Solving for g: A Homework Equation Mystery?

[Klymene15]

Homework Statement

If the period of a 70.8-cm-long simple pendulum is 1.91 s, what is the value of g at the location of the pendulum?

Homework Equations

I don't know of any that relate the period, radius and the value of g

The Attempt at a Solution

The thing is, I'm completely clueless. I'm guessing it has something to do with force, because how else would g be related to the equation? And... probably angular velocity. But I am so clueless.

 

[Doc Al]

Homework Equations

I don't know of any that relate the period, radius and the value of g

Google is your friend.

Seriously, you should be able to easily find an expression for the period of a simple pendulum.

 

[tadchem]

http://hyperphysics.phy-astr.gsu.edu/ is a terriffic resource. There is a page for the Simple Pendulum.

 

[Klymene15]

@tadchem: Um... The link only said "It works!" What works, I don't know...

@Doc Al: I'm looking to learn how to do it, not simply find an equation.

 

[haruspex]

@tadchem: Um... The link only said "It works!" What works, I don't know...

@Doc Al: I'm looking to learn how to do it, not simply find an equation.

Draw a free body diagram with the pendulum at some angle to the vertical. Show the forces acting on the bob. Assign identifiers (algebraic variables) to the angle, the mass, etc. Obtain an equation for the acceleration.
At this point, you should hit a snag, a mix of trig and linear functions of the angle. The trick is to assume the pendulum only swings through quite small angles. That allows you to approximate sin(θ) as θ. You should now have a classic simple harmonic motion differential equation.

 

[Doc Al]

@Doc Al: I'm looking to learn how to do it, not simply find an equation.

Did you even attempt to Google it? Or use the excellent hyperphysics reference? (Or your text.) Full derivations (similar to what haruspex outlined) are readily available.

Simple Pendulum

 

[tadchem]

My apologies for the incomplete link.
The home page is http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
It has a graphic tree navigation system that can quickly get you down to the nuts and bolts of whatever physics problem you are interested in. There is also an index on the right side of the page.