Momentum:End of chapter Review Q.9(8 marks)

Three balls,A,B and C ,are in that order in a straight line on a smooth horizontal surface.A has mass 0.4 kg and is moving at 4 m/s towards B.B has mass "m"kg and is stationary.C has mass 0.25 kg and is moving at 0.8 m/s away from B. A hits B and then B hits C.There are no further impacts. A and C now each have a speed of 1 m/s and are both moving in direction away from B.Find the range of possible values of m.

Please help me how to start this question.

Reply 1

mqb2766

21

Original post by alevelmath1

Three balls,A,B and C ,are in that order in a straight line on a smooth horizontal surface.A has mass 0.4 kg and is moving at 4 m/s towards B.B has mass "m"kg and is stationary.C has mass 0.25 kg and is moving at 0.8 m/s away from B. A hits B and then B hits C.There are no further impacts. A and C now each have a speed of 1 m/s and are both moving in direction away from B.Find the range of possible values of m.

Please help me how to start this question.

You obviously have to model the two impacts, using conservation of momentum/energy. You also know something about the final relative speeds of A and C, so start by setting up the equations.

Reply 2

alevelmath1

OP

9

please try to give me some intermediate steps.

Reply 3

mqb2766

21

Original post by alevelmath1

please try to give me some intermediate steps.

So what equations have you set up. If its the end of chapter question, you should be able to set up the momentum / energy balances for each collision?

Reply 4

RogerOxon

21

Original post by alevelmath1

Three balls,A,B and C ,are in that order in a straight line on a smooth horizontal surface.A has mass 0.4 kg and is moving at 4 m/s towards B.B has mass "m"kg and is stationary.C has mass 0.25 kg and is moving at 0.8 m/s away from B. A hits B and then B hits C.There are no further impacts. A and C now each have a speed of 1 m/s and are both moving in direction away from B.Find the range of possible values of m.

Please help me how to start this question.

Start by modelling the collision of A and B. You know that A collides once (only) with B, and you know its post-collision speed (and direction).

Reply 5

alevelmath1

OP

9

well, I got these two equations :
mv=2 and mv1= -1.95 or mv1= 0.05, how to proceed further ?

Reply 6

old_engineer

11

Original post by alevelmath1

well, I got these two equations :
mv=2 and mv1= -1.95 or mv1= 0.05, how to proceed further ?

OK, so you have the momentum of B after its collision with A as 2. But you know that the velocity of B after its collision with A must be greater than 0.8m/s. Otherwise it would not collide with C as required. Setting v > 0.8 will allow you to establish one constraint on the possible values of m.

Momentum:End of chapter Review Q.9(8 marks)

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