How Do You Solve Equilibrium Problems in Physics?

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Homework Help Overview

The discussion revolves around a physics problem involving a uniform thin rod and a bullet, focusing on the principles of momentum and energy conservation during a collision. The original poster expresses confusion about setting up the problem and identifying the relevant concepts, mistakenly referring to it as an equilibrium problem.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the conservation of momentum and energy, questioning the nature of the collision (elastic vs. inelastic) and the conservation laws that apply. There is discussion about the correct equations to use and the definitions of linear and angular momentum.

Discussion Status

Participants are actively engaging with the problem, clarifying concepts and correcting misunderstandings. Some guidance has been offered regarding the conservation of momentum, particularly in the context of inelastic collisions, but there is no explicit consensus on the approach to take.

Contextual Notes

There is a noted confusion regarding the classification of the problem as an equilibrium problem, which is not applicable here. Participants are also grappling with the implications of the rod being fixed at a rotational axis, affecting the conservation of linear momentum.

jinman
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I don't understand how to do equilibrium problems. I don't know how to set them up and where to start. here is an example. Can anyone please help?

Homework Statement



A uniform thin rod of length 0.50m and mass 4.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0g bullet traveling in the rotation plane is fired into one end of the bullet's path makes angle = 60.0 degrees with the rod. If the bullet lodges into the and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet's speed just before impact.


Homework Equations



1/2mv^2=1/2Iw^2
I=1/12ML^2

The Attempt at a Solution



K-initial=K-final

1/2mv^2=1/2Iw^2


solve for v>>>>

v=sq. root[Iw^2/m]

v=sq. root[(1/12*ML^2)w^2/m]

v=sq.root.[(1/12*4.003*.50^2)*10^2/.003]

v=52.7m/s

The answer is 1.3*10^3m/s.
 
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Welcome to PF jinman,

The collision isn't elastic and therefore kinetic energy isn't conserved. What is always conserved?
 
This is not an equilibrium problem (not sure what you mean by that, anyway).

I assume the bullet lodges itself in the rod, making this a perfectly inelastic collision. Kinetic energy is not conserved. But something else is. What?
 
I don't know why i put Equilibrium. It must be momentum.

P=P

mv=Iw??
 
jinman said:
I don't know why i put Equilibrium. It must be momentum.

P=P

mv=Iw??
Don't mix up linear momentum (p) with angular momentum (Iw). In this case, only one of them is conserved. Which one?
 
I would say linear.

m1v1=m2v2

v1=m2(wr)/m1

v1=4.003(10*.25)/ .003

v1*sin 60=2888.91m/s?
 
No, linear momentum is not conserved. I assume the rod is restrained by some fixed axis to only rotate about its center. That axis exerts a force on the rod, thus linear momentum is not conserved.
 
Ok.

I1w1=I2w2

w1=I2w2/I1

OK so I have to find the angular velocity of the bullet before the collision? How can i find the Inertia of the bullet?
 
http://hyperphysics.phy-astr.gsu.edu/Hbase/amom.html"
 
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