Can someone help me with Equilibirum?

  • Thread starter jinman
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In summary, the conversation discusses a problem involving a uniform thin rod rotating about a vertical axis, with a bullet being fired into one end at a certain angle. The bullet lodges itself in the rod, making it a perfectly inelastic collision. The conversation goes on to discuss the conservation of momentum and how it applies to this problem. The participants also mention that kinetic energy is not conserved in this case and that only one type of momentum is conserved. The conversation ends with a question about finding the angular velocity of the bullet before the collision.
  • #1
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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  • #2
Welcome to PF jinman,

The collision isn't elastic and therefore kinetic energy isn't conserved. What is always conserved?
 
  • #3
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?
 
  • #4
I don't know why i put Equilibrium. It must be momentum.

P=P

mv=Iw??
 
  • #5
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?
 
  • #6
I would say linear.

m1v1=m2v2

v1=m2(wr)/m1

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

v1*sin 60=2888.91m/s?
 
  • #7
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.
 
  • #8
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?
 
  • #9
http://hyperphysics.phy-astr.gsu.edu/Hbase/amom.html"
 
Last edited by a moderator:

1. What is equilibrium in science?

Equilibrium in science refers to a state of balance or stability in a system or process. It occurs when the forces or factors acting on the system are equal and opposite, resulting in no overall change or movement.

2. How do you calculate equilibrium?

The calculation of equilibrium depends on the specific system being studied. However, in general, equilibrium can be determined by setting the rate of the forward reaction equal to the rate of the reverse reaction, or by using the equilibrium constant equation.

3. What is the difference between dynamic and static equilibrium?

Dynamic equilibrium refers to a state where the forward and reverse reactions are occurring at equal rates, resulting in no net change in the system. Static equilibrium, on the other hand, refers to a state where there is no movement or change in a system, such as a stationary object.

4. How does equilibrium relate to Le Chatelier's principle?

Le Chatelier's principle states that when a system at equilibrium is subjected to a stress, it will shift in a direction that minimizes the effect of that stress. This means that when equilibrium is disturbed, the system will try to return to the state of equilibrium by shifting in the opposite direction of the stress.

5. What factors can affect equilibrium?

Several factors can affect equilibrium, including temperature, pressure, and concentration of reactants and products. Changes in these factors can shift the equilibrium position, leading to a change in the concentrations of reactants and products.

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