/s and rebounds up at 20m/s. The impulse during the collision would be:

my work:
0.2 (-30m/s) - 0.2 (20m/s) = 10 upward

Please let me know if I am on the right track and let me know where I might have gone wrong:redface:
 
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  • #2
blackout85 said:
Would the answer be the larger body would have the same amount amount of momentum as the other body because P(before)=P(after). The momentum would have to come out the same in order for that to be right.

Yes, but you should use the fact that the impulse of the force equals the change of momentum, and since the impulse is equal for both bodies, you have F*t = m1v1 = m2v2.

blackout85 said:
A 0.2kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30m/s and rebounds up at 20m/s. The impulse during the collision would be:

my work:
0.2 (-30m/s) - 0.2 (20m/s) = 10 upward

Please let me know if I am on the right track and let me know where I might have gone wrong:redface:

Looks good.

Edit: the change in momentum (i.e. the impulse) should actually be: [tex]0.2\cdot 20\vec{j}-0.2\cdot(-30)\vec{j}=10\vec{j}[/tex], which means 10 upwards.
 
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  • #3


I can confirm that your reasoning is correct. In the first scenario, the body of greater mass will have the same amount of momentum as the other body due to the conservation of momentum principle. This means that the total momentum before and after the equal forces are applied will remain constant.

In the second scenario, your calculation for the impulse during the collision is correct. The change in momentum (impulse) is equal to the mass times the change in velocity, which in this case is 0.2kg times the difference between -30m/s and 20m/s, resulting in 10 upward. This shows that the rubber ball experienced an upward impulse during the collision, causing it to rebound at a lower speed than it initially hit the ground. Overall, your understanding of momentum and impulse seems to be accurate. Keep up the good work!
 

1. What is momentum?

Momentum is a measure of an object's motion, which takes into account both its mass and velocity. It is calculated by multiplying an object's mass by its velocity.

2. Which has greater momentum: a heavy object moving slowly or a light object moving quickly?

The heavy object moving slowly will have greater momentum. This is because momentum is directly proportional to an object's mass, meaning that the heavier the object, the greater its momentum will be.

3. How does momentum affect collisions?

Momentum is conserved in a closed system, meaning that the total momentum before a collision will be equal to the total momentum after the collision. In a collision between two objects, the object with greater momentum will exert a greater force on the other object.

4. Can an object with a smaller mass have greater momentum than an object with a larger mass?

Yes, an object with a smaller mass can have greater momentum if it is moving at a much higher velocity than the object with a larger mass. This is because velocity is also a factor in calculating momentum.

5. How is momentum different from velocity?

Velocity is a measure of an object's speed and direction, while momentum takes into account an object's mass as well. An object can have different velocities, but its momentum will depend on both its mass and velocity.

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