Collision between two croquet balls

[whereisccguys]

A 0.308 kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. What is the mass of the second ball?

so i used the formula m1v1initial + m2v2initial = m1v1final + m2v2final
v2initial=0 therefore m1v1initial = m1v1final + m2v2final

i know that v1initial = v1final + v2final
and the questions tells me v2final = (1/2)v1initial

i plug everything in and i get m1(1/2)v1initial = m2(1/2)v1initial
therefore m1 = m2... but it's the wrong answer
anyone know what i did wrong?

 

[whereisccguys]

nm i figured it out it's not v1initial = v1final + v2final
it's v1intial = v2final - v1final

*edit* okay i dunt get the 2nd part of the question though
What fraction of the original kinetic energy gets transferred to the second ball? Do not enter units

do i use 1/2m1(v1final)^2 - 1/2m1(v1initial)^2 = 1/2m2(v2final)^2-1/2m2(v2initial)^2?

 

[dextercioby]

Hold one a second.KE is a scalar,momentum is a vector.U wrote the conservation of momentum incorrectly.Choose an axis (with a sense on it) and project the vector equation...

Daniel.

 

[whereisccguys]

what do u mean i wrote it wrong?

 

[dextercioby]

U should have written
$$m_{1}\vec{v}_{1}+m_{2}\vec{v}_{2}=m_{1}\vec{v'}_{1}+m_{2}\vec{v'}_{2}$$

and then write the scalar equation(s) by orthonormal projection.

Daniel.

 

[HallsofIvy]

m1v1initial = m1v1final + m2v2final

Yes, that's correct.

"i know that v1initial = v1final + v2final"

?? HOW do you know that? There is no "conservation of velocity" law! You are essentially ASSUMING that m1= m2 when you right that.

You are told that v2final= (1/2)v1initial so
m1 v1initial= m1 v1final+ (1/2)m1 v2final

Since this is an elastic collision, we also have conservation of energy:
(1/2)m1 v1initial²= (1/2)m1 v1final²+ (1/2) m2 v2final²

(1/2)m1 v1initial²= (1/2)m2 v1final²+ (1/2)m2 (1/4)v1initial²

m1 v1initial²= m2 v1final²+ (1/8)m2 v1initial²

You know m1 and v1initial so these two equations have two "unknowns": m2 and v1final which you can solve for.

Two answer the second question, once you know m2 and v1 final, you can calculate the initial kinetic energy of the first ball and the final kinetic energy of the second ball, then divide the second by the first (since that is a ratio, there would be no units).

 

[whereisccguys]

aite got it thanks for the help

 

[ajhunte]

How does he know the initial velocity of the incoming croquet ball. It is not listed in the problem statemt. Two equations, three unknowns.

Unknowns
$$v_{1_{initial}}$$
$$v_{1_{final}}$$
$$m_{2}$$