TBR Physics Passage 1 #3

[LuminousTruth]

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A scientist operating a pendum in an elevator sees that the pendulum's period is shorter than can be accounted for by gravity alone if she takes measurements when the pendulum apparatus is moving with a constant:

A) Upward velocity
B) Downward velocity
C) Downward acceleration
D) Upward acceleration

A greater 'g' means a shorter period. To get a greater ‘net’ gravitational force in the pendulum, T=2p*root(L/g), in addition to gravity, there should be constant acceleration that is in the SAME DIRECTION as g.

Here is where I do not understand:
In a free-body diagram, a downward acceleration would indicate: T-mg=m(-a) => g=(T+ma)/m. Wouldn't that mean an increase in acceleration to be an increase in g? So I got C.

Can anyone show me how you would do the freebody diagram so you get the correct answer D instead of C?

 

[jstigler]

Can't help with the free body diagram but you want the perceived net force on the pendulum to increase. To do this you have to accelerate against gravity. Think of what would happen if you stood on a scale in the same elevator and watched your perceived weight change based on accelerating with or against gravity.
If you already knew this and just wanted help with free body you are welcome to throw things at me.

 

[circulus vitios]

I'm sure there is a way to do this with free body diagrams but you're over thinking this like jstigler said. You know that the period of a pendulum is inversely proportional to gravitational acceleration, so you want a situation that increases G. You know that gravitational acceleration gives you the feeling of weight, so think about the last time you road an elevator. When did you feel heaviest: when the elevator accelerated upward, when the elevator moved upward with constant velocity, when the elevator accelerated downward, or when the elevator moved downward with constant velocity?

 

[milski]

You cannot increase gravity - it is a constant, at least at small distances from Earth. What the previous two posters said should be fairly helpful. If you want to approach the problem in a more formal way, you have to consider that the g in the formula for the period is related to the tension of the string, so a way to "increase g" is to increase the tension in the string and the way to do that is by a force applied upward, which means an acceleration upward. That's still only an estimation but the exact derivation of what the motion will be gets too complicated.