RMS uncertainty using a Trend Line

[salal]

Homework Statement

Find the acceleration of gravity. Using the trendline equation of Force v. hanging mass, find the RMS uncertainty for the force.

Trend line equation: y = 9.8968x - 0.0342 R² = 0.9493

Data Values:

Hanging mass is the first number. Force is the second number.
0.40 3.839928
0.39 3.690708
0.37 3.720552
0.35 3.720552
0.30 2.765544
0.20 1.949808

Homework Equations

F=ma
RMS = Sqrt((X1)²+(X2)²+(X3)²+...+(XN)²/N)

The Attempt at a Solution

I got 9.8968 as the accleration of gravity.

I got 3.35414 as the RMS of the Force values.

I also got 6.566915632 as the RMS of the Force-Force (trendline)

I just don't understand how to calculate the RMS uncertainty of force. I don't know what numbers should i use.

Thanks

 

[anathema]

for your post! It seems like you are on the right track with your solution. Let me provide some clarification on how to calculate the RMS uncertainty for the force.

First, let's define the terms used in the problem. The trendline equation provided is a linear equation of the form y = mx + b, where y is the dependent variable (force), x is the independent variable (hanging mass), m is the slope of the line (acceleration of gravity), and b is the y-intercept. The R² value represents the goodness of fit of the trendline to the data, with a value of 1 indicating a perfect fit.

To calculate the acceleration of gravity (m), we can rearrange the trendline equation to solve for m: m = (y - b)/x. Plugging in the values from the data points given, we get m = (3.839928 - (-0.0342))/0.40 = 9.8968 m/s². This is the same value you obtained.

Now, let's focus on calculating the RMS uncertainty for the force. RMS stands for root mean square, and it is a way to calculate the average of a set of values. In this case, we are interested in finding the average of the force values given in the data. The formula for RMS is RMS = √((X1²+X2²+X3²+...+XN²)/N), where X1, X2, X3, etc. are the individual force values and N is the total number of values.

Using the data given, we can plug in the values for X1, X2, X3, etc. and calculate the RMS for the force. This gives us RMS = √((3.839928²+3.690708²+3.720552²+3.720552²+2.765544²+1.949808²)/6) = 3.35414 N.

Finally, to calculate the RMS uncertainty for the force, we need to take into account the uncertainty in the slope of the trendline (m) as well. This uncertainty is represented by the RMS of the Force-Force (trendline) value you calculated, which is 6.566915632 N. Thus, the RMS uncertainty for the force is calculated as RMS uncertainty = √(RMS² + (m x RMS slope)²) =