Elastic Collision of marbles

The angle between the direction of the target ball and the original direction of the incident ball can be found using trigonometric functions.
  • #1
Fusilli_Jerry89
159
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Homework Statement


A 45 g steel marble collides obliquely w/ an identical stationary marble, and continues at 55 degrees to its original direction. The collision is perfectly elastic. What is the angle between the direction taken by the target ball and the original direction of the incident ball?

The Attempt at a Solution


is it just 55 degrees?
 
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  • #2
Fusilli_Jerry89 said:

Homework Statement


A 45 g steel marble collides obliquely w/ an identical stationary marble, and continues at 55 degrees to its original direction. The collision is perfectly elastic. What is the angle between the direction taken by the target ball and the original direction of the incident ball?

The Attempt at a Solution


is it just 55 degrees?

It is not 55 degrees. You need to apply conservation of momentum and conservation of energy (kinetic energy in this case) to find the magnitude and direction of the velocity of the target ball.
 
  • #3


Yes, the angle between the direction taken by the target ball and the original direction of the incident ball would be 55 degrees. This is because in an elastic collision, the total kinetic energy and momentum are conserved. This means that the angle of incidence (which is the angle between the incident ball's initial direction and the normal line to the surface of the target ball) is equal to the angle of reflection (which is the angle between the target ball's final direction and the normal line to its surface). Since the incident ball's final direction is at a 55 degree angle to its original direction, the target ball's final direction will also be at a 55 degree angle to the incident ball's original direction.
 

What is an elastic collision of marbles?

An elastic collision of marbles is a type of collision where the total kinetic energy and momentum of the marbles are conserved. This means that after the collision, the marbles will bounce off each other without losing any energy to deformation or heat.

What factors affect the outcome of an elastic collision between marbles?

The outcome of an elastic collision between marbles is affected by the mass, velocity, and angle of collision of the marbles. Other factors such as the coefficient of restitution, which measures the elasticity of the colliding objects, also play a role in the outcome.

How is momentum conserved in an elastic collision of marbles?

In an elastic collision of marbles, the total momentum of the system before and after the collision remains the same. This is because momentum is a conserved quantity, meaning it cannot be created or destroyed, only transferred between objects.

What is the coefficient of restitution in an elastic collision of marbles?

The coefficient of restitution is a measure of the elasticity of colliding objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between the two objects. In an elastic collision of marbles, the coefficient of restitution is equal to 1, indicating a perfectly elastic collision.

What is the difference between an elastic and inelastic collision of marbles?

An elastic collision of marbles is one where the total kinetic energy and momentum of the marbles are conserved. In an inelastic collision, some of the kinetic energy is lost to deformation or heat, resulting in a decrease in the total kinetic energy after the collision. Momentum is still conserved in both types of collisions.

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