Issac Physics 'Three Collisions' High School Homework - Kinematic

[radhxy]

Homework Statement

Three particles A, B, and C, each of mass 𝑚, lie at rest in that order in a straight line on a smooth horizontal table. The particle A is then projected directly towards B with speed 𝑢.

The masses of A, B, and C are now 𝑚, 2𝑚 and 3𝑚 respectively:

Again find the fraction of 𝑢 that C moves with immediately after the second impact, assuming the collisions are perfectly elastic. Give your answer as a decimal to three significant figures.

Relevant Equations

Kinetic energy: 𝐾=0.5𝑚𝑣^2
Momentum: 𝑝=𝑚𝑣

Homework Statement: Three particles A, B, and C, each of mass 𝑚, lie at rest in that order in a straight line on a smooth horizontal table. The particle A is then projected directly towards B with speed 𝑢.

The masses of A, B, and C are now 𝑚, 2𝑚 and 3𝑚 respectively:

Again find the fraction of 𝑢 that C moves with immediately after the second impact, assuming the collisions are perfectly elastic. Give your answer as a decimal to three significant figures.
Homework Equations: Kinetic energy: 𝐾=0.5𝑚𝑣^2
Momentum: 𝑝=𝑚𝑣

Increase in mass = increase in momentum, but not sure if that means an increase in momentum transferred.

3?

I know this may be too easy for advanced physics, but I need urgent help! Thank you!

The link to the question: https://isaacphysics.org/questions/three_collisions_num?board=a48e1e5b-c230-44b8-85c5-d38076cb543f

 

[BvU]

Hello radhxy, $\quad$ $\quad$ !

Your text is a bit self-contradicting, with

Three particles A, B, and C, each of mass 𝑚, ...

and

The masses of A, B, and C are now 𝑚, 2𝑚 and 3𝑚 respectively:

as if the collisions make the masses go different. But apparently the first quote applies to part a and the second to part b.

How did you solve part a) and why can't you apply the same math to part b) ?

 

[haruspex]

Increase in mass = increase in momentum

There is no increase in mass. These are two separate questions. In part a the masses are equal, in part b they are different.

 

[Fdtroya]

Homework Statement: Three particles A, B, and C, each of mass 𝑚, lie at rest in that order in a straight line on a smooth horizontal table. The particle A is then projected directly towards B with speed 𝑢.

The masses of A, B, and C are now 𝑚, 2𝑚 and 3𝑚 respectively:

Again find the fraction of 𝑢 that C moves with immediately after the second impact, assuming the collisions are perfectly elastic. Give your answer as a decimal to three significant figures.
Homework Equations: Kinetic energy: 𝐾=0.5𝑚𝑣^2
Momentum: 𝑝=𝑚𝑣

Increase in mass = increase in momentum, but not sure if that means an increase in momentum transferred.

3?

you have to remember that increased mass means increased inertia which means that it would takje more momentum to move this particle a a certain speed.
if you have 3 particles in a perfectly elastic collision both energy and momentum would be conserved, you should put the equations that say that the momentum before the collision is equal to the momentum after the collision (of the WHOLE system) , and then another equation that states that the kinetic energy before the collision is equal to the kinetic energy after the collision (Of the whole system, by this I mean of the 3 particles)

 

[haruspex]

you have to remember that increased mass means increased inertia which means that it would takje more momentum to move this particle a a certain speed.
if you have 3 particles in a perfectly elastic collision both energy and momentum would be conserved, you should put the equations that say that the momentum before the collision is equal to the momentum after the collision (of the WHOLE system) , and then another equation that states that the kinetic energy before the collision is equal to the kinetic energy after the collision (Of the whole system, by this I mean of the 3 particles)

That whole system approach does not in itself furnish enough equations. Each collision needs to be treated separately.