Can someone help me with Equilibirum?

  • Thread starter jinman
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  • #1
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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.
 

Answers and Replies

  • #2
Hootenanny
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Welcome to PF jinman,

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

P=P

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

m1v1=m2v2

v1=m2(wr)/m1

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

v1*sin 60=2888.91m/s???
 
  • #7
Doc Al
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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
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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
Doc Al
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http://hyperphysics.phy-astr.gsu.edu/Hbase/amom.html" [Broken]
 
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