Elastic collision between two billiard balls

In summary, two balls collide on a frictionless surface with mass m1 = .4 kg and mass m2 = .3 kg. The initial velocity of m1 is 3 m/s while m2 is at rest. After the collision, the velocity of m1 is 1.5 m/s at θ1 above the horizontal, while m2 gains an unknown velocity of v2f at θ2 below the horizontal. Using the conservation of kinetic energy, v2f can be found, but finding the angles using the conservation of momentum can be challenging due to the presence of both sine and cosine terms. A trig identity can be used to relate these terms and solve for the angles.
  • #1
phyme814
2
0

Homework Statement


Two balls collide on a frictionless surface. Mass m1 = .4 kg and Mass m2 = .3 kg . The initial velocity of m1 is 3 m/s. While m2 is at rest. After the collision the velocity of m1 is 1.5 m/s, θ1 above the horizontal. While m2 gains an unknown velocity of v2f, θ2 below the horizontal.
Find v2f, θ1, and θ2


Homework Equations



Conservation of kinetic energy
Conservation of momentum

The Attempt at a Solution


I can find v2f, but I am having trouble with finding the angles.
 
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  • #2
phyme814 said:
I can find v2f, but I am having trouble with finding the angles.
Show what you did.
 
  • #3
I presume you used conservation of energy to solve for v2f. Now use conservation of momentum to solve for the angles. (You'll get two equations and two unknowns.)
 
  • #4
Yepp I used conservation of kinetic energy.
I was using the conservation of momentum equation for the unknowns of the angles but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
 
  • #5
phyme814 said:
but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
Sine and cosine can be related by a trig identity.
 

Related to Elastic collision between two billiard balls

1. What is an elastic collision between two billiard balls?

An elastic collision between two billiard balls is a collision in which the total kinetic energy of the two balls is conserved. This means that the balls bounce off each other without losing any energy, resulting in a perfectly elastic collision.

2. How is the momentum conserved in an elastic collision between two billiard balls?

In an elastic collision, the total momentum of the two balls before the collision is equal to the total momentum after the collision. This is due to the law of conservation of momentum, which states that the total momentum of a closed system remains constant.

3. What factors affect the outcome of an elastic collision between two billiard balls?

The outcome of an elastic collision between two billiard balls is affected by several factors, including the mass and velocity of the balls, the angle at which they collide, and the coefficient of restitution, which is a measure of the elasticity of the collision.

4. How does an elastic collision differ from an inelastic collision?

In an inelastic collision, some of the kinetic energy is lost during the collision, resulting in a decrease in the total kinetic energy of the system. This means that the objects involved in the collision will not bounce off each other like in an elastic collision.

5. What are some real-life examples of elastic collisions between two billiard balls?

Some examples of elastic collisions between two billiard balls in real life include a game of pool, where the balls bounce off each other without losing energy, and a game of billiards, where the balls are designed to have a high coefficient of restitution to ensure an elastic collision.

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