# Physics - Elastic Collision: Solving for Unknowns

• J.live
In summary, the initial velocities of two balls of equal mass, ball A and ball B, are given. After the collision, they stick together and move at an angle of 26.3 degrees above the horizontal. The ratio of the final velocity of the combined mass to the initial velocity of ball A is 1/3. The final energy of the system is also 1/3 of the initial energy.
J.live

## Homework Statement

Two balls of equal mass collide and stick together as shown in the figure. The initial velocity of ball B is twice that of ball A. (Take θ = 56°.)

(a) Calculate the angle above the horizontal of the motion of mass A + B after the collision.

(b) What is the ratio of the final velocity of the mass A + B to the initial velocity of ball A, vf/vA?

(c) What is the ratio of the final energy of the system to the initial energy of the system, Ef/Ei?

## The Attempt at a Solution

a) x= m ( 2vcos(56) + vcos(56) ) = 2mVfx

2vcos(56) + vcos(56)= mvfx

y = m ( 2vsin(56) + vsin(56) ) = 2mVfy

2vsin(56) + vsin(56) = 2mVfy

Am I suppose to take the magnitude of this ? How do I solve for two unknowns ?
Do all the m's and v's cancel out?

Thanks

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y = m ( 2vsin(56) + vsin(56) ) = 2mVfy

2vsin(56) + vsin(56) = 2mVfy

There is something bad in the setup of the first equation.

Am I suppose to take the magnitude of this ? How do I solve for two unknowns ?
Do all the m's and v's cancel out?

Divide by the total mass of the body.
v remains.

2vcos(56) + vcos(56) = 2vfx => 3vcos(56)

2vsin(56) + -vsin(56) = 2vfy => vsin(56)

tan-1 ( y/x) => (1/3) => 26.3 degree

## 1. What is the concept of elasticity in physics?

Elasticity is a property of materials that describes their ability to return to their original shape or size after being deformed by an external force.

## 2. How is elasticity related to the Hooke's law?

Hooke's law states that the force applied to a spring is directly proportional to the amount of deformation or stretch it undergoes. This shows the relationship between force and elasticity, as a more elastic material will experience a larger deformation for the same amount of force applied.

## 3. What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the total energy and total momentum before and after the collision remain the same. In an inelastic collision, some kinetic energy is lost in the form of heat or sound, and momentum may not be conserved.

## 4. How is the coefficient of restitution related to elasticity?

The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach of two objects after a collision. A higher coefficient of restitution indicates a more elastic collision.

## 5. Can elasticity be applied to other fields besides physics?

Yes, the concept of elasticity can be applied to various fields such as economics, finance, and engineering. In these fields, elasticity refers to the responsiveness of a variable to changes in another variable. For example, price elasticity of demand in economics measures the change in demand for a product in response to a change in its price.

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