What are the velocities of the carts after a perfectly elastic collision?

In summary: Thank you for your help. In summary, the initial velocities of the two carts were given as 2 m/s and 0 m/s, with masses of 1 kg and 2 kg respectively. Using the equations for kinetic energy and momentum, the final velocities of the carts were calculated to be -2 m/s and 2 m/s. However, upon checking the equations, it was determined that these velocities do not satisfy both equations simultaneously. Therefore, the given solution is not correct.
  • #1
southernbelle
35
0

Homework Statement


In an isolated system, cart1 (with mass = 1 kg and vi1 = 2) has a perfectly elastic collision with cart2 (with mass = 2 kg and vi2 = 0). Find the velocity of cart1 and the velocity of cart2 after the collision.


Homework Equations


1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2

m1vi1 + m2v2i = m1v1f + m2v2f


The Attempt at a Solution



I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f2 + 2V2f2

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2
 
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  • #2
southernbelle said:

Homework Statement


In an isolated system, cart1 (with mass = 1 kg and vi1 = 2) has a perfectly elastic collision with cart2 (with mass = 2 kg and vi2 = 0). Find the velocity of cart1 and the velocity of cart2 after the collision.


Homework Equations


1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2

m1vi1 + m2v2i = m1v1f + m2v2f


The Attempt at a Solution



I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f2 + 2V2f2

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2
You could check your answers yourself. Do they satisfy both the kinetic energy and momentum equations?
 
  • #3
No, they don't. You're right that was an easy way to check myself.
 

1. What is a perfectly elastic collision?

A perfectly elastic collision is a type of collision where kinetic energy is conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

2. What is the difference between a perfectly elastic collision and an inelastic collision?

In a perfectly elastic collision, kinetic energy is conserved, while in an inelastic collision, kinetic energy is not conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

3. Can a perfectly elastic collision occur in real life?

Yes, perfectly elastic collisions can occur in real life, although they are rare. Examples include collisions between gas molecules, collisions between atoms in a crystal lattice, and collisions between subatomic particles.

4. How is the coefficient of restitution related to perfectly elastic collisions?

The coefficient of restitution is a measure of how much kinetic energy is conserved in a collision. In a perfectly elastic collision, the coefficient of restitution is equal to 1, meaning that all of the kinetic energy is conserved. In other types of collisions, the coefficient of restitution is less than 1.

5. What is the formula for calculating the velocity after a perfectly elastic collision?

The formula for calculating the velocity after a perfectly elastic collision is v1f = ((m1-m2)v1i + 2m2v2i)/(m1+m2), where v1f is the final velocity of the first object, v1i is the initial velocity of the first object, m1 is the mass of the first object, v2i is the initial velocity of the second object, and m2 is the mass of the second object.

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