Perfectly elastic collision

In summary, in an isolated system, cart1 with mass 1 kg and initial velocity 2 has a perfectly elastic collision with cart2 with mass 2 kg and initial velocity 0. Using kinetic energy and momentum equations, the velocity of cart1 after the collision is 2/3 and the velocity of cart2 after the collision is 4/3. To solve for these velocities, the equations m1vi1 + m2vi2 = m1v1f + m2v2f and 1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2 were used.
  • #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.
I have to solve this using kinetic energy and momentum equations.


Homework Equations


m1vi1 + m2vi2 = m1v1f + m2v2f
1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2


The Attempt at a Solution


I have gotten to this point:
2= V1F + 2V2F
4= V1F2 + 2V2F

but I cannot get the numbers to work out correctly.
Using another equation I know that V1f = 2/3 and V2f = 4/3

I am doing substitution wrong or something.
Please help!
 
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  • #2
southernbelle said:

The Attempt at a Solution


I have gotten to this point:
2= V1F + 2V2F
This makes sense.
4= V1F2 + 2V2F
How did you get this?
 
  • #3
I got that by solving the kinetic energy equation.
I mutiplied both sides by 2 to get rid of the halves.

It is actually supposed to read:

4 = Vif^2 + 2V2f^2
 
  • #4
southernbelle said:
It is actually supposed to read:

4 = Vif^2 + 2V2f^2
That's good.

Take the first equation and solve for one of your variables. Then substitute that into the second equation. Solve the quadratic.
 

What is a perfectly elastic collision?

A perfectly 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 rebound without any loss of energy.

What are the conditions for a perfectly elastic collision?

In order for a collision to be perfectly elastic, the objects must not deform upon impact and there must be no external forces acting on the system. This means that the collision must occur in a vacuum or in an environment with minimal air resistance.

What is the equation for calculating the final velocities in a perfectly elastic collision?

The equation for calculating the final velocities in a perfectly elastic collision is:

v1f = (m1-m2)v1i + 2m2v2i / (m1+m2)

v2f = 2m1v1i + (m2-m1)v2i / (m1+m2)

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

In a perfectly elastic collision, the kinetic energy of the system is conserved, while in an inelastic collision, there is a loss of kinetic energy due to deformation or other external forces. In an inelastic collision, the objects may stick together or move with reduced velocity after the collision.

Can a real-life collision be perfectly elastic?

In theory, a perfectly elastic collision is possible, but in reality, it is difficult to achieve. Most collisions involve some loss of energy due to friction, air resistance, or deformation of the objects involved. However, in situations where these factors are minimal, a collision can be close to perfectly elastic.

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