Question

Elastic collision problem: A .10 kg object, moving at .2 m/s makes an elastic head-on collision with a stationary object. The final velocity of the .10 kg object after the collision is in the direction opposite its initial movement. The final velocity pf the .15 kg object is in the same direction as the object which strikes it. What are the final velocities of the two objects?

My class was given this problem to work on as a group and we got about halfway through it before we all started getting different answers.

Answer 1

This is my work so far. I've tried substitution and cancellation but I never end up with the right answer.

Answer 2

Help me

Answer 3

Is it 1.2m/s

Answer 4

Tony, there is a mathematical error in the first part of your solution. You reduced the equation 0.002 = 0.05v1f^2 + 0.075v2f^2 by individually applying square root on each term. This is mathematically wrong. Keep the equation in the ^2 form. Then, substitute for v1f in terms of v2f from your second equation (0.002 = 0.1v1f +0.15v2f).
Another tip: On your first equation where you equate initial and final Kinetic Energy, you can cancel out all the 1/2 on either sides of the equation. Makes solving easier

Answer 5

what you did was absolutely correct (some mathematical mistakes as pointed out by @tambi)
you can even use the equation of coefficient of restitution(e)
and e= velocity of separation/velocity of approach
both of these are the relative velocities after the collision and after the collision respectively
so you get an equation from momentum conservation and the another from the equation of coefficient of restitution i.e. two unknowns and two equations
always remember that for elastic collisions, e=1
for in-elastic collisions, 0〈 e〈 1 (will be specified in the question)
and for perfectly inelastic collisions, e=0
so here , e=1
next,
you'll get two equations as
0.15v1-0.10v2=0.02 (momentum conservation)
v2+v1=0.2 (coefficient of restitution)
next,
you may get the velocity of block with mass 0.15kg (v1)=0.16m/s
and you may get the velocity of the block of mass 0.1kg(v2)=-0.04m/s(-ve as the velocity is in the opposite side of the initial motion)
i don't know this is right or wrong
but i hope this maybe helpful:)

Answer 6

velocity of the striking object=-.04 m/s as it retraces path
velocity of .15kg object =0.16m/s