What is the Momentum Change in Pairs Figure Skating?

[uni2820]

Homework Statement

Question: In pairs figure skating, the heavy muscular male and the petite female skater skate towards each other and come to a stop when the female is lifted. Who undergoes a bigger momentum change?

a. the heavier skater
b. the lighter skater
c. same momentum change
d. we must know the exact masses and velocities to answer this question

Second part of the question: Continuing from the previous question, the heavy male skater proceeds to toss the lighter female skater, what happens to the male skater?

a. he moves back just as fast as the lighter skater
b. he does not move at all
c. he starts spinning
d. he moves back but at a lower speed than the lighter skater

Homework Equations

moment = mass x velocity

The Attempt at a Solution

First part of the question:
This is a question my friend posted on Snapchat and it got me wondering. His answer is (c (same momentum change)), but I think the answer should me (d). Here is my explanation: since "momentum = mass x velocity", if the petite female skater is going at a higher speed than the heavy muscular male, it is possible that they might have the same momentum change, which is why we must know the exact masses and velocities to answer this question. Is my explanation correct? Which is the correct answer?

Second part of the question:
My answer for this one would be (d). Here is my explanation: Since momentum is conserved, and momentum is defined as "mass x velocity", and the female skater is lighter, the heavier skater needs to be at a lower speed in order to be equal to the momentum of the female skater. Is my answer and explanation correct for this question?

 

[Doc Al]

but I think the answer should me (d). Here is my explanation: since "momentum = mass x velocity", if the petite female skater is going at a higher speed than the heavy muscular male, it is possible that they might have the same momentum change, which is why we must know the exact masses and velocities to answer this question. Is my explanation correct? Which is the correct answer?

No, your explanation is not correct. You applied momentum conservation to the second part of the question, but it also applies here.

Second part of the question:
My answer for this one would be (d). Here is my explanation: Since momentum is conserved, and momentum is defined as "mass x velocity", and the female skater is lighter, the heavier skater needs to be at a lower speed in order to be equal to the momentum of the female skater. Is my answer and explanation correct for this question?

Good.

 

[uni2820]

No, your explanation is not correct. You applied momentum conservation to the second part of the question, but it also applies here.

Do you mind correcting my explanation? What would the answer be in that case then?

 

[Doc Al]

Do you mind correcting my explanation?

You had written:

Here is my explanation: since "momentum = mass x velocity", if the petite female skater is going at a higher speed than the heavy muscular male, it is possible that they might have the same momentum change,

Your reasoning is backwards. Since momentum is conserved, any change in one skater's momentum must be equal and opposite to the change in the other's.

Given that they end up at rest, then you can conclude that the lighter female skater must have been going faster. But that's not the issue here. The answer to this part of the question would be the same regardless of their speeds.

What would the answer be in that case then?

Your friend's answer was correct.

 

[CWatters]

The clue is the statement that they "come to a stop". That means after they meet the total momentum is zero. So by conservation of momentum the total momentum before they meet must also be zero. That's possible because they are going in opposite directions. eg..

m_mv_m + m_gv_g = 0
or
m_mv_m = - m_gv_g

 

[CWatters]

Second part of the question:
My answer for this one would be (d). Here is my explanation: Since momentum is conserved, and momentum is defined as "mass x velocity", and the female skater is lighter, the heavier skater needs to be at a lower speed in order to be equal to the momentum of the female skater. Is my answer and explanation correct for this question?

Correct.

 

[Doc Al]

The clue is the statement that they "come to a stop".

Even if they didn't "come to a stop", the answer to the first part would be the same.