4.0kg ball with a velocity of 4.0m/s inthe +x-direction collides head on elastically wuth a stationary 2.0kg ball . What are the velocitiesof the balls after the collison? How would I start this problem?

sodni3

sodni3

Answered question

2021-04-04

4.0kg ball with a velocity of 4.0m/s inthe +x-direction collides head on elastically wuth a stationary 2.0kg ball . What are the velocitiesof the balls after the collison? How would I start this problem?

Answer & Explanation

timbalemX

timbalemX

Skilled2021-04-06Added 108 answers

Conservation of linear momentum:
m1iv1i+m2iv2i=m1fv1f+m2fv2f
(4)(4)+(2)(0)=4v1f+2v2f
16+0=4v1f+2v2f
Simplifying: 8=2v1f+v2f
Conservation of kinetic energy:
12m1v{1i}2+12m2v{2i}2=12m1v{1f}2+12v{2f}2
32+0=2v1f2+v2f2
32=2v1f2+v2f2
2 eqns, 2 unknowns; solve for the two final velocities
Substitute into 32=2v1f2+(82v1f)2=2v1f2+6432v1f+41f2=6v1f232v1f+64
Simplifying: 3v1f216v1f+16=0
Solving with the quadratic formula:
v1f=43 or 4
Substituting into equation 3
v2f=63 or 0
The result (4,0) is discarded (this would indicate no change in thevelocities of the balls). The final answer:
v1f=43=1.33ms v2f=163=5.33 m/s
Theres

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?