Calculating 'g' with Slope of Pendulum Graph

In summary, 'g' refers to the acceleration due to gravity and is used in the formula for calculating the period of a pendulum. The slope of a pendulum graph is directly related to 'g' and can be used to calculate it using the formula g = 4π²L/slope. This method can be quite accurate, but other factors may affect the results. 'g' can also be calculated using other methods, but using the slope of a pendulum graph is a simple and effective method for educational purposes.
  • #1
physicsguy101
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Homework Statement



Using the slope from a graph of the square root of the pendulum's length vs period (which would be a linear relationship), calculate the experimental acceleration due to gravity.


Homework Equations



I'm trying to figure out what equation I can use to solve for 'g'.

I know that T = 2*pi*√(L/g), but will that help here? I need to use the slope of the graph in order to calculate g.


Thanks in advance!
 
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  • #2
Use the fact that √ (a/b) = √a/√b and get your equation in the form Y = MX so that the gradient is M.
 

FAQ: Calculating 'g' with Slope of Pendulum Graph

What is 'g' in the context of calculating with slope of pendulum graph?

'g' refers to the acceleration due to gravity, which is a constant value of 9.8 m/s² on Earth. It is used in the equation for calculating the period of a pendulum, which is dependent on the length of the pendulum and the acceleration due to gravity.

How is the slope of a pendulum graph related to 'g'?

The slope of a pendulum graph is directly related to 'g'. The slope represents the change in the vertical position (distance) of the pendulum over the change in time. This is equivalent to the acceleration of the pendulum, which is equal to 'g'.

What is the formula for calculating 'g' using the slope of a pendulum graph?

The formula for calculating 'g' using the slope of a pendulum graph is g = 4π²L/slope, where L is the length of the pendulum and slope is the slope of the graph. This formula can be derived from the equation for calculating the period of a pendulum, T = 2π√(L/g), by solving for 'g'.

How accurate is calculating 'g' using the slope of a pendulum graph?

Calculating 'g' with the slope of a pendulum graph can be quite accurate, as long as the pendulum is a simple pendulum (meaning it swings back and forth in a straight line) and the measurements are precise. However, other factors such as air resistance and friction may affect the accuracy of the results.

Can 'g' be calculated using other methods besides the slope of a pendulum graph?

Yes, 'g' can also be calculated using other methods such as free fall experiments, motion equations, or using a pendulum with a known period. However, using the slope of a pendulum graph is a simple and effective method for calculating 'g' in a classroom or laboratory setting.

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