If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 11 Physics (India)>Unit 10

Lesson 9: Elastic and inelastic collisions

# How to use the shortcut for solving elastic collisions

In this video, David solves an example elastic collision problem to find the final velocities using the easier/shortcut approach. Created by David SantoPietro.

## Want to join the conversation?

• so V1i + v1f = V2i + V2f only used for Elastic Collision?
• Yes, it is correct as it was derived from conservation of momentum and conservation of kinetic energy which will happen only in elastic collisions
• What if there is elastic collision in two dimension?
Will we take components and then apply the formula?
• Yes, apply conservation of momentum for each dimension separately. That means breaking up the momentum vectors into components parallel to each dimension.
If the collision is elastic, kinetic energy will also remain unchanged before and after the collision, but for inelastic collisions, this is not true. Momentum however will always be conserved for both elastic and inelastic collisions.
• Dear Tutors:
Please explain how the golf ball gained speed after the collision? Initial velocity of the golf ball was 50 m/s. Final velocity of golf ball was calculated to be 51.36 m/s. Is this an error?
• @S26Patel, as explained here by Andrew M here above, it means in other words that the energy of the objects is transferred to one another. The law of conservation of energy says that energy is never really 'lost', it only is transferred to another object or another form of energy. Either within the system of the problem or to outside of the problem, but that is another story.

Basicly this means that a huge mass(M1) with high velocity (and thus high energy) when colliding with a way smaller mass(M2) with a certain velocity, M1 will transfer some of it's energy to M2. And because E_kin = 1/2 * mass * velocity^2; this means that M2 will gain more velocity because it has less mass. If the exactly same amount of velocity lost by M1 would be gained by M2, there must have been some energy transferred into heat or something else.
• can you solve of either velocity originally or should you pick a certain one to make it easier? Say if one object was at rest already would it be easier to solve for it's velocity since it's initial KE is 0?
• If one of the objects was initially at rest, then its initial momentum would cancel out because the initial velocity of that object would be zero. So, the momentum equation would be just V1f = V2i + V2f.
Hope this helps!
• So am I correct in assuming that V1ix + V1fx = V2ix + V2fx and the same for any other dimension if I needed to decompose velocity vectors in a higher dimensional problem?
• The best way to start a collision problem in 2 or 3 dimensions (3 dimensional collisions problems are very rare) is to select an appropriate set of coordinates. If you have two dots or spheres colliding, which is almost always the case, then the best coordinates will have an axis connecting their centres at the moment of collision, and an axis perpendicular to that. This system will give you the easiest equations. In one of the axis, the one connecting the centres, the solution is exactly like a one dimensional collision, and the other 2 axis show no change in each of the objects' velocity (if there's no friction).
• Is there a way of roughly estimating how much final velocity is lost, for example, by heat and sound? How would I deduct this from my final answer?
• When elastic collisions occur, the momentum is conserved (or constant), so there is no velocity lost to heat and sound, in this specific problem, with particular factors assumed.
(1 vote)
• is there any video explaining coeffeicient of restitution
(1 vote)
• what happened to the kilograms when he multiplied it
(1 vote)
• Canceled out
• Hello! I had an exam today and the first question was asking to find the INITIAL and FINAL velocities of the second ball, when the first ball's initial and final velocity values were given. How would one go about solving this problem?

Ball 1: m=3.0kg
vi= 6.0m/s
vf= 0.5m/s

ELASTIC COLLISION

Ball 2: m= 2.0kg
Vi= ?
Vf= ?
(1 vote)
• >Let Ball 1(A) have a mass(m) of 3kg velocity of vi m/s initially and vf m/s finally in the +x direction.
>Let Ball 2(B) have a mass(M) of 2kg velocity of Vi m/s initially and Vf m/s finally in the +x direction.

So, applying the conservation of linear momentum:
=> m(vi)+M(Vi)=m(vf)+M(Vf)
OR:
=> 3(6)+2Vi=3(1/2)+2Vf
=> 18+2Vi=(3+4Vf)/2
=> 36+4Vi=3+4Vf
=> 4Vf-4Vi=33 ...(i)

Now, using the formula for the coefficient of restitution:
e=(v2-v1)/(u1-u2)
OR:
(Vf-0.5)/(6-Vi)=1 [Elastic Collision]
=> Vf-(1/2)=6-Vi
=> 2Vf-1=12-2Vi
=> 2Vf+2Vi=13
=> 4Vf+4Vi=26 ...(ii)