Physics help! Elastic collision with 15 g object please help!?

Question

A 10.0 g object moving to the right at 21.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 31.0 cm/s. Find the velocity of each object after the collision. I need to find the velocity of the 10 g object and 15 g object.. in cm/s.. thanks!!

Answer 1

While the previous answer is correct, there is a less hair raising solution...

We can get one equation from cons. of momentum
pi = 10x21 - 15x31
let v1 be 10 g object moving left (neg) and v2 be 15 g object moving right (pos)
pf = -10v1 + 15 v2
-10v1 + 15v2 = -255 (check math!)

Now we get the second equation using cons of KE
or we can use the relative velocities must be the same (see below for algebra)
that is

21 - (-31) = -(-v1 - v2)
52 = v1 + v2
So now you have 2 eqn 2 unknowns, but it is nicer...
v1 + v2 = 52
-10v1 + 15v2 = -255

(multiply eqn 1 by 10 and add)
10v2 + 15v2 = 520-255
25v2 = 265 solve for v2


Proof of the relation above....
Extreme algebra
v1i = initial vel of 1, v1f final vel of 1 et

m1v1i^2 + m2v2i^2 = m1v1f^2 + m2v2f^2
collect 1, 2 terms
m1(v1i^2 - v2f^2) = m2(v2i^2 - v2f^2)
these are difference of squares
m1(v1i-v1f)(v1i+v1f) = m2(v2f-v2i)(v2i+v2f)
but cons of momentum (rearranged) gives
m1(v1i-v1f) = m2(v2f-v2i)
divide the two equations
v1i + v1f = v2f + v2i
or
v1i - v2i = -(v1f-v2f)

Answer 2

This isn't a complete solution; you'll see why in a moment. But perhaps it will be enough to get you started.

Conservation of momentum: initial momentum = final momentum.

Initial momentum: ( 10.0 g ) ( 21.0 cm / s ) + ( 15.0 g ) ( -31.0 cm / s )

Final momentum: ( 10.0 g ) ( v1 ) + ( 15.0 g ) ( v2 )

Alas, you have one equation and two unknowns. If the collision were PERFECTLY elastic you could also say that kinetic energy is conserved and

initial KE = 1/2 ( 10.0 g ) ( 21.0 cm / s ) ^ 2 + 1/2 ( 15.0 g ) ( 31.0 cm / s ) ^2

final KE = 1/2 ( 10.0 g ) ( v1^2 ) + 1/2 ( 15.0 g ) ( v2^2 )

Then you would have two equations and two unknowns and could solve for both. However your problem statement only says "elastic" and not "perfectly elastic."

Answer 3

A 10.zero g item relocating to the proper at sixteen.zero cm/s makes an elastic head-on collision with a fifteen.zero g item relocating within the reverse path at 35.zero cm/s. Find the speed of each and every item after the collision. cm/s (10.zero g item) cm/s (15.zero g item)