How Does Elevator Motion Affect Pendulum Period?

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    Elevator Pendulum
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The period of a pendulum suspended in an accelerating elevator is affected by the change in effective gravitational force. When the elevator moves upward with constant acceleration, the effective gravitational force increases, leading to a shorter period for the pendulum. This is because the pendulum's motion is influenced by both the actual gravitational force and the inertial force due to the elevator's acceleration. The relationship can be described using the formula T=2pi(√(L/g')), where g' is the adjusted gravitational force. Understanding this concept is crucial for analyzing pendulum behavior in non-inertial reference frames like an accelerating elevator.
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Homework Statement


A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration? Explain.

Homework Equations



T=2pi (\sqrt{l/g})

The Attempt at a Solution


i know that..the period relies on the gravitational force which changes as the elevator is moving. i THINK that when the elevator moves up, gravity increases..but i am not sure why. please help!
 
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If you are sitting in the bus and bus suddenly starts, you were thrown in the opposite direction. If you are sitting in the moving bus and if the driver suddenly applies the brakes you were thrown in the forward direction. Why is it so? Same reason applies to the lift problem.
 
I believe it is due to a thing called the "inertial force", it is an apparent force acting on the object when it is inside a non-inertial reference frame (such as the accelerating elevator)
this is the prime reason why the "Foucault pendulum" can be used to test whether the Earth is rotating.
 
sheepy said:
i know that..the period relies on the gravitational force which changes as the elevator is moving. i THINK that when the elevator moves up, gravity increases..but i am not sure why. please help!

On all objects in the frame of reference of the lift, there acts the pseudo force or the inertial force -ma, opposite to the direction of a. It's as if there's an added g-field of strength a, acting downward, in addition to the actual g.

Can you find T now?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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