Collision and friction problem

[nach]

Two carts having the same mass travel towards each other, each with a speed of 1m/s relative to teh surface. The carts collide head on and are reported to rebound after teh collision, each with a speed of 2m/s relative to teh surface. Which of the following assesments of this report is correct?

a) Momentum was not conserved therefore the report is false
b) If potential energy was released to the carts during the collision, the report could be true
c) If teh carts had different masses, the report could be true
d) If the surface was inclined the report could be true
e) If there was no friction between the carts and the surface the report could be true

I feel it'll be either b) or d) but arent they essentially talking about the same idea? If they were on an incline, the potential energy will be released

 

[tiny-tim]

Welcome to PF!

Hi nach! Welcome to PF!

b) If potential energy was released to the carts during the collision, the report could be true
d) If the surface was inclined the report could be true
…
b) or d) but arent they essentially talking about the same idea? If they were on an incline, the potential energy will be released

No, gravity has no effect … immediately after the collision, the carts are the same distance apart (zero! ) and therefore at the same heights, as they were immediately before the collision.

 

[nach]

But momentum is always conserverd in a collision.Does it mean option d)
If there was no friction...
is correct?
how to say there is no friction between cart and surface,

 

[tiny-tim]

But momentum is always conserverd in a collision.Does it mean option d)
If there was no friction...
is correct?
how to say there is no friction between cart and surface,

ah … I think you're misunderstanding what they mean by "potential energy" in (b) …

they mean something like a spring, which is wound up (or compressed) before the collision, so that it has potential energy, and then allowed to expand again, so as to release that potential energy.

 

[nach]

More thought on this question...
Does it mean that potential energy is released whenever there is head on collision and the two bodies travel in opposite direction?

 

[tiny-tim]

More thought on this question...
Does it mean that potential energy is released whenever there is head on collision and the two bodies travel in opposite direction?

No … the situation in the question is highly artificial …

in most collisions, either no potential energy is involved (why would there be a spring?), or potential energy is taken up, not released …

when a car crashes, it has a "crumple zone" which absorbs some of the energy … you could say that some of that absorbed energy has been converted into potential energy.

 

[nach]

Even if potential energy was released, how can it be that the RESULTANT speed after the collision is greater than that before??becuase they are moving at 1m/s initially and after the collision the speed is 2m/s...

 

[tiny-tim]

Even if potential energy was released, how can it be that the RESULTANT speed after the collision is greater than that before??becuase they are moving at 1m/s initially and after the collision the speed is 2m/s...

Because PE + KE = constant,

so if the PE decreases, then the KE increases.

"Releasing" PE means that there was PE before and there isn't now, so the PE has decreased …

so that supplies the extra KE needed to give the extra speed.

 

[nach]

Since there was no PE before collision,so part of KE gets converted in PE in the collision.This same PE is released after the collision ,but how can it increase the KE ?

 

[tiny-tim]

Since there was no PE before collision,so part of KE gets converted in PE in the collision.This same PE is released after the collision ,but how can it increase the KE ?

No, there was PE before the collision … probably in the form of a compressed spring.

 

[nach]

OHH..i think i understand...thanks alot!