Solving for g: A Homework Equation Mystery?

In summary: Click on "Pendulum" in the graphic tree, and you will see a list of topics including "period," "radius," "g," and "force."The period of a simple pendulum is 1.91 s. The value of g at the location of the pendulum is 9.81 N/m. The forces acting on the bob are:-Friction: mg = 9.81 N/m^2-Gravitational: mg = 9.81 N/m^2-Angular: mg = 9.81 N/m^2The equation for the acceleration of the bob is:-A = 9.81 N/m^2*sin(
  • #1
Klymene15
10
0

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.
 
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  • #2
Klymene15 said:

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.
 
  • #3
  • #4
@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.
 
  • #5
Klymene15 said:
@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.
 
  • #6
Klymene15 said:
@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
 
  • #7
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.
 

Related to Solving for g: A Homework Equation Mystery?

1. What is the equation for solving for g?

The equation for solving for g is g = F/m, where g represents the acceleration due to gravity, F represents the force applied, and m represents the mass of the object.

2. How do you solve for g in the equation?

To solve for g, you must divide the force applied (F) by the mass of the object (m). This will give you the value of the acceleration due to gravity (g).

3. What is the significance of solving for g?

Solving for g allows us to understand the effects of gravity on objects and how they move. It is an important concept in physics and is used in many real-world applications such as calculating the trajectory of projectiles and designing roller coasters.

4. What are the units for g in the equation?

The units for g in the equation are meters per second squared (m/s²). This represents the rate of change of velocity over time due to the force of gravity.

5. Can the value of g change?

Yes, the value of g can change depending on the location and elevation on Earth. It also varies slightly due to factors such as the rotation of the Earth and the density of the Earth's crust. However, for most practical purposes, the average value of g is used, which is approximately 9.8 m/s².

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