# Momentum and Conservation of energy

• wcjy
In summary, the conversation discusses equations involving the variables V, Va, Vb, and Vc. The equations are used to determine the value of Vb when A hits B and when B hits C, and to find V in terms of Vb. They also discuss finding Vb in terms of V and solving for Vb.
wcjy
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

#### Attachments

• phpQvI4xA.png
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Hello @wcjy ,

You have $$v = 2v_b - v_a \qquad \& \qquad v^2 = v_a^2 + 2v_b^2$$ which should be enough to get ##v_b##.

BvU said:
Hello @wcjy ,

You have $$v = 2v_b - v_a \qquad \& \qquad v^2 = v_a^2 + 2v_b^2$$ which should be enough to get ##v_b##.

oh yea. i think my brain is fried for not seeing that. great thanks!

## 1. What is momentum?

Momentum is a measure of an object's motion. It is the product of an object's mass and its velocity. In other words, momentum is the quantity of motion an object has.

## 2. How is momentum conserved?

Momentum is conserved in a closed system, meaning that the total momentum of all objects in the system remains constant. This is known as the law of conservation of momentum.

## 3. What is the relationship between force and momentum?

Force is directly proportional to the change in momentum of an object. This is described by Newton's second law of motion, which states that force equals mass times acceleration.

## 4. How is energy conserved in a collision?

In a collision between two objects, the total amount of kinetic energy before the collision is equal to the total amount of kinetic energy after the collision. This is known as the law of conservation of energy.

## 5. Can momentum and energy be transferred between objects?

Yes, momentum and energy can be transferred between objects through collisions or interactions. This is due to the conservation laws of momentum and energy, which state that these quantities can be transferred but cannot be created or destroyed.

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