Solve Elastic Collision: Momentum vs Kinetic Energy

[BradP]

Homework Statement

Two hard spheres collide elastically. Sphere 1 has a mass of 2 kg and an initial velocity of 3 m/s. Sphere 2 has a mass of 4 kg and is initially at rest. Sphere 1 collides head on with sphere 2 and comes to an immediate stop. Solve for the velocity of mass 2 using (a) conservation of momentum and (b) conservation of kinetic energy.

Homework Equations

Momentum = constant
m1*v1 = m2*v2

Kinetic energy = constant
m1*(v1^2) = m2*(v2)^2

The Attempt at a Solution

Using conservation of momentum,

2*3 = 4*v
v = 1.5 m/s.

Using conservation of kinetic energy,

.5*2*3^2=.5*4*v^2
v = 2.12 m/s.

My question is why the velocities are different. If this collision is elastic, shouldn't using kinetic energy and conservation of momentum give the same answer?

 

[tiny-tim]

Hi BradP!

(try using the X² and X₂ icons just above the Reply box )

Two hard spheres collide elastically. Sphere 1 has a mass of 2 kg and an initial velocity of 3 m/s. Sphere 2 has a mass of 4 kg and is initially at rest. Sphere 1 collides head on with sphere 2 and comes to an immediate stop. Solve for the velocity of mass 2 using (a) conservation of momentum and (b) conservation of kinetic energy.
…
My question is why the velocities are different. If this collision is elastic, shouldn't using kinetic energy and conservation of momentum give the same answer?

Yes, it's a ridiculous question.

"Elastically" means with conservation of energy, but on the given figures, energy and momentum can't both be conserved.

The teacher is obviously trying to illustrate something for you … but I've no idea what!

 

[BradP]

Oh, I see. Is it because that sphere 2 is heavier, sphere 1 would not actually stop when it hit it? It would collide and roll backwards at a slower velocity, right?

 

[tiny-tim]

Can't remember.

But it definitely wouldn't stop dead.

 

[BradP]

It would if they were the same mass, like a cue ball. But the heavier the second sphere is, the more it approaches something like a ball hitting a wall. So in this problem, it would roll backwards. Thanks :)