The rod (angular momentum angular velocity etc.) help eksam tomorrow

[jhthorn]

Homework Statement

a homogeneous rod of length 2l and mass M can turn without friction in a horizontal plane and about a fixed vertical axis O through the center of mass of the rod. initially, the rod is at rest. A particle of mass m collides in a short, completely elastic collision with one end of the rod. it is assumed that the collision time Δt is so short that the rod does not turn during the collision. the velocity of the particle (both before and after the collision) is horizontal, and perpendicular to the original direction of the rod. the magnitude of the velocity of m before the collision is u.

1. find the velocity of m and the angular velocity ω of the rod after the collision

2. it is assumed that the force F by witch the particle acts on the rod is constant during the colision. Find F. numerical eksample: l=0.30m, M=0.3kg, m=0.04kg, u=20 m/s, Δt=10^-2s.

Homework Equations

1. the relevant must be there's must be energy conservation and conservation of angular momentum

2. i don't have a clue

The Attempt at a Solution

1.
to find the velocity of m I think i need to use that:

1/2mu^2=1/2mv^2+1/2Iω^2

I=1/12M(2^l)^2

and the solution would then be:

mu^2=mv^2+1/3Mu^2

i use that ω=u/r and r=l

(3m-M)u^2=3mv^2

is this right? (i don't think so! but what is wrong?)


to find the angular velocity i use conservation of angular momentum

L[/i] = mul
L[/f]= Iω+ml^2ω

I=(1/12)M4l^2

mul=(1/3)Ml^2ω+ml^2ω

3mul=ω(Ml^2+3ml^2)⇔

ω=(3mu)/(Ml+3ml)

is this right?


2.
and the last question i don't know how to start I'm not sure.

I hope you can help me, ´thanks

 

[voko]

to find the velocity of m I think i need to use that:

1/2mu^2=1/2mv^2+1/2Iω^2

I=1/12M(2^l)^2

and the solution would then be:

mu^2=mv^2+1/3Mu^2

i use that ω=u/r and r=l

What is the basis for "ω=u/r"? Imagine a very massive rod and a very tiny mass. Do you really think the rod will spin as fast as the incoming projectile?

L[/f]= Iω+ml^2ω

Also incorrect, same reason.

You need to have equations relating u, v and ω. From conservation of energy and angular momentum you will have two equations, which you should be able to solve for the two unknowns u and ω.

 

[jhthorn]

the reason i choose ω=u/r was because of the rod wil perform a uniform circular motion and i couldn't se what else to do. But all the energy from the speed will not be transferred to the rod because it is an elastisc collision, i get that. So i have to use (u-v) insted of ω?

L[/f] is that equal to Iω+ml(u-v) then and then i plot in the equation for v?

 

[andrien]

for the second one I will say to find out the change in momentum of particle and divide it by time Δt ,since velocity of particle is in same line after collision so it is simple.but correct your first part first.