# Momentum

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https://imgur.com/a/u8cgwff

I started with the conservation of momentum

so 3 mu = 3mv

so 3 u = 3 v

Was unsure what to do now, so I looked at answer and the answer is v = 3u/5

so for this to be true, I need v

I started with the conservation of momentum

so 3 mu = 3mv

_{Q}+ 2mv_{P}so 3 u = 3 v

_{Q}+ 2 v_{P}Was unsure what to do now, so I looked at answer and the answer is v = 3u/5

so for this to be true, I need v

_{Q}= v_{P}, but how do I reach this? Can someone explain please?
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(Original post by

The inextensible string becomes taut. They must be moving with the same velocity.

**mqb2766**)The inextensible string becomes taut. They must be moving with the same velocity.

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#4

(Original post by

How do you know?? I don't understand this part

**golgiapparatus31**)How do you know?? I don't understand this part

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(Original post by

How fast does a caravan move when coupled to a car?

**mqb2766**)How fast does a caravan move when coupled to a car?

But then, what is the point of giving the length of the string and the initial separation of the particles?

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#6

(Original post by

Same speed as the car. So applying this analogy to the question, the particles must move with same speed..??

But then, what is the point of giving the length of the string and the initial separation of the particles?

**golgiapparatus31**)Same speed as the car. So applying this analogy to the question, the particles must move with same speed..??

But then, what is the point of giving the length of the string and the initial separation of the particles?

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(Original post by

So initially they have different speeds (one is zero). As the string becomes taut, you have to apply conservation of momentum to calculate the new speed(s)

**mqb2766**)So initially they have different speeds (one is zero). As the string becomes taut, you have to apply conservation of momentum to calculate the new speed(s)

I think it makes sense to me now that the speeds must be the same. I think the separation of particles and length of string are not needed to work out the answer

Thanks for your help!

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#8

(Original post by

Thanks, I understand this part.

I think it makes sense to me now that the speeds must be the same. I think the separation of particles and length of string are not needed to work out the answer

Thanks for your help!

**golgiapparatus31**)Thanks, I understand this part.

I think it makes sense to me now that the speeds must be the same. I think the separation of particles and length of string are not needed to work out the answer

Thanks for your help!

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(Original post by

The only thing it affects is that the string is initially slack then becomes taut.

**mqb2766**)The only thing it affects is that the string is initially slack then becomes taut.

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#10

I have some sympathy with the OP here. The given answer is clearly based on the assumption that P and Q will travel with the same speed once the string has initially become taut, but it's not obvious to me that that must be the case. Why, for instance, could P not be jerked towards Q when the string snaps taut so that P then catches up with Q some time later? One important consequence of P and Q travelling at the same speed after the string has gone taut (if that's what they do) is that kinetic energy is lost somewhere. KE can't be expended in the string, which is light and inextensible, so it must be expended in momentary deformation of P and Q. I won't bore everyone with the working here, but if P and Q were to interact without loss of KE, then after the initial jerk when the string goes taut, P would have to be travelling at 6u/5 and Q would have to be travelling at u/5.

The question would be fine if it explicitly stated that P and Q would remain the same distance apart after the string initially goes taut, but it doesn't state that.

The question would be fine if it explicitly stated that P and Q would remain the same distance apart after the string initially goes taut, but it doesn't state that.

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(Original post by

I have some sympathy with the OP here. The given answer is clearly based on the assumption that P and Q will travel with the same speed once the string has initially become taut, but it's not obvious to me that that must be the case. Why, for instance, could P not be jerked towards Q when the string snaps taut so that P then catches up with Q some time later? One important consequence of P and Q travelling at the same speed after the string has gone taut (if that's what they do) is that kinetic energy is lost somewhere. KE can't be expended in the string, which is light and inextensible, so it must be expended in momentary deformation of P and Q. I won't bore everyone with the working here, but if P and Q were to interact without loss of KE, then after the initial jerk when the string goes taut, P would have to be travelling at 6u/5 and Q would have to be travelling at u/5.

The question would be fine if it explicitly stated that P and Q would remain the same distance apart after the string initially goes taut, but it doesn't state that.

**old_engineer**)I have some sympathy with the OP here. The given answer is clearly based on the assumption that P and Q will travel with the same speed once the string has initially become taut, but it's not obvious to me that that must be the case. Why, for instance, could P not be jerked towards Q when the string snaps taut so that P then catches up with Q some time later? One important consequence of P and Q travelling at the same speed after the string has gone taut (if that's what they do) is that kinetic energy is lost somewhere. KE can't be expended in the string, which is light and inextensible, so it must be expended in momentary deformation of P and Q. I won't bore everyone with the working here, but if P and Q were to interact without loss of KE, then after the initial jerk when the string goes taut, P would have to be travelling at 6u/5 and Q would have to be travelling at u/5.

The question would be fine if it explicitly stated that P and Q would remain the same distance apart after the string initially goes taut, but it doesn't state that.

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