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Old Oct 29th 2011, 02:02 PM   #1
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Pendulum In a Car

A pendulum of mass 1.0 kg is suspended from the roof of a car travelling on a level road. An observer in the car notices that the pendulum string makes an angle of 10 deg with the vertical. What is the acceleration of the car?

I drew the FBD diagram (attached) and I wrote the vertical and horizontal force equations:
Vertically: Tcos 10 deg=mg
Horizontally: Fc=mv^2/r=Tsin10deg.
So I got he equation mgtan10deg=mv^2/r after putting the equations together. But I don't know the radius of the pendulum, so I don't know how to solve the problem.

Thanks!

Never mind, I'm not supposed to use centripetal force since the pendulum is not going in a circle. Any hints on how to start the problem?

Pendulum In a Car-pendulum-problem.jpg

Last edited by teddybear9; Oct 29th 2011 at 04:52 PM.
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Old Oct 29th 2011, 10:56 PM   #2
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Hmm, you don't have circular motion here. The bob remains in that position for some time.

So that:

Along the vertical: vector sum of forces on the bob = 0 N
Along the horizontal: vector sum of forces on the bob = 0 N

Can you do that from this? Or, do you maybe need some more guides?
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Old Oct 30th 2011, 07:32 AM   #3
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Oh I got it!

Tcos10=mg
Tsin10=ma

Sub T=mg/cos10 into Tsin10=ma, cancel out the m's and solve for a.

But what's the use of the mass given in the problem? Am I supposed to cancel it out?
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Old Oct 30th 2011, 07:35 AM   #4
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Sometimes they give you values which you can very well do without

Someone else might have solved for the value of T, and used that in the second equation to get the same answer.

But I would say you did a good job here, well done!
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Old Oct 30th 2011, 08:42 AM   #5
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Thank you so much!
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