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### Course: Physics library>Unit 6

Lesson 2: Elastic and inelastic collisions

# Solving elastic collision problems the hard way

In this video, David shows how to solve elastic problems the hard way. In other words, using conservation of momentum and conservation of kinetic energy, David substitutes one equation into the other and solves for the final velocities. Created by David SantoPietro.

## Want to join the conversation?

• Is it impossible for an object to come to a complete stop after an elastic collision?
• If a ball of mass m and velocity v hits another ball of mass m but without any speed, the first ball will come to a complete stop due to the elastic collision, while the second ball acquires speed v ( assuming they collided with their centres aligned with the velocity).
• I know that it's not possible for an elastic (or "perfectly elastic") collision in nature. However, is it possible for a perfectly inelastic collision to occur?
Why, or why not?
• Yes, when objects stick together after the collision, that's perfectly inelastic. Clay balls can collide and stick together, train cars link together, paint balls go splat, etc.
• When we rewrote Vg in terms of Vt, why didn't we substitute it directly in the momentum equation instead of the kinetic energy equation?
• Let's try(omitting the units):
(0.07 - 0.058*V_t)/0.045 = V_g
1.56 - 1.29 * V_t = V_g
Insert it:
0.07 = 0.058 * V_t + 0.045 * V_g
0.07 = 0.058 * V_t + 0.045 * (1.56 - 1.29 * V_t)
0.07 = 0.058 * V_t + 0.07 - 0.058 * V_t
0.07 = 0.058 * V_t - 0.058 * V_t + 0.07
0.07 = 0.07
• Could you have found an expression for Vg using the KE formula, and then used it to solve the momentum equation, rather than the other way around?
(1 vote)
• What if you had two balls with the same mass, but one ball bounces off and one ball sticks on a block. How can you tell which direction the block moves after the collision?
(1 vote)
• how can we know whether the two balls after collision will move in same direction or opposite? Both in Elastic & Inelastic collision?
(1 vote)
• You'd have to work out the momentum before and after the collision. Without knowing the masses of the two balls and their velocity before the collision, plus the trigonometry of the collision, it's impossible to say what the outcome of the collision will be.
• For a collision to be accepted as elastic, how close do the kinetic energies have to come to become equal to one another? I understand that nothing is perfect, so to be known as 'elastic', do the kinetic energies differ by 0.01 or 0.1 J, etc.?
(1 vote)
• That’s arbitrary. An elastic collision is defined as one in which kinetic energies(initial and final) are equal. However, if the difference in energy is insignificant compared to the total final and initial energies, we can say that the collision is elastic for the sake of the experiment.
(1 vote)
• If it weren't an elastic collision could we do it? (Without knowing anything but what it is know in this one)
(1 vote)
• Yes we could, in case we were given the fact that it is perfectly inelastic collision. Because if it is inelastic collision then we know that final velocities are same and it would be pretty straightforward.
(1 vote)
• you assumed almost no time while collision as a provision for momentum conservation by avoiding external impulse due to external forces, and said "like gravity". why do we concern about the impulse due to gravitational force while it acts perpendicular to the velocity and momentum direction which implies that it will not affect our velocities and momentum in the x direction. even the kinetic energy in the x direction will not be affected. actually i think that this duration of time is required for momentum conservation, it is the time where momentum redistributed or partially interchanged between the collided objects. and eventually we are concerned with the impulses due to forces in the same direction of our interest, you made emphasis on the one direction in our example here, again, is gravitational force live in our dimension?
(1 vote)
• How can the difference in the objects' initial momentum be equal to the sum of the objects final momentum and momentum still be conserved?
(1 vote)
• Listen, if you made good enough attention you can see that both balls have direction. And you just have to choose one of them as negative because that the direction of balls are opposite to each other. And because we don't know directions of balls after the hit, we simply add two momentum that we would get after the hit.
(1 vote)