Lab 1: Measurements and uncertainty estimation

Introduction:

The purpose of this lab is to measure aquantity related to the static friction of glass. Static frictionis the force required to start moving an object from rest. You willplace a coin on the glass and lift one end until the coin begins tomove. Your goal is to measure the angle at which the coin moves andunderstand what affects the precision and accuracy of yourmeasurements.

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

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

1. 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 elevatethe other end slowly until the coin moves (watch carefully as thecoin may move suddenly or very slowly).
2. Stop moving the surface.
3. Measure the inclination angle (the angle from your table to thesurface you’ve used). Do this by measuring the height of the raisedsurface and the length of the surface to infer the angle by awell-known trigonometric identity.
4. Considering your measuring technique and device, estimate theuncertainty in the angle. You may assume that the percentuncertainty in the sine of the angle is equal to the percentuncertainty of the angle itself.
5. Repeat this measurement (including uncertainties) a total of 5times.
6. Tabulate your data (include absolute uncertainties):

FORHEADS

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 andaverage uncertainty. Compute the difference between the measuredangles in each trial and the averaged angle. Quantitatively how dothe differences compare to the average uncertainty?

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

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

FORTAILS

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

1. 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.
2. Based on your measurements and your answer from 11) would yousay that the angle depends on which side of the coin is facing up?Explain.
3. List at least 2 things that contributed to the uncertainty ofyour measurements and explain how you might improve them.
4. List at least 2 things that might have contributed to anyinaccuracy of your measurements and explain how you might improvethem.