# What are the velocities of the balls after the collision?

• lozah
In summary, the problem involves a 0.50 kg ball with a speed of 1.5 m/s colliding elastically with a stationary 0.80 kg ball. Using the equation Ek = (1/2)m(v^2), the kinetic energy of the moving ball was found to be 0.5625 J. Since the collision is elastic, all of this kinetic energy is conserved, giving a combined kinetic energy of 0.5625 J for both balls after the collision. The challenge lies in determining the velocities of each ball post-collision. To solve this, total momentum is conserved and substitution can be used. However, this may result in 0=0 and further assistance may be needed to
lozah

## Homework Statement

A 0.50 kg ball with a speed of 1.5 m/s in the positive direction has a head-on elastic collision with a stationary 0.80 kg ball. What are the velocities of the balls after the collision?

## Homework Equations

I've used the Ek = (1/2)m(v^2) so far.

## The Attempt at a Solution

I used the Ek formula above to find that the kinetic energy of the ball that was initially moving (0.50 kg at 1.5 m/s). It was 0.5625 J, and because it's an elastic collision, all of that Ek is conserved and the combined Ek of both moving balls post-collision should be 0.5625. I'm just unsure of how to find out which ball has which velocity now (the actual hard part of the question, lol). I've used substitution but I keep getting 0=0, lol! Can anyone help me out?

what substitution have you used? remember, it's total momentum that's conserved.

## 1. How do you calculate the velocities of the balls after a collision?

The velocities of the balls after a collision can be calculated using the law of conservation of momentum. This states that the total momentum of the two balls before the collision is equal to the total momentum after the collision. The equation for this is m1v1 + m2v2 = m1v1' + m2v2', where m1 and m2 are the masses of the two balls, v1 and v2 are their velocities before the collision, and v1' and v2' are their velocities after the collision.

## 2. Does the type of collision affect the velocities of the balls after the collision?

Yes, the type of collision can affect the velocities of the balls after the collision. In an elastic collision, the kinetic energy and momentum of the balls are conserved, resulting in the balls bouncing off each other with the same speed and direction as before the collision. In an inelastic collision, some of the kinetic energy is lost and the two balls may stick together after the collision, resulting in a lower velocity for both balls.

## 3. What factors can influence the velocities of the balls after the collision?

The velocities of the balls after a collision can be influenced by factors such as the masses of the balls, the type of collision, the angle at which the balls collide, and any external forces acting on the balls during the collision. Friction and air resistance can also affect the velocities of the balls after the collision.

## 4. Can the velocities of the balls after the collision be greater than their initial velocities?

No, the velocities of the balls after the collision cannot be greater than their initial velocities. This is because the law of conservation of energy states that energy cannot be created or destroyed, only transferred. Therefore, the total kinetic energy of the two balls after the collision cannot exceed the total kinetic energy before the collision.

## 5. How does the angle of collision affect the velocities of the balls after the collision?

The angle of collision can affect the velocities of the balls after the collision. If the angle of collision is head-on, meaning the two balls are moving directly towards each other, the velocities after the collision will be lower compared to a glancing collision, where the two balls collide at an angle. This is because in a head-on collision, the momentum of one ball is completely transferred to the other, while in a glancing collision, only a portion of the momentum is transferred, resulting in higher velocities for both balls after the collision.

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