Why is the answer C never possible for the collision of two vehicles?

[PhysicStud01]

Homework Statement

Speed of vehicle

Relevant Equations

Momentum and Kinetic energy

Attempt:
I know that the conservation of momentum and energy also applies.

Solution:
Correct answer is C.

But I can't understand how any of the two conservation laws lead to the answer C.

The exam report to this question did not even mention anything about this - so, I guess it should be something very simple. But I still cannot understand why C is never possible.

Thanks

 

[PeroK]

Why do you say momentum is conserved?

Why do you say energy is conserved?

I think you have to do some calculations. I don't think you can just see an obvious answer.

 

[Orodruin]

The answer is wrong. Consider the case of an elastic collision where M >> m and v > V. The speed of the lighter (and faster) object after collision will be v+2V as the relative speed v+V of the objects is preserved (elastic collision) and the speed of the heavier is not affected much. The objects are traveling in the same direction after the collision.

 

[PhysicStud01]

The answer is wrong. Consider the case of an elastic collision where M >> m and v > V. The speed of the lighter (and faster) object after collision will be v+2V as the relative speed of the objects is preserved (elastic collision) and the speed of the heavier is not affected much.

this is what the mark scheme says and even the exam report gives the same answer. i assume that if it was wrong, the exam report would correct it.

also, can we assume elastic collision for the collision between vehicles?

 

[PeroK]

this is what the mark scheme says and even the exam report gives the same answer. i assume that if it was wrong, the exam report would correct it.

also, can we assume elastic collision for the collision between vehicles?

If you assume an elastic collision, then A is impossible.

 

[PeroK]

this is what the mark scheme says and even the exam report gives the same answer. i assume that if it was wrong, the exam report would correct it.

I guess you're right. An exam report couldn't possibly be wrong. There's nothing for it then ... it's time to change the laws of physics!

 

[PhysicStud01]

If you assume an elastic collision, then A is impossible.

i meant that it cannot be elastic. so, the explanation provided for C being possible above would not hold.

if C is incorrect, would you explain which one is correct and why?

 

[PeroK]

i meant that it cannot be elastic. so, the explanation provided for C being possible above would not hold.

if C is incorrect, would you explain which one is correct and why?

With a bit of calculation you can see that all four scenarios are possible. You really need some constraint like energy conservation or equal mass collision to rule out one or more of the options.

 

[PhysicStud01]

With a bit of calculation you can see that all four scenarios are possible. You really need some constraint like energy conservation or equal mass collision to rule out one or more of the options.

could you tell me please the conditions that would make each option possible?

example, in my opinion,

A is only possible when the momentum of both are equal.
B: ?
C: if the fast moving one has a smaller mass and mass of slow one is much larger ..??
D: ?

thanks

 

[PeroK]

For A I guess you mean: equal and opposite momentum, totally inelastic collision.

For C you've been given the example.

Can you do B with a totally elastic collision? Try with some numbers. Hint: unless one of the initial speeds is zero, you'll need unequal masses.

D should be very easy. Isn't that what you actually expect to happen in equal mass collisions?

 

[PhysicStud01]

For A I guess you mean: equal and opposite momentum, totally inelastic collision.

For C you've been given the example.

Can you do B with a totally elastic collision? Try with some numbers. Hint: unless one of the initial speeds is zero, you'll need unequal masses.

D should be very easy. Isn't that what you actually expect to happen in equal mass collisions?

but for B, we are assuming a total elastic collision. what if it is inelastic?

by the way, can we explain in terms of kinetic energy - it remains the same (in elastic), decreases (in inelastic) but it cannot increase ??

 

[Orodruin]

also, can we assume elastic collision for the collision between vehicles?

The problem does not specify either elastic or inelastic. If you then want to consider what is never possible you must consider both (as well as anything in between elastic and completely inelastic).

i assume that if it was wrong, the exam report would correct it.

There are errors in most published textbooks. Why do you think people would spend more time on writing an exam report for a handful of students than a textbook author spends on a textbook that will potentially be read by thousands?

 

[Orodruin]

but for B, we are assuming a total elastic collision. what if it is inelastic?

Completely irrelevant. The question asks which statement is never true. If it is never true you must argue that it cannot be true for any type of collision. If it is true for an inelastic collision, there are cases when the statement can be true and it is therefore irrelevant if it also holds for elastic collisions.

 

[PeroK]

but for B, we are assuming a total elastic collision. what if it is inelastic?

by the way, can we explain in terms of kinetic energy - it remains the same (in elastic), decreases (in inelastic) but it cannot increase ??

For each option you are free to choose your masses and whether the collision is elastic or inelastic to try to find an example. All you need is one example, because the question wants you to find something that can never happen.

Total KE cannot increase, but the KE of either vehicle can increase.

You need to calculate. Unless you are doing a physics course that does not demand any mathematics or calculation?

 

[PhysicStud01]

should the change in momentum should be the same for both vehicles?

 

[PeroK]

should the change in momentum should be the same for both vehicles?

You always have conservation of momentum (by Newton's third law). Remember that momentum is a vector, so that the change in one momentum is equal and opposite the change in the other.

 

[PhysicStud01]

You always have conservation of momentum (by Newton's third law). Remember that momentum is a vector, so that the change in one momentum is equal and opposite the change in the other.

so, if the magnitude of momentum of the fast vehicle increases, there should be a similar change in momentum of the other vehicle?

also, can the vehicles continue in their original direction or the only possibility is that they bounce off?

 

[PeroK]

so, if the magnitude of momentum of the fast vehicle increases, there should be a similar change in momentum of the other vehicle?

also, can the vehicles continue in their original direction or the only possibility is that they bounce off?

You have to do these calculations for yourself. In all your posts you have not posted a single formula or calculation. If you can't calculate, you cannot answer the question.

You need to start doing some calculations.

 

[archaic]

With a bit of calculation you can see that all four scenarios are possible. You really need some constraint like energy conservation or equal mass collision to rule out one or more of the options.

How can A be possible? If they collide and stop, doesn't it count as an inelastic collision necessarily?

 

[Orodruin]

How can A be possible? If they collide and stop, doesn't it count as an inelastic collision necessarily?

So what? Nothing is stating that the collision must be elastic.

 

[archaic]

So what? Nothing is stating that the collision must be elastic.

I know, and I am saying indirectly that I think A is the answer because of inelastic collisions. I am just asking why PeroK said that you need other constraints.

 

[PeroK]

I know, and I am saying indirectly that I think A is the answer because of inelastic collisions. I am just asking why PeroK said that you need other constraints.

What your saying is that if the question said "never happens for an elastic collision", then A would be the answer.

And, that's what I meant. With the constraint of elasticity you have one impossible outcome.

Alternatively, assuming equal masses gives you a different answer.