Percentage of kinetic energy after an elastic collision

In summary, the conversation discusses a problem involving a stationary object with mass mb being struck by an object with mass ma moving at speed v0 in an elastic collision. The question is what percentage of the original energy does each object have after the collision. The equations K1 and K2 are used to represent the kinetic energy before and after the collision, and the attempt at a solution involves finding the velocities of the objects in terms of mass and initial velocity. The final step is to plug these velocities into the kinetic energy equations and solve for the percentage of energy.
  • #1
clope023
992
131

Homework Statement



A stationary object with mass mb is struck head-on by an object with mass ma that is moving initially at speed v0.

If the collision is elastic, what percentage of the original energy does each object have after the collision?

KA2/K1 = ?

KB2/K1 = ?

Homework Equations



K1 = 1/2mav1a^2 + 1/2mbv1b^2

K2 = 1/2mav2a^2 + 1/2mbv2b^2

The Attempt at a Solution



K1/K2A = (1/2mav1a^2 + 1/2mbv1b^2)/(1/2mav2a^2)

= v1a^2/v2a^2 + mbv1b^2/mav2a^2

I'm not sure how to proceed from here and get a percentage.

any help is appreciated.
 
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  • #2
mbvo=mbv1+mav2(mv conserved)
mbvo^2= mbv1^2+mav2^2(KE conserved)
making use of these equations, find v1,v2 in terms of mass. and vo...
 
  • #3
v0 = v1 + mav2/mb

v1 = v0 - mav2/mb

v2 = mbv0/ma - mbv1/ma




found the velocities, but I'm not sure how to proceed.
 
  • #4
nobody?

I'm not sure what to do with these values?

plug them into the kinetic energy equations and solve perhaps?
 

1. What is the formula for calculating the percentage of kinetic energy after an elastic collision?

The formula for calculating the percentage of kinetic energy after an elastic collision is:

Percentage of kinetic energy = (Final kinetic energy / Initial kinetic energy) x 100%

2. How is elastic collision different from inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved, meaning that the total kinetic energy and momentum before the collision are equal to the total kinetic energy and momentum after the collision. In contrast, in an inelastic collision, some of the kinetic energy is converted into other forms, such as heat or sound, and the total kinetic energy is not conserved.

3. Can the percentage of kinetic energy after an elastic collision be greater than 100%?

No, the percentage of kinetic energy after an elastic collision cannot be greater than 100%. This is because the law of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. Therefore, the total kinetic energy after the collision cannot be greater than the initial kinetic energy.

4. How does the mass and velocity of the objects affect the percentage of kinetic energy after an elastic collision?

The percentage of kinetic energy after an elastic collision is affected by the mass and velocity of the objects involved. The greater the mass and velocity of the objects, the greater the initial kinetic energy and therefore the greater the percentage of kinetic energy after the collision. However, the percentage of kinetic energy will still be less than 100% due to the conservation of energy.

5. Is the percentage of kinetic energy after an elastic collision always the same for all types of collisions?

No, the percentage of kinetic energy after an elastic collision can vary depending on the type of collision. For example, a head-on collision between two objects of equal mass and velocity will result in a different percentage of kinetic energy than a glancing collision between the same two objects. However, in all cases of elastic collisions, the total kinetic energy will be conserved.

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