TBR Pendulum Question

[salsasunrise123]

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Can someone please explain the intuition behind this question. I am trying to visualize it in equation form but I am kinda stuck and don't really follow the explanation the book gives. Thanks.


A scientist operating a pendulum 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.

Answer is D

 

[brood910]

scale = w(1 + a/g)

If you accelerate upwards, you will feel heavier because a is + in the equation above. In other words, g feels "larger".
Same goes for other equations with g in it.

T = 2pi x sqrt of L/g
Accelerate upward = g is larger = T is shorter.

 

[siffster]

so the period is given by T=2pi*sqrt(L/g). so if your period is shorter, it's either due to g or L. Since L stays constant, is has to be the g constant that is too big. If you have a pendulum in an elevator that is accelerating, the FBD on the mass at the end of the pendulum would be T(tension)-mg=ma (positive direction up). so the tension in the rope would be T=ma+mg or T=m(a+g), as you can see, if a is positive(accelerating upwards), the tensions that would be felt in the rope of the pendulum would be a+g. If you were accelerating downward, the equation would have been T=m(-a+g) or T=m(g-a) since the acceleration is in the opposite direction of what we defined as positive(up).

It's basically the same idea as trying to weigh yourself on a scale in a moving elevator as brood910 implied, but instead of the tension felt by the rope of the pendulum, we're looking at the normal force.