Calculating Error Bars for Height and Time in Ball Drop Experiment

[aron silvester]

1. The problem statement, all variables, and given/known data

• Take the ball and drop it from chest level 5 times recording the times and the height. Do this same procedure once again for knee, waist, and eye level. You should now have four data points for your height and four data points for the time, each with uncertainty estimates. We used the average (calculated in the Collecting data section below) of the times to plug in the t variable in the X column for each level. MY QUESTION IS, HOW DO I CALCULATE THE THE ERROR BAR ALONG THE X AXIS? I already know the error bar along the Y axis (height), my group member

• Collecting data

• Data set: Similar to Table 3

Homework Equations

The end goal is to plot a graph on excel that looks something like the image below. I have both the X and Y values, but I just need to figure out the error bars for the X axis.

 

[haruspex]

HOW DO I CALCULATE THE THE ERROR BAR ALONG THE X AXIS?

How did you calculate them for the Y axis?

 

[aron silvester]

How did you calculate them for the Y axis?

My partner just eyed the uncertainty when she measured the height (height is used as the y-axis later for the graph) from which to drop the ball. My partner said in order to get the uncertainty for the x-axis, she multiplied the standard deviation by the average times. For example, to get the error bar for the knee level she multiplied the average time for knee-level, 0.244, and multiplied it with the standard deviation of 0.0622. These measurements are recorded in the Collecting Data of my post. Does that make sense? Isn't the error bar just the standard deviation? I'm not sure why she's multiplying it by the average.

 

[haruspex]

For Y, I would take the standard deviation, or some constant multiple of it, like 2 or 3, as the error bar length. Certainly makes no sense to multiply by the average.
But as the text says, it is a bit different for the X axis because of the quadratic term. For that you should use the same constant multiplier as you used for the Y, and multiply by the actual t reading (not the average).