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Collision in 2D

# 2-dimensional momentum problem (part 2)

We finish the 2-dimensional momentum problem. Created by Sal Khan.

## Want to join the conversation?

• At - Is it necessarily true that having a smaller mass will mean it (ball B) is deflected at a larger angle?

Does having a smaller mass result in a larger degree of deflection? To me I think it is more complicated than that. •   Without doing any rigorous proof, I'll try to explain it.

1/ "An object at rest tends to stay at rest."
Initially, both balls have no y-component value, thus they are at rest in the y direction, thus they will tend to resist moving in the y direction.

2/ We also know F = ma -> a = F/m. Essentially, this tells us that the mass is inversely proportional to the acceleration (or change in movement, so to imagine). This translates into "The more mass something has, the higher its tendency to maintain its motional state."

From the above 2 premises, we can conclude that both ball A and ball B will resist their movement in the y direction (the deflection angle), but ball A will be more successful due to its higher mass.
• • How is energy conserved in this system? I get that you have momentum conserved because the Y components cancel out.
But it seems like if you took the kinetic energy of the balls separately and added them together you would have a greater amount of energy than there was before? • Assuming that there is no difference in potential energy, the change in energy would be completely accounted for by kinetic energy.
The kinetic energy of ball A initially is (1/2)mv^2 = (1/2)(10)(3^2) = 45J
The kinetic energy of ball B initially is (1/2)mv^2 = (1/2)(5)(0^2) = 0J.
So, initial kinetic energy = 45 + 0 = 45J.

Final kinetic energy for ball A = (1/2)(10)(2^2) = 20J.
Final kinetic energy for ball B = (1/2)(5)(3.2^2) = 25.6J.
Final kinetic energy = 20 + 25.6 = 45.6J (but wait!)

Now it may seem that kinetic energy has increased, but Sal has been rounding his values and this extra 0.6J can be wholly attributed to rounding errors. It is completely safe to say that kinetic energy is conserved. If you re-do the problem with a good calculator and take values at 4 (or so) decimal places, you'll get a value of 45J for the final kinetic energy
• at how do you know momentum is conserved? does it tell you this in the problem?? • What everone will tell you is that momentum is not conserved only when an external force acts on the system.
It's not a matter of what forces are acting, it's just a matter of including all object exerting forces in the system. For example, (2 pendulums, one held at 90o to the left and one held at 90o to the right. They are let go and collide at the bottom (zero degree). is momentum conserved? the answer is no because gravity is acting on both pendulums.) the two pendulums have gravity acting on them. That's exerted by the Earth itself. Either you need to include the Earth in the system and account for the transfer of momentum from the pendulum to the Earth or you have to consider the Earth as an external force. The former has no external forces and has a constant momentum, the later does not since gravity is an external force.
Think about a canary in a cage, then let the canary out of the cage but in your room. If you treat the cage as the system, the canary is not preserved. But if you expand your system to include more objects (your room), the canary is preserved.
To sum it up, if momentum is not conserved, your system is not big enough.
• Initial momentum of A + Initial momentum of B = 30. Final moentum of A + Final momentum of B = 20 + 16 = 36. Now where does this 6 additional momentum come from and how is it conserved? • Okay, so this is just a weird thought - if momentum is conserved, does that mean that the universe, taken as a system, has a momentum of zero (or some other such constant)? • Throughout the question, we assume that ball A is deflected at 30 degrees. Would ball A actually deflect at 30 degrees? If not, how could we find the actual angle it would deflect at? • • I'm taking a physics class right now and we had an experiment just like that. The output angle between the two balls is ALWAYS 90 DEGREES, something must be wrong with thoses numbers Sal is inputing because the angle between the two balls at output can't be 68 degrees.
(1 vote) • I cant completely understand what is momentum? is it another form of potentional energy converting to kinetic and vice versa?

Also, this is a stupid qquestion but im gonna ask it anyway, if a skier accelerates from a hill downwards for a while, has he a momentum or a force? because
F = ma but momentum is p=mv

(1 vote) • No, momentum is not energy, it is its own thing. It is mass*velocity. You can think of it as how hard it is to stop an object that is in motion. A big heavy object is hard to stop once it is moving. A light object is easier. The light object has less momentum.

Also, It is harder to stop the big object if it is moving faster. than when it is moving slow. It has more momentum.

Momentum is useful because it is conserved.

Newton's law F = ma was originally formulated with momentum: F = rate of change in momentum