- #1

wcjy

- 73

- 10

- Homework Statement
- Objects A, B, and C with masses m, 2m, and 2m respectively, slide on a horizontal frictionless surface and object C is connected with a massless spring with spring constant k. Object A travels at a velocity v to the right and objects B and C are stationary initially. During the collisions between A, B, and C, show that the maximum change in the length of the spring is sqrt (4mv^2/9k). Note that the collision between A and B is elastic.

- Relevant Equations
- EPE = 0.5kx^2

When A hits B,

COLM

mV = -mVa + 2mVb

V = 2Vb - Va

COKE

0.5mv^2 = 0.5mVa^2 + 0.5(2m)Vb^2

V^2 = Va^2 + 2Vb^2

When B hits C

COLM

2mVb=4mVc

Vc = 0.5Vb

COE

0.5(2m)Vb^2 = 0.5kx^2 +0.5(4m)Vc^2

sub Vc = 0.5b

mVb^2 = KX^2

After that I am stuck, cause i can't find V in terms of Vb only

COLM

mV = -mVa + 2mVb

V = 2Vb - Va

COKE

0.5mv^2 = 0.5mVa^2 + 0.5(2m)Vb^2

V^2 = Va^2 + 2Vb^2

When B hits C

COLM

2mVb=4mVc

Vc = 0.5Vb

COE

0.5(2m)Vb^2 = 0.5kx^2 +0.5(4m)Vc^2

sub Vc = 0.5b

mVb^2 = KX^2

After that I am stuck, cause i can't find V in terms of Vb only