Measurement of Gravity (Simple Harmonic Motion)

[KillerQueen20]

Homework Statement

If the slope of your gradient turns out to be 4.041 s^2.m^-1 then what value would you obtain for g? State your answer in m.s^2 and to 3 significant figures.

Homework Equations

T^2 = (4 pi^2 e1 / g) - (4 pi^2 e0 / g)

This is the one I'm supposed to use. Other ones given are...

T^2 = (4 pi^2 e) / g

e = e1 - e0

The Attempt at a Solution

I have no idea what I'm supposed to be doing. Graph is T^2 vs. e1
I did, however, look on the internet. There is a lot of stuff about a spring constant, but that's not mentioned anywhere on my sheet. Values are different and I can't get my head around it properly.

Thanks for your help =)

 

[rl.bhat]

The gradient m is supposed to be T^2/e1.
Now g = 4*pi^2*e/T^2 = 4*pi^2/m

 

[nlightner]

I would first clarify the context and purpose of the experiment. Is this a lab experiment or a theoretical calculation? What is the physical system being studied? Is it a simple pendulum or a mass attached to a spring? This information is important in determining the appropriate equations and units to use.

Assuming this is a lab experiment measuring the acceleration due to gravity using a simple pendulum, I would first identify the variables and their units. T is the period of the pendulum in seconds (s), e1 is the length of the pendulum in meters (m), g is the acceleration due to gravity in meters per second squared (m/s^2), and e0 is the initial length of the pendulum in meters (m).

Next, I would rearrange the equation T^2 = (4 pi^2 e1 / g) - (4 pi^2 e0 / g) to solve for g. This gives g = (4 pi^2 e1 - T^2) / (4 pi^2 e0).

Plugging in the given values, g = (4 pi^2 * 4.041 s^2.m^-1 - T^2) / (4 pi^2 * 0.00 m). Since the initial length, e0, is zero, it cancels out and we are left with g = (4 pi^2 * 4.041 s^2.m^-1 - T^2) / 0.00 m.

I would also note that dividing by zero is not a valid mathematical operation and would question the accuracy of the given values. However, assuming this is just a theoretical exercise, I would continue with the calculation.

The final step is to convert the units to m/s^2 and round to 3 significant figures. This gives g = (4 pi^2 * 4.041 s^2.m^-1 - T^2) / 0.00 m = 40.27 s^2.m^-1 / 0.00 m = 4027 m/s^2. Rounded to 3 significant figures, the value for g is 4030 m/s^2.

In conclusion, the value for g obtained from the given slope of 4.041 s^2.m^-1 is 4030 m/s^2, assuming this is a theoretical calculation. If this is a lab experiment, I