Conservation of Angular Momentum in Collision with Rotations

[maniacp08]

A uniform rod of length L1 = 2.2 m and mass M = 2.8 kg is supported by a hinge at one end and is free to rotate in the vertical plane. The rod is released from rest in the position shown. A particle of mass m is supported by a thin string of length L2 = 1.8 m from the hinge. The particle sticks to the rod on contact. After the collision, θmax = 40°.

(a) Find m.
kg
(b) How much energy is dissipated during the collision?
J

Relevant Equations:
Angular momentum = I * omega


I'm having trouble starting this problem. I should compare using energy of conservation before and after collision correct?

I for the thin rod = 1/3 ML^2

Energy of conservation for the rod before collision
Kf - Ki + Uf - Ui = 0
Ki = 0
Kf + Uf - Ui = 0
1/2(1/3ML^2) * omega ^2 + Uf - Ui = 0
What will Uf and Ui be?

Im not even sure if what I am doing is correct, can someone guide me?

 

[maniacp08]

Anyone can help me get started with this problem please.

 

[alphysicist]

Hi maniacp08,

A uniform rod of length L1 = 2.2 m and mass M = 2.8 kg is supported by a hinge at one end and is free to rotate in the vertical plane. The rod is released from rest in the position shown. A particle of mass m is supported by a thin string of length L2 = 1.8 m from the hinge. The particle sticks to the rod on contact. After the collision, θmax = 40°.

(a) Find m.
kg
(b) How much energy is dissipated during the collision?
J

Relevant Equations:
Angular momentum = I * omega


I'm having trouble starting this problem. I should compare using energy of conservation before and after collision correct?

You will compare them for part b, because kinetic energy is not conserved in this collision and the difference in energies will be equal to how much energy is dissipated.

You can use conservation of energy for other parts of this problem (you have to consider the swinging motion before the collision, and the swinging motion after the collision), but for the collision itself, what is conserved?

 

[maniacp08]

Hi, alphysicist, thanks for responding.

The collision itself, the angular momentum is conserved.
Angular momentum = I * omega

Do I consider the before collision or after collision first?
Do I use conservation of energy on the particle or the rod?
Im just confuse on how to start this.

 

[alphysicist]

Hi, alphysicist, thanks for responding.

The collision itself, the angular momentum is conserved.
Angular momentum = I * omega

Do I consider the before collision or after collision first?
Do I use conservation of energy on the particle or the rod?
Im just confuse on how to start this.

To use conservation of angular momentum for the collision, you don't do either one first, you set them equal to each other.

So the angular momentum of the system right before the collision (the instant the rod touches the particle) is equal to the total angular momentum of both of them right after the collision is over. Setting up that equation will then show you what else you need to find in the problem.