Question

Lab 1: Measurements and uncertainty estimation

Introduction:

The purpose of this lab is to measure a quantity related to the static friction of glass. Static friction is the force required to start moving an object from rest. You will place a coin on the glass and lift one end until the coin begins to move. Your goal is to measure the angle at which the coin moves and understand what affects the precision and accuracy of your measurements.

1) Pick a coin to use based on your birth month and the list here:

Jan – March	$0.05
Apr – June	$0.10
July – Sept	$0.25
Sept – Dec	$1.00

2. Place the coin “heads up” (with the persons head facing up) flat on a horizontal surface made of glass (could be a mirror, tablet, smartphone screen, etc.). Keep one end fixed and elevate the other end slowly until the coin moves (watch carefully as the coin may move suddenly or very slowly).
3. Stop moving the surface.
4. Measure the inclination angle (the angle from your table to the surface you’ve used). Do this by measuring the height of the raised surface and the length of the surface to infer the angle by a well-known trigonometric identity.
5. Considering your measuring technique and device, estimate the uncertainty in the angle. You may assume that the percent uncertainty in the sine of the angle is equal to the percent uncertainty of the angle itself.
6. Repeat this measurement (including uncertainties) a total of 5 times.
7. Tabulate your data (include absolute uncertainties):

FOR HEADS

Trial #	Length	Height (Cm)	Angle (in Radians)
1	28.3 Cm	10 cm	0.35
2	28.3 Cm	9.4	0.33
3	28.3 Cm	9.4	0.33
4	28.3 Cm	9	0.31
5	28.3 Cm	9.2	0.32

8) Compute the average angle and average uncertainty. Compute the difference between the measured angles in each trial and the averaged angle. Quantitatively how do the differences compare to the average uncertainty?

9) Based on 8) would you say that the average uncertainty accounts for the different trial measurements (i.e. are the differences large or small compared to the uncertainty)?

10) Repeat the steps 2-9 for the coin “tails up”.

FOR TAILS

Trial #	Length	Height (Cm)	Angle (in Radians)
1	28.3 Cm	9.5 cm	0.33
2	28.3 Cm	9.7	0.34
3	28.3 Cm	10.4	0.37
4	28.3 Cm	9.7	0.34
5	28.3 Cm	9.6	0.34

11. Compute the difference between the measured angles in each “tails up” trial to the average of the “heads up” trail. Quantitatively compare this to the average uncertainty of the “heads up” trial.
12. Based on your measurements and your answer from 11) would you say that the angle depends on which side of the coin is facing up? Explain.
13. List at least 2 things that contributed to the uncertainty of your measurements and explain how you might improve them.
14. List at least 2 things that might have contributed to any inaccuracy of your measurements and explain how you might improve them.

Answer 1

Consider the following arrangement where a book is used and a fair coin of your choice is placed over it and then book cover is tilted such that it makes an angle θ with the hotizontal;

Now, from this FBD, for static case

Length (L) in cm	Height(H) in cm	θ in rad	θ - <θ>	(θ - <θ>)²
28.3	10	0.3611	0.0226	0.00051076
28.3	9.4	0.3385	0.0000	0
28.3	9.4	0.3385	0.0000	0
28.3	9.0	0.3236	0.0149	0.0002223
28.3	9.2	0.3310	0.0075	0.0000570
		Average of θ, <θ> = 0.33855	Average of uncertainty = 0.009012

In this table we have used ;

and

From table it is evident that the differences are very much small between the average measured values, hence the value is close to 0.33855. Similar procedure can be followed for the second case.