# Verifying the acceleration of gravity in our lab (help with error please)

• feynmansorange
feynmansorange
Homework Statement
Hi! I'm doing a lab where my class is verifying the acceleration due to gravity. We dropped an object and recorded the time with a spark timer, then measured the meters every 1/30th of a second. So, I have distance (meters) and time (seconds). THEN we square the time, and plot that on a graph of dist. vs time^2. But my slope is only roughly half of gravity??? isn't the acceleration supposed to be equal to gravity?
Relevant Equations
s=ut+1/2at^2
Data and graphs here (the time is measured every 1/30 of a second, but for some reason, Google Sheets thought 1/30 wasn't a number so its in decimals!!! very confusing!!! so sorry about that!). why is the slope only 4.68, should it not be 9.81m/s^2? is the slope of m/s^2 not supposed to be acceleration due to gravity? is my data weird? thanks!

In your experiment, s = (1/2)g t2

After your conversion and plot, your graph is similar to following equation.
y = (1/2)g x .... general equation of a straight line.
Slope is therefore (1/2)g, .... there's nothing wrong, right?

Tomy World said:
In your experiment, s = (1/2)a t
You mean s = (1/2)a t2. Then x = t2 in the straight line plot.

feynmansorange
kuruman said:
You mean s = (1/2)a t2. Then x = t2 in the straight line plot.
YEs. When you plot s vs t2, it becomes a straight line equation.

feynmansorange said:
Homework Statement: Hi! I'm doing a lab where my class is verifying the acceleration due to gravity. We dropped an object and recorded the time with a spark timer, then measured the meters every 1/30th of a second. So, I have distance (meters) and time (seconds). THEN we square the time, and plot that on a graph of dist. vs time^2. But my slope is only roughly half of gravity??? isn't the acceleration supposed to be equal to gravity?
Relevant Equations: s=ut+1/2at^2

Data and graphs here (the time is measured every 1/30 of a second, but for some reason, Google Sheets thought 1/30 wasn't a number so its in decimals!!! very confusing!!! so sorry about that!). why is the slope only 4.68, should it not be 9.81m/s^2? is the slope of m/s^2 not supposed to be acceleration due to gravity? is my data weird? thanks!
Now that your question abut the slope has been answered, how do you explain the intercept of about -6 cm? You need to address that question in your report and it seems that you already have the necessary information to do just that.

kuruman said:
Now that your question abut the slope has been answered, how do you explain the intercept of about -6 cm? You need to address that question in your report and it seems that you already have the necessary information to do just that.
yeah, I also noticed that the intercept was off and makes no sense. My physics teacher (who has 0 background in physics because the previous teacher quit a few days before school started) made us measure it like that. I really wish I had an actual teacher.

feynmansorange said:
yeah, I also noticed that the intercept was off and makes no sense. My physics teacher (who has 0 background in physics because the previous teacher quit a few days before school started) made us measure it like that. I really wish I had an actual teacher.
Please don't blame your teacher. You can figure this out on your own because it's your doing. Look at your data. No intercept means that at t = 0 the object is at distance = 0. Your table shows that distance = 0 at time t = (1/30) s.

Hi @feynmansorange,

A clue to the source of plot problem:
Note that the plot shows minor variations from a straight line at times
0, 0.3, 0.55. That repetition at similiar intervals make me suspicious that the either the Time or Distance measurements (or both) may have a systematic error.

Don't expect your test setup or equipment is always perfect. I think @kuruman is hinting at that possibility.

Cheers,
Tom
p.s. It would be interesting to see if others in the class had similiar results.
Please let us know if you find out.

## How do we set up the experiment to measure the acceleration of gravity?

To measure the acceleration of gravity, you typically set up an experiment where you drop an object from a known height and measure the time it takes to reach the ground. Use a stopwatch or a high-speed camera to accurately measure the time. Ensure the object falls freely without any initial velocity and that air resistance is minimized. The height should be measured precisely using a ruler or a laser distance meter.

## What formula should we use to calculate the acceleration of gravity?

The formula used to calculate the acceleration of gravity (g) is derived from the equations of motion. The most common formula is $$g = \frac{2h}{t^2}$$, where h is the height from which the object is dropped, and t is the time it takes to reach the ground. This formula assumes that the initial velocity is zero and that air resistance is negligible.

## How can we minimize errors in our measurements?

To minimize errors, ensure that your height measurements are precise and that the timing is accurate. Use a high-speed camera or an electronic timing system to reduce human reaction time errors. Conduct multiple trials and take the average of the results to reduce random errors. Also, ensure that the object falls freely without any obstruction and that air resistance is minimized by using a dense object.

## What are the common sources of error in this experiment?

Common sources of error include inaccurate height measurements, timing errors due to human reaction time, air resistance affecting the fall of the object, and initial velocity not being zero. Additionally, variations in local gravitational acceleration due to altitude or geological formations can also introduce errors.

## How can we account for air resistance in our calculations?

To account for air resistance, you can use a denser object to minimize its effect, or you can perform a more complex analysis involving drag coefficients. Alternatively, you can conduct the experiment in a vacuum chamber where air resistance is eliminated. If these options are not feasible, you can estimate the effect of air resistance and include it as a correction factor in your calculations, although this requires more advanced knowledge of fluid dynamics.

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