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anonymous
 5 years ago
In an isolated system, two roller skaters, each with a mass of 100 kg, collide. Skater 1 was initially at rest, while Skater 2 was moving at 6 m/s. They move off together. What is their speed?
anonymous
 5 years ago
In an isolated system, two roller skaters, each with a mass of 100 kg, collide. Skater 1 was initially at rest, while Skater 2 was moving at 6 m/s. They move off together. What is their speed?

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JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2You need to to use conservation of momentum.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Let p1 be the momentum of the first skater before the collision on p1' afterwards. Likewise p2 and p2' for skater 2. Then by conservation of momentum \[ p_1 + p_2 = p_1' + p_2' \] Now, use that the definition of momentum to find the joint velocity afterwards.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2what's the definition of momentum?

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Yes. So p1 = ? and p2 = ?

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2\[ p_1 = 0 \ kg.m/s \] yes. But \[ p_2 = m_2.v_2 = ... what? \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2what's m2 = ? what's v2 = ?

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2\[ v_2 = 6 m/s \] \[ m_2 = 100 kg \] Hence \[ p_2 = m_2.v_2 = (100 kg)(6 m/s) = 6000 kg.m/s \] Therefore the total momentum before the collision is \[ p_1 + p_2 = 0 + 6000 = 6000 \] Now what about afterwards? What do you know about v1' and v2' ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is it 6 m/s...that's all i need to know..

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2No. That's wrong. After the collision, they both move off together so their velocities are the same. Call it v: \[ v = v_1' = v_2' \] Hence the total momentum after the collision is \[ p_1' + p_2' = m_1v_1' + m_2v_2' = (m_1 + m_2)v \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Now, set that equal to the total momentum before the collision and you can solve for v.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2No. That can't possibly be right. If they are both stationary, v = 0, then their total momentum is zero. But we know it must be equal to 6000.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Work the algebra here. Set that last expression for the total momentum equal to the total momentum before the collision.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it has to be one of them, its a multiple choice question.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you please just tell me the answer i'll ask my teacher tomorrow

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2You're just guessing the answers. I'm trying to show you how to find it. By Conservation of Momentum, momentum before and after the collision are equal: \[ p_1 + p_2 = p_1' + p_2' \] We know that \[ p_1 + p_2 = 6,000 \ kg.m/s \] We also know that \[ p_1' + p_2' = (m_1 + m_2)v \] where v is their shared velocity after the collision. Hence we have that \[ (m_1 + m_2)v = 6000 \] Now solve for v.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2**correction: p1 + p2 = 600, because m2.v2 = (100)(6) = 600. Hence you have that \[ (m_1 + m_2)v = 600 \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Now, what's the value of \[ m_1 + m_2 \]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well one is 6...so the other has to be 10!

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2they both weight 100 kg. Hence \[ m_1 + m_2 = ... what? \] and hence what is the solution to \[ (m_1 + m_2)v = 600 \ kg.m/s \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if they weigh 100, it must be 6

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2\[ m_1 = m_2 = 100 \ kg \] hence \[ m_1 + m_2 = 200 \ kg \] therefore \[ (200 \ kg) v = 600 \ kg.m/s \] hence \[ v = ...what? \]

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2v = 3 m/s, yes. Makes intuitive sense as well, as that's half the original velocity.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0god i'm stupid. thank you!

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Now, do yourself a favor, and write this solution out again on a blank piece of paper. When you can do that without looking at this or anything else, then you understand the problem.
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