Finding velocity of elastic collision with angles

In summary: You'll have to use trigonometry to convert the velocity vectors to components that you can plug into the equations.In summary, the problem involves two balls colliding in an elastic collision on a frictionless surface. Using conservation of energy and momentum, the speed of each ball after the collision can be determined. The conservation of momentum equation must be used, taking into account the vector nature of the equation and using trigonometry to convert the velocity vectors to components.
  • #1
Valenti
15
0

Homework Statement


A red ball and blue ball are sliding on a frictionless surface, each ball has a mass of 40g. They collide in an elastic collision. Initially the red one is at rest and the blue one is traveling in the x direction with a speed of 4 m/s. After the collision the blue one is traveling in the direction +35 degrees, with the red one traveling in the direction ‐55 degrees. Using conservation of energy and momentum find the speed of each puck after the collision

Homework Equations


Conservation of momentum: M1Vi1+ M2Vi2 = M1Vf1 + M2Vf2
Conservation of kinetic energy: 1/2MVi12 + 1/2MVi22 = 1/2MVf12 + 1/2MVf22

The Attempt at a Solution


Started using conservation of kinetic energy and got 4 = Vf1 + Vf2
Wasn't sure how to isolate V plugged it into Conservation of momentum factored out m setting Vf1 + Vf2 to 4
0.04kg(4m/s)+ 0 = 0.04kg (4)
It didn't seem to do anything and I'm not exactly sure where I'm supposed to use the angles
 
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  • #2
Valenti said:
Started using conservation of kinetic energy and got 4 = Vf1 + Vf2

Good start.

To use the conservation of momentum equation you have take into account that it's a vector equation. Which means it's really two equations. One in the x-direction, one in the y-direction. That's where those angles will enter.
 

1. How do you find the velocity of an elastic collision with angles?

The velocity of an elastic collision with angles can be found using the conservation of momentum and conservation of kinetic energy equations. These equations take into account the masses and velocities of the objects before and after the collision, as well as the angles at which they collide.

2. What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the objects involved in the collision do not lose any kinetic energy to other forms, such as heat or sound, and the total momentum of the system is also conserved.

3. How does the angle of collision affect the velocity in an elastic collision?

The angle of collision affects the velocity in an elastic collision by changing the direction of the velocities of the objects involved. The magnitude of the velocities may also change depending on the angle, but the total kinetic energy and momentum of the system will remain constant.

4. Are there any assumptions made when calculating the velocity of an elastic collision with angles?

Yes, there are a few assumptions that are typically made when calculating the velocity of an elastic collision with angles. These include assuming that the collision is happening in a vacuum, that there are no external forces acting on the system, and that the objects involved are rigid and do not deform during the collision.

5. Can the velocity of an elastic collision with angles be negative?

Yes, the velocity of an elastic collision with angles can be negative. This would occur if one of the objects involved in the collision changes direction after the collision and has a velocity in the opposite direction. However, the total momentum of the system will still be conserved, even if it includes negative values.

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