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Newton second law and pendulum

A pendulum is hanged in the car.
Car starts to move by constant acceleration
How to measure acceleration by angle the pendulum?

Asked Afshin

 

Answer

If the pendulum makes an angle θ with the vertical, then a = g tan θ

This is based on the idea of pseudo force experienced by a body in an accelerated frame of reference.

When a body is in an accelerated frame of reference, it feels as if it is acted upon by a force equal to its mass multiplied by the acceleration of the system. Please have a look at the diagram below.

pendulum-pseudo-force

Please feel free to ask further doubts on the topic via comments

Equilibrium

Shubham Mukherjee asks:

“A ball suspended by a thread swings in a vertical plane so that its acceleration values in the extreme and lowest position are equal. Find the thread deflection angel in the extreme position?”

Answer will take some time. Visitors are requested to respond

Time Period of a Simple Pendulum in Space

Mary Beth asked:

“if you set up a pendulum aboard an orbiting space vehicle, would the period be less than, the same as, or greater than it would be in our lab? explain.”

Ans:

In a space vehicle orbiting around the earth, the apparent weight is zero as the entire gravitational pull is being utilized in providing the centripetal force required for revolving. This is called weightlessness in space.

i.e; in effect, the acceleration due to gravity is zero which make the time period of the satellite infinity. The pendulum will not oscillate at all.

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Tailpiece:

However, in manned space vehicles, there is an option to simulate gravity by making the system rotate at a particular rate so as to make the inhabitants feel as if there is weight and gravity.

Pendulum on Mount Everest !

Michelle Guzman Asked:

If you set a pendulum atop Mt. Everest, would the period be less than, greater than or equal to the period you would get in the lab?  Explain.

Ans:

As you know, the acceleration due to gravity decreases as we go upwards from surface of earth.

The time period of a simple pendulum is given by

Where l is the length of the pendulum, and g is the acceleration due to gravity.

From the equation, we can conclude that, the Time period of the pendulum increases (i.e. it goes slower)  if the pendulum is set up on top of Mount Everest.

For Creative and Critical Thinkers

Here we have not considered the change in temperature between the laboratory conditions and the temperature on top of Mount Everest which is very low. A decrease in temperature would decrease the length of the pendulum (Unless it is made up of such a substance which does not change its length with change in  temperature) and will also decrease the time period of the pendulum, making it move faster.

My first answer is correct only if the laboratory conditions are the same as on top of Mt. Everest or vice versa, except for the difference in altitude (height)

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