# AP Physics C Mechanics: Linear Momentum for Colliding Billiard Balls

• Daniel Guh
In summary, the law of conservation of momentum states that the total momentum of two objects is conserved.
Daniel Guh
Homework Statement
A billiard ball moving at 5 m/s strikes a stationary ball of the same mass. after the collision, the original ball moves at a velocity of 4.35 m/s at an angle of 30° below its original motion. find the velocity and angle of the second ball after the collision.
Relevant Equations
Pi = Pf
P = mv
I'm guessing this question can be solved using the law of conservation of momentum
Vi = 5 m/s

(5 m/s) M = (4.33 m/s) cos30 M + V sinθ M

I don't know what to do after this... I'm also not sure if I use the sin and cos correctly.

Assuming planar motion, you want to look at conservation of momentum in each direction. I believe that will give you two equations two unknowns i.e. the velocity of the initially stationary ball after collision, and the mass of the billiard balls.

Edit: I guess you aren’t after the mass (couldn’t solve for it anyway). Either way two equations two unknowns to find the angle.

Last edited:
So momentum in the y direction should cancel out?
4.33 M sin30 = MV sin θ
And the momentum in the x direction will equal the original momentum so
5M = 4.33 M cos30 + MV cosθ

Yeah, but remember you are going to find the component of the second balls velocity in each direction.

Edit: I guess you can have the unknown angle in those equations, but I wouldn’t bother in this step. I would just find ##v_x## and ##v_y##. Then get the angle from their ratio. Up to you though.

Also, the question says ##4.35~ \rm {m/s}## not ##4.33##. Which is it?

Last edited:
Daniel Guh said:
So momentum in the y direction should cancel out?
4.33 M sin30 = MV sin θ
And the momentum in the x direction will equal the original momentum so
5M = 4.33 M cos30 + MV cosθ
That looks OK. You have two equations and two unknowns, V and θ. How are you going to extract them from the equations?

I would use V0 for the initial speed of the first ball, V1 for the final speed of the first ball and V2 for the final speed of the target ball. I would then find V2 and θ algebraically and substitute numbers at the very end. The algebra is easier to troubleshoot that way, for you and for us.

Daniel Guh

## 1. What is linear momentum?

Linear momentum is a measure of an object's motion, specifically its mass multiplied by its velocity. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is linear momentum conserved in a collision?

In a collision between two objects, the total linear momentum of the system remains constant. This means that the sum of the momenta of the two objects before the collision is equal to the sum of the momenta after the collision.

## 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 objects involved bounce off each other without any loss of energy. In an inelastic collision, some kinetic energy is lost and the objects stick together after the collision.

## 4. How do you calculate the final velocities of colliding objects?

The final velocities of colliding objects can be calculated using the conservation of momentum equation: m1v1i + m2v2i = m1v1f + m2v2f, where m is the mass and v is the velocity of each object before and after the collision.

## 5. What are some real-life applications of linear momentum?

Linear momentum is a fundamental concept in physics and has many practical applications. It is used in fields such as engineering, sports, and transportation to understand and predict the motion of objects. For example, the momentum of a moving car can be used to calculate its stopping distance or the force of impact in a collision.

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