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Past paper question about momentum collision

nina.png
I am currently working on this question and I understand that the momentum is conserved, and before and after the collision between them is both 0, and that Nina would have a faster velocity as she weighs less than Matt.
However, I don't understand how they move after the collision. I understand that I need to use the "explosion" theory where the momentum is the same after the collision as it was before and that the forces are equal and opposite, but in this instance there was 0 momentum beforehand, so why would they begin moving apart when there is 0 momentum being exerted on them?
Thank you
(edited 8 years ago)
Original post by blobbybill
nina.png
I am currently working on this question and I understand that the momentum is conserved, and before and after the collision between them is both 0, and that Nina would have a faster velocity as she weighs less than Matt.
However, I don't understand how they move after the collision. I understand that I need to use the "explosion" theory where the momentum is the same after the collision as it was before and that the forces are equal and opposite, but in this instance there was 0 momentum beforehand, so why would they begin moving apart when there is 0 momentum being exerted on them?
Thank you


Has the mark scheme explicitly refers to the conservation of momentum, because I wouldn't think that's the case here as there is no initial momentum?

However, there are the equal but opposite forces that cause the momentum, that is:

F=−FF=-F but F=mv−mutF=\dfrac{mv-mu}{t}

Therefore we have:

m1v1−m1u1t=−(m2v2−m2u2)t\dfrac{m_1v_1 -m_1u_1}{t}=-\dfrac{(m_2v_2-m_2u_2)}{t}

Which if you rearrange so that you have the combined products of mass and velocity of each body's initial and and final state of motion you get the conservation of momentum, one of the consequences of Newton's third law.
Original post by blobbybill
nina.png
I am currently working on this question and I understand that the momentum is conserved, and before and after the collision between them is both 0, and that Nina would have a faster velocity as she weighs less than Matt.
However, I don't understand how they move after the collision. I understand that I need to use the "explosion" theory where the momentum is the same after the collision as it was before and that the forces are equal and opposite, but in this instance there was 0 momentum beforehand, so why would they begin moving apart when there is 0 momentum being exerted on them?
Thank you


The force they exert on each other is equal and opposite -

The force causes equal changes in momentum on both skaters.
Original post by blobbybill
nina.png
I am currently working on this question and I understand that the momentum is conserved, and before and after the collision between them is both 0, and that Nina would have a faster velocity as she weighs less than Matt.
However, I don't understand how they move after the collision. I understand that I need to use the "explosion" theory where the momentum is the same after the collision as it was before and that the forces are equal and opposite, but in this instance there was 0 momentum beforehand, so why would they begin moving apart when there is 0 momentum being exerted on them?
Thank you


you should be thinking about force being exerted - they can hang around for an unlimited amount of time before starting to exert force on each other.

the force is what causes them to accelerate apart
Reply 4
Avatar for blobbybill
blobbybill
OP
11
Original post by Muttley79
The force they exert on each other is equal and opposite -

The force causes equal changes in momentum on both skaters.


Original post by Joinedup
you should be thinking about force being exerted - they can hang around for an unlimited amount of time before starting to exert force on each other.

the force is what causes them to accelerate apart

But the momentum worked out to be 0. How would you work out the forces? And how would you work out the changes in momentum caused by the force?
The momentums cancelled each other out to make 0, so how does this change?
Original post by blobbybill
But the momentum worked out to be 0. How would you work out the forces? And how would you work out the changes in momentum caused by the force?
The momentums cancelled each other out to make 0, so how does this change?


If you you look at the equation above, and using the fact that the initial velocities of them were zero, then you arrive at m1v1=−m2v2m_1v_1=-m_2v_2
Original post by blobbybill
But the momentum worked out to be 0. How would you work out the forces? And how would you work out the changes in momentum caused by the force?
The momentums cancelled each other out to make 0, so how does this change?


Velocity is a vector - so momentum is too.

total momentum = 0

60 x -5 + 100 x 3 = 0

Impulse on Boy = change in momentum = 300 - 0

There is an equal and opposite impulse on the girl ...
Original post by blobbybill
But the momentum worked out to be 0. How would you work out the forces? And how would you work out the changes in momentum caused by the force?
The momentums cancelled each other out to make 0, so how does this change?


momentum is conserved because the force exerted by A on B is the same as the force exerted by B on A (Newton's second law)
The rates of acceleration will be dependent on the masses because F=ma (Newton's third law) which also gives us the direction of the force vector (opposite directions to each other)
clearly the paired forces are applied for the same amount of time as each other so the final velocities depend on the mass ratios (because v=u+at)...
this is where conservation of momentum 'comes from'
Reply 8
Avatar for lerjj
lerjj
13
You can answer this in two ways:

1) Conservation of momentum - there was no momentum before and so there will be none afterwards. This is because the only force acting is an internal force, not an external one.

Therefore, m1v1=−m2v2 m_1v_1 = - m_2v_2
and so m1m2=∣v2v1∣\dfrac{m_1}{m_2}=|\dfrac{v_2}{v_1}|

2) Newton's 2nd and 3rd laws - these say that the forces on both of them are equal and opposite. Using Newton's 2nd law we can then say:

m1a1=−m2a2 m_1a_1 = -m_2a_2
m1m2=∣a2a1∣\dfrac{m_1}{m_2}=|\dfrac{a_2}{a_1}|

Since the accelerations are different, so will the velocities be (we can assume that the acceleration happens over a short enough time to be continuous, so the velocity is directly proportional to the acceleration).

The fact that these two laws both explain the same thing in pretty much identical ways is due to the fact that they are equivalent expressions. Once you've defined a force as the "rate of change of momentum" then Newton's 3rd law follows from Conservation of Momentum.
(edited 8 years ago)
We can reverse the process as, both Nina and Matt are moving towards each other and the law of conservation of momentum says that after and before the collision the momentum are the same.(60*5)=(100*3)300 kg m/s = 300 kg m/sThe object which have less mass have more velocity this is prove by derivation of the impulse formulae.Force = mass*velocityVelocity = (v-u)/tForce *time = mass*velocityMass*velocity =momentumFt = momentumImpulse = ftFt = momentum
Original post by Science1234
We can reverse the process as, both Nina and Matt are moving towards each other and the law of conservation of momentum says that after and before the collision the momentum are the same.(60*5)=(100*3)300 kg m/s = 300 kg m/sThe object which have less mass have more velocity this is prove by derivation of the impulse formulae.Force = mass*velocityVelocity = (v-u)/tForce *time = mass*velocityMass*velocity =momentumFt = momentumImpulse = ftFt = momentum


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