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mHo2
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Homework Statement
Problem:
A pendulum with a 1kg mass hangs from the roof of a car traveling on a level road. The pendulum string makes an angle of 10° with the vertical as shown. Determine the cars acceleration (Hint: The acceleration of the car is the same as that of the pendulum)
(i'm assuming this is centripetal acceleration as it's on a centripetal force worksheet).
Known Variables:
g = -10m/s/s
mass = 1kg
string is assumed massless, ridgid, and even tension throughout.
Homework Equations
a=v^2/r
F=ma
The Attempt at a Solution
[PLAIN]http://k.min.us/imvCIg.jpg The problem isn't so much in the calculation, which is what i solved in the picture.
My question is, why does the pendulum make the 10° angle with the vertical? Would it be the cause of a reaction force since the tension is pulling the object in a horizontal direction? Is it because it wants to go in its original direction?
If it is a cause of the latter, wouldn't taking this corner at a higher velocity cause the angle to be smaller, since centripetal acceleration is a power relationship of velocity? Also if it is the latter again, can someone explain to me why its velocity is always in a different trajectory than that of the car? Couldn't they equalize? (and therefore be straight up and down along the vertical)
Can someone explain this intuitively to me?
And extending upon this question, why does a pendulum go back and forth when a car is accelerating?
Any insight would be fantastic, thanks!
- Mat
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