Gravitational Field Strength Calculations with a Pendulum

In summary: This is what is meant by the pendulum moving in "simple harmonic motion." The use of the term "plane" refers to the assumption that the pendulum's motion is restricted to a single plane.In summary, the equation for calculating gravitational field strength using a pendulum assumes that the pendulum bob is moving in simple harmonic motion. However, if the length is too small and causes circular motion instead, it will not affect the time period and the value for g will be less accurate. The equation also assumes a plane pendulum and small oscillations for accuracy.
  • #1
matt_crouch
161
1
As a pendulum can be used to calculate the gravitational field strength by using the equation


Time period= 2(pi) sqrt (length/g)

this equation assumes that the pendulum bob is moving in Simple harmonic motion. However at very small lengths the pendulum bob tends to move in a more circular motion will this at all effect the time period and hense my value for g?

hopefully that makes sense =]
cheers
 
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  • #2
It doesn't make sense, at least for me, because if you all you care about is to find "g", then why even make the length that small that it causes such circular motion?

And no, if you want it to be accurate, such circular motion can only add more systematic error to your estimation of g. Note that the formula for the period that you wrote assumes important simplifications: that the motion is a plane pendulum (not a 3D conical pendulum), and that it undergoes small oscillations, meaning a long pendulum with a small angle of oscillation. The more you deviate from that, the less accurate that period expression becomes.

Zz.
 
  • #3
ahh thanks alot... one thing how do you mean that the motion is a "plane" pendulum?
 
  • #4
The motion of the pendulum is always circular, no matter whether it is small amplitude or large amplitude. It does not depend on the length of the pendulum.

The reason for assuming small amplitudes is so that the equation of motion can be linearized and reduced to a harmonic differential equation. For this to apply, only small amplitudes can be considered.
 

Related to Gravitational Field Strength Calculations with a Pendulum

1. What is a gravitational field strength?

A gravitational field strength is a measure of the force of gravity at a particular point in space. It is dependent on the mass of the objects creating the gravitational field and the distance between them.

2. How is gravitational field strength calculated?

Gravitational field strength can be calculated using the equation g = GM/r^2, where g is the gravitational field strength, G is the universal gravitational constant, M is the mass of the object creating the field, and r is the distance from the object.

3. Can gravitational field strength be measured?

Yes, gravitational field strength can be measured using a variety of instruments such as a pendulum, a spring scale, or a gravimeter. These instruments measure the effect of gravity on a known mass and can calculate the gravitational field strength at that location.

4. How does a pendulum help in calculating gravitational field strength?

A pendulum can be used to measure gravitational field strength by observing the period (time taken for one swing) of the pendulum. The period is affected by the length of the pendulum, which is in turn affected by the gravitational field strength. By measuring the period and knowing the length of the pendulum, the gravitational field strength can be calculated.

5. What are some real-world applications of calculating gravitational field strength with a pendulum?

Calculating gravitational field strength with a pendulum has various real-world applications, such as determining the mass of the Earth or other celestial bodies, measuring changes in gravitational field strength due to tectonic movements or underground resources, and even in navigation systems like GPS. It is also used in industries such as oil and gas exploration, where changes in gravitational field strength can indicate the presence of underground resources.

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