How do I find e?
#momentum problem
lean sapphire
crisp crystalBOT
How do I find e?
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waxen fox
How do I find e?
By definition, e^2 = T(final)/T(initial).
lean sapphire
By definition, e^2 = T(final)/T(initial).
How did you derive this formula?
I was told that the coefficient for restitution
waxen fox
How did you derive this formula?
As I said, this is the definition of coefficient of restitution.
lean sapphire
Was equal to the ratio of the velocities of separation
To the velocities of approach
waxen fox
Was equal to the ratio of the velocities of separation
Ah, that's just a consequence.
lean sapphire
As I said, this is the definition of coefficient of restitution.
Ah
lean sapphire
As I said, this is the definition of coefficient of restitution.
Let me google that in that case
@waxen fox
None of em mention the formula
You’re talking about
waxen fox
Hm, unusual. I guess different textbooks mention different definitions. Doesn't really matter.
lean sapphire
Hm, unusual. I guess different textbooks mention different definitions. Doesn't ...
What the formula again?
That you mentioned?
waxen fox
What the formula again?
Well, as I said above, the squared coefficient of restitution is equal to the ratio of final to initial kinetic energy.
lean sapphire
Well, as I said above, the squared coefficient of restitution is equal to the ra...
Ok let me plug the values in this formula and then find out the result
e^2= k.e(final)/k.e(initial) right?
waxen fox
e^2= k.e(final)/k.e(initial) right?
Yes. I prefer to denote kinetic energy by T, though.
As long as there isn't a tension force in context, of course.
lean sapphire
As long as there isn't a tension force in context, of course.
Wrong answer mr pinger
It should be 0.5 or 1/2
I’m getting 0.7
:/
waxen fox
Hm. I'd also say that e = 1/√(2). That's a bit odd.
waxen fox
:/
I don't know. I'd say there's a mistake in their answer. Let me check the velocity of p, too.
lean sapphire
I don't know. I'd say there's a mistake in their answer. Let me check the veloci...
Okie dokie
waxen fox
Okie dokie
Hold on, the derivation is pretty long. I think I'll do it in Word.
waxen fox
I don't think that's a good idea.
lean sapphire
It gave the right answer tho
Can’t post the whole thing
Coz there’s apparently a world limit
But I got the right answer
waxen fox
Well, I'm currently writing the general case. Give me 10-15 minutes.
waxen fox
Ahh, I see where I went wrong in my definition. That only worked when one object is completely stationary. The energy definition in case of two moving objects is more complex.
Well, that's fine - we'll use the velocity definition.
waxen fox
Okie thanks I’ll look into your solution once you post it as well
Alright, I got it! In our case:
m(P) = m
v0(P) = 3u
m(Q) = 2m
v0(Q) = 0
So:
(a).
e(crit) = ((m(P)/m(Q))v0(P) + v0(Q))/(v0(P) - v0(Q)) = ((1/2)*3u + 0)/(3u - 0) = 1/2
(b).
e = √(1 - (1 - T/T0)(1/m(P) + 1/m(Q))(m(P)v0(P)^2 + m(Q)v0(Q)^2)/(v0(Q) - v0(P))^2) = √(1 - (1 - 1/2)(1/m + 1/(2m))(m*(3u)^2 + 2m*0^2)/(0 - 3u)^2) = 1/2
v(P) = (m(P)v0(P) + m(Q)v0(Q) + em(Q)(v0(Q) - v0(P)))/(m(P) + m(Q)) = (m*(3u) + 2m*0 + (1/2)*(2m)(0 - 3u))/(m + 2m) = 0
