Determining Acceleration due to gravity using a Spring

In summary, the conversation discusses the process of using a helical spring to determine the acceleration due to gravity at a specific location. This involves calculating the extension in length of the spring for a particular load, plotting graphs for load vs extension and load vs time period, and using a formula derived from the equation for time period to calculate the acceleration due to gravity. The formula used is derived from YouTube videos and the overall result is considered to be accurate. There is a question about the second formula not having L in it, but it is believed to be correct.
  • #1
Wrichik Basu
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I want to determine the acceleration due to gravity at a place using a helical spring.

For this, I've first calculated the extension in length of the spring (##x##) for a particular load (##L##) on the pan. Then I've plotted a graph for ##L## vs ##x## for different values of L and corresponding values of ##x##, and calculated it's slope.
Next, I've calculated the time period for 20 oscillations of the spring for each of the weights I've used before. I've calculated the time period for one oscillation, and taken the average of 3 readings (##T##). I've plotted a graph for ##L## vs (##T ^2 ##), and calculated it's slope.
I've used this formula for the calculation of acceleration due to gravity: $$g= 4 \pi ^2 \frac {Slope \; of \; L \; vs \; T^2 \; graph}{Slope \; of \; L \; vs \; x \; graph} $$ which I derived from the formula $$ T = 2\pi \sqrt {\frac {x}{g} } $$ from where we can get $$\begin{align} g = 4 \pi ^2 \frac {x}{T ^2} \nonumber \\ &= 4 \pi ^2 \dfrac {\frac {L}{T ^2}}{\frac {L}{x}} \nonumber \end {align}$$.
Are these formule correct? I've got the value of ##g=10 m/ s^2##, which seems to be approximately correct, but I wanted to know whether the process I used is correct.
 
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  • #2
The second formula has x in it, which depends on L, but it doesn't have L in it. That is odd. Where does the formula come from?

The overall result looks fine.
 
  • #3
mfb said:
The second formula has x in it, which depends on L, but it doesn't have L in it. That is odd. Where does the formula come from?

The overall result looks fine.
From these youtube videos:

 

Related to Determining Acceleration due to gravity using a Spring

What is the purpose of determining acceleration due to gravity using a Spring?

The purpose of determining acceleration due to gravity using a Spring is to accurately measure the acceleration due to gravity at a specific location. This information can be used in various scientific experiments and calculations.

How does a Spring help in determining acceleration due to gravity?

A Spring can be used as a simple pendulum to measure the time period of its oscillations. By using the equation T=2π√(m/k), where T is the time period, m is the mass attached to the Spring, and k is the Spring constant, the acceleration due to gravity (g) can be calculated using the equation g=4π²(m/k).

What factors can affect the accuracy of the measurement?

The accuracy of the measurement can be affected by factors such as air resistance, friction, and the accuracy of the Spring itself. Other factors such as temperature and humidity can also impact the Spring's behavior and therefore affect the accuracy of the measurement.

Can the same Spring be used to determine acceleration due to gravity at different locations?

Yes, the same Spring can be used to determine acceleration due to gravity at different locations. However, it is important to ensure that the Spring is not affected by external factors and that it is calibrated properly for accurate measurements.

What are the units of measurement for acceleration due to gravity using a Spring?

The units of measurement for acceleration due to gravity using a Spring are typically meters per second squared (m/s²) or centimeters per second squared (cm/s²).

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