Lab 2: Determining the Value of Gravity (g) 8/27

Purpose 

In this lab, we will determine the value of gravity (g) by using an apparatus consisting of an electro-magnet and spark generator.

Procedure + Equipment

On the left is the electromagnet. On the right is the apparatus that  provides the reading of the falling object. 

When the free fall object is held at the top by the electromagnet and then released, the spark generator then records the object’s position at every 1/60th of a second. This data is recorded on a strip of spark paper that shows each mark of the falling object. With the strip of paper, the distance of each mark can measured by aligning the 0cm mark of the meter stick with one of the dots. Each mark is then measured from the 0cm mark. This data gives us the time and the distance of the object as it fell. From the data collected, a data table was created with ∆X, the mid-interval time and speed. This allowed us to graph time vs distance and a velocity vs time. 

Data

Data collected from experiment and some calculations to help with graphing. 

This graph shows the relationship between distance and time. 

This is the velocity vs time graph. The slope of the equation of the graph gives us the acceleration  of the falling object. The acceleration is g, which is 963 cm/s².

Analysis + Calculations

With the velocity vs time graph we can find our value for g by finding the slope of the linear fit, which is an acceleration of 963 cm/s² , which is equivalent to 9.63 m/s². We know that the true value of g is 9.81 m/s², and the experimental value to be 9.63 m/s², so we can find the percent error. Using the formula % error = | true value - experimental value | / true value * 100% we find that the percent error is 1.83%. 

This data table shows each groups value of g when g is in m/s². From that data the average value of g was determined, along with the standard deviation. 

We also took each group's value of g and found that the class average for the value of g is 9.55 m/s². With this data we were also able to find the standard deviation.

Questions

1.  
2. The slope of the equation of the graph is the acceleration. This acceleration is your value for g. When comparing that value to the mean value, we find that our value of g falls within the 1st standard deviation. The mean value is 9.55m/s² + 0.1630. That means that the value for g should range from 9.387 m/s² and 9.713 m/s². Our value of g is 9.63 m/s², so it is within the desired range. 

   

   This shows where our value of g lies compared to the standard deviation.  It lies within the 1st standard deviation, so I believe it's still an acceptable value.

   When comparing our value to the actual value of g, we find a relative difference of -1.83%, and with the mean value we find a relative difference of -2.65%. This means that as a single group we had less of a difference when as a group.  
3. With the given equation, you have y=481.42x² + 138.04x - 0.0003. The derivative of the equation gives y'=962.84x + 138.04, so this equation gives you the acceleration. Compared to the other value of g, it is very close.

Summary

In this lab, we found the value of gravity (g) by using an electromagnet and spark generator. We used the position and time to get ∆x,  mid-interval time and speed. With that data we were able to graph a distance-time and velocity-time graphs. The graphs helped in deterring the value for g, which came to be 9.63 m/s². Then the values of each group's g was collected and used to determine the standard deviation. The standard deviation provided us with what values were closest to the mean value of g. We found that ours did lie close to the mean value with a percent error of 0.84%. This percent error tells us that our value was close to the experimental mean value for g. 

When taking the actual value of g to be  9.81 m/s², the relative difference is -1.83%. Our value of g was smaller than the actual value of g. There might be several reasons for the difference in our value of g compared to the actual value of g. Those reasons might be due to human error, somewhere along an error in measuring the distance of each mark could have been made. Another source of error is that in doing this, we aren't taking into account the air resistance.