Collision Problem

[loveoforganic]

(#402 in EK 1001 Physics): A large object moving at 10 m/s to the right collides with a lighter object that is initially stationary. Which of the following is a possible velocity of the lighter object after the collision?

A. 1 m/s to the right
B. 5 m/s to the right
C. 18 m/s to the right
D. 25 m/s to the right

The answer is C, but I'm not getting it. I'm honestly not even seeing how the small object can move faster than the large object was initially.

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[johndoe3344]

It's a poorly phrased question. But they're assuming that the first object becomes stationary after the collision.

They're testing conservation of momentum; m1iv1i + m2iv2i = m2fv2f + m1fv1f, where v2i = 0. So in fact, the small object *must* move faster than the large object was initially (assuming the first object becomes stationary).

Here's another way to look at it: let's say you had a ball that was moving 10 m/s with a mass of 2 kg. It hits a ball that's 1 kg, and the first ball is stationary after the collision. You get that 20 = 1*v2 and v2 ~ 20 m/s.

EDIT: I just looked at the answer they had in the back of the book. Could anyone derive/explain where they got this magical "2vo" from in a perfectly elastic collision?

 

[loveoforganic]

That makes sense, thanks.

 

[Dr Gerrard]

I don't have 1001, but that does not make sense. You would need the initial masses in order to determine that.

For example, lets say the following:

m1 = 5
vi1 = 10
vf1 = 0

m2 = 2
vi2 = 0
vi2 = ????

I had to assume that the second ball was stationary after collision, because I am pretty sure it is impossible to do without that.

Anyways, then using conservation of momentum, you have the folllowing:

10*5 = 2 * ?

? = vf2 = 25

In this case, the answer would be d.

Also, John Doe, maybe if you can give a bit more info about this 2vo, maybe someone will be able to clarify.

 

[loveoforganic]

Wait, johndoe, just realized. The situation you presented isn't possible. You're gaining kinetic energy in that case.

 

[johndoe3344]

My apologies. I was just making a random example off the top of my head, forgetting to consider that in a perfectly elastic collision both momentum and KE is conserved.

Basically, EK asserts that regardless of the type of collision, regardless of the masses of the two objects, if you have a heavier ball A at a velocity v0, smashing into ball B, the resulting velocity of ball B after the crash can never exceed 2*v0.

I think it's safe to say that this is a horribly worded question, and a question on the actual MCATs would definitely be more specific.

 

[loveoforganic]

What about choices A and B? Those are impossible only if you assume that ball 1 comes to rest after collision, correct?

 

[johndoe3344]

That is correct.

 

[loveoforganic]

Thanks

 

[Dr Gerrard]

I don't have 1001, but that does not make sense. You would need the initial masses in order to determine that.

For example, lets say the following:

m1 = 5
vi1 = 10
vf1 = 0

m2 = 2
vi2 = 0
vi2 = ????

I had to assume that the second ball was stationary after collision, because I am pretty sure it is impossible to do without that.

Anyways, then using conservation of momentum, you have the folllowing:

10*5 = 2 * ?

? = vf2 = 25

In this case, the answer would be d.

Also, John Doe, maybe if you can give a bit more info about this 2vo, maybe someone will be able to clarify.

John Doe, how about in this example?

 

[johndoe3344]

Doesn't KE need to be conserved for a elastic collision? It's the same thing that was wrong with the example I made up a few posts above.

 

[Dr Gerrard]

How do we know it is elastic?

If it is, did you ever figure out that 2vo derivation?

 

[Bernoull]

How do we know it is elastic?

If it is, did you ever figure out that 2vo derivation?

Good question u raised about the V2f being 25m/s given the masses u used. One thing to keep in mind, is the vector nature of momentum, if M1 hits M2 at angle, you'll need to consider momentum & velocity in x,y (maybe, even z) axes. The questions is utterly imprecise.

Another complication in the problem is that it gives no info on the Vf of M1 (but ur example controlled for this)..

C is possible, if EK didn't make ur assumption of 0m/s for M1's Vf. All anwers can be plausible BASED on impact angle, I can envision 1m/s for M2 if M1 barely glances it.. Poorly worded question..

the velocity equations depend on the "elasticity of collision"..

 

[Dr Gerrard]

Bump, so can we basically ignore that final velocity is never greater than 2vo s*** EK put as the answer?