Finding speed of objects after elastic collison

  • Thread starter joe426
  • Start date
  • #1
44
0

Homework Statement



7I8OI.png


Homework Equations



1/2m1v12 + 1/2m2v22 = 1/2m1v1f + 1/2m2v2f
m1v1 + m2v2 = m1v1f + m2v2f
v1 - v2 = -(v1f - v2f)

The Attempt at a Solution


So I solved the momentum of conservation for the final velocity of object 1. I then plug that equation into the third equation listed above, as v1f. But the thing is the equation i get for v1f has v2f in it and that is what I am solving for and this is where I am stuck.
 

Answers and Replies

  • #2
44
0
I don't think any of the velocity equals 0 at any point. Initially they are moving in the same direction. Then since it says its perfectly elastic, one object will bounce back and have a velocity in the opposite direction. I think the 60g tennis ball will bounce back in the negative direction but I still can't figure out how to find the velocities after the collision :(
 
  • #3
ehild
Homework Helper
15,543
1,909
Show your whole work please.

ehild
 
  • #4
44
0
First use conservation of momentum
( m1v12 + m2v22 - m2v2f2 ) / m1 = v1f2

Then plug this v1f into this helper equation, the third equation listed in first post.
v2f = v1 - v2 + [( m1v12 + m2v22 - m2v2f2 ) / m1 ]1/2


And I'm stuck because I can't get both v2f to one side so i can solve for it. then once i get v2f i plug it back into the first equation, [( m1v12 + m2v22 - m2v2f2 ) / m1 ], and solve for v1f
 
  • #5
ehild
Homework Helper
15,543
1,909
Use the last two equations. Plug in the numbers first. Express v1f from the third equation.

ehild
 
  • #6
ehild
Homework Helper
15,543
1,909
1/2m1v12 + 1/2m2v22 = 1/2m1v1f + 1/2m2v2f
m1v1 + m2v2 = m1v1f + m2v2f
v1 - v2 = -(v1f - v2f)
Use the last two equations. Plug in the data first, express vif form the last equation, and substitute into the second one.

ehild
 
  • #7
44
0
v1f = -v1 + v2 - v2f

Plugged that into,
(m1v1 + m2v2 - m1v1f) / m2 = v2f

v2f = -.368m/s
 
  • #8
ehild
Homework Helper
15,543
1,909
  • #9
44
0
Check it.
v1f = -v1 + v2 - v2f is really v1f = -v1 + v2 + v2f. ..

(m1v1 + m2v2 - m1v1f) / m2 = v2f turns into (m1v1 + m2v2 + m1v1f) / m2 = v2f

so v2f = .307m/s
 
  • #10
ehild
Homework Helper
15,543
1,909
v1f = -v1 + v2 - v2f is really v1f = -v1 + v2 + v2f. ..

(m1v1 + m2v2 - m1v1f) / m2 = v2f turns into (m1v1 + m2v2 + m1v1f) / m2 = v2f
Check.

ehild
 
  • #11
ehild
Homework Helper
15,543
1,909
Plug in the numbers for v1 and v2: v1f = v2f - 1.35.
Plugging in the data into the equation m1v1+m2v2=m1v1f+m2v2f and also substituting v2f - 1.35 for v1f: 0.2535 = 0.06(v2f - 1.35)+0.09v2f.
Expand and collect the terms with v2f, solve.

ehild
 
  • #12
3
0
Its 3.75 or 1.35?
 
Last edited:
  • #13
ehild
Homework Helper
15,543
1,909
Its 3.75 or 1.35?
What is 3.75 or 1.35?

ehild
 

Related Threads on Finding speed of objects after elastic collison

  • Last Post
Replies
2
Views
1K
Replies
10
Views
710
Replies
12
Views
9K
Replies
2
Views
890
  • Last Post
2
Replies
26
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
2
Views
6K
Replies
5
Views
569
Top