Is the Collision Between Two Moving Carts Elastic?

[SteelDirigibl]

Homework Statement

A 20kg cart traveling to the right at 8 m/s collides head-on with a 10 kg car traveling 6 m/s to the left. After the collision, the 10 kg cart is traveling 10 m/s to the right
a) What is the velocity of the 20 kg cart after the collision?
b) determine whether or not the collision is elastic (show calculations)
c) Discuss whether or not your answers to part a and b are reasonable. Include specific reasons why you think the answers are or are not reasonable

Homework Equations

p=mv

KE=1/2mv^2

The Attempt at a Solution

So pretty simple I think for the first two parts, but I got to thinking.

Well here's the math: 8*20=160 right, 10*6=60 left, so total 100 to right. Then after, the small cart is 10*10 or 100 to the right, so the 20kg cart would be stopped, according to the math.
Is this reasonable? it's larger and going faster?

Moving on... elasticity just means KE is equal before and after. before is 820 and after is 500. Therefore not elastic. This seems to make sense in the real world because energy would be lost by sound, and i want to say friction as heat, even though we didnt factor friction into the motion.

So I have my numbers, pretty sure they are right. is it reasonable? it doesn't seem like a larger cart moving faster would stop, but then I also think back to those metal balls that bounce back and forth and transfer their energy. Does this seem right?

 

[ideasrule]

All your math is right. The carts don't need to behave like those balls because the collisions between them are very nearly elastic, whereas the collision between these two carts is not.

 

[SteelDirigibl]

if it were elastic, shouldn't i get the same KE for before and after? it's 320 (Joules?) difference.

 

[ideasrule]

The collision between the carts is NOT elastic. The collision between those steel balls is.

 

[SteelDirigibl]

ok that's what i thought. so since the larger mass is larger and moving faster, how does it stopping make sense? obviously the math shows it but it just seems like it would have some motion left. I guess that it transfers all it's energy to the smaller box and the rest (the extra 320) is dispersed through sound, etc, other energy loss sources?

 

[ideasrule]

ok that's what i thought. so since the larger mass is larger and moving faster, how does it stopping make sense? obviously the math shows it but it just seems like it would have some motion left. I guess that it transfers all it's energy to the smaller box and the rest (the extra 320) is dispersed through sound, etc, other energy loss sources?

Yes. All the smaller box does is bring the larger box to a halt. The larger box has to stop the smaller one and force it to go in the opposite direction.