Simple Pendulum & Elevator Homework | Period Formula for Accelerating Elevator

In summary, the conversation discusses the period of a simple pendulum suspended from the ceiling of an elevator that is accelerating upwards with an acceleration of a. The possible equations for the period are given in terms of the length of the pendulum, gravity (g), and the acceleration of the elevator (a). The correct equation is determined to be T = 2\pi*(L/(g+a))^(1/2) and it is supported by Einstein's theory of the equivalence of a gravitational field and acceleration.
  • #1
hansel13
51
0

Homework Statement


A simple Pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is:
2[tex]\pi[/tex]*(L/a)^(1/2)
OR
2[tex]\pi[/tex]*(L/(g+a))^(1/2)
OR
2[tex]\pi[/tex]*(L/g)^(1/2)

Homework Equations


T = 2[tex]\pi[/tex]*(L/g)^(1/2)

The Attempt at a Solution


Not sure where to start. It doesn't seem like there's really math involved here. I tried drawing a free body diagram, but that made things worse. I'm pretty sure it's the middle one, because the other 2 just don't make sense, because the formula needs to both a and g into account, right?
 
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  • #2
Right.

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)
 
  • #3
OK thanks
 

Related to Simple Pendulum & Elevator Homework | Period Formula for Accelerating Elevator

1. What is a simple pendulum and how does it work?

A simple pendulum is a weight or mass suspended from a fixed point that is free to swing back and forth. The motion of a simple pendulum is governed by the laws of gravity and inertia. As the pendulum swings, it experiences a force due to gravity that causes it to oscillate back and forth.

2. What factors affect the period of a simple pendulum?

The period of a simple pendulum is affected by the length of the pendulum, the mass of the pendulum, and the acceleration due to gravity. The longer the pendulum and the larger the mass, the longer the period of the pendulum. The acceleration due to gravity is a constant and does not affect the period of the pendulum.

3. How is the period of a simple pendulum calculated?

The period of a simple pendulum can be calculated using the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This equation assumes the amplitude of the pendulum's swing is small (less than 15 degrees).

4. How does an elevator affect a simple pendulum?

If a simple pendulum is inside an elevator that is accelerating or decelerating, the period of the pendulum will change. If the elevator is accelerating upwards, the pendulum's period will increase. If the elevator is accelerating downwards, the pendulum's period will decrease. The period of the pendulum will remain constant if the elevator is moving at a constant velocity or is stationary.

5. What is the difference between a simple pendulum and a compound pendulum?

A simple pendulum has a single point of suspension and a single point of mass, whereas a compound pendulum has multiple points of suspension and multiple points of mass. The motion of a compound pendulum is more complex and not as easily predictable as a simple pendulum. Compound pendulums are often used in clocks and other timekeeping devices.

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