4 March 2015. Propagated Uncertainty in Measurements.

Purpose
to calculate uncertainties in a measurements from the calculation of measuring the Density of Metal Cylinders and determination of an Unknown Mass.

Apparatus:

Part 1

1. Vernier Caliper: A vernier caliper is a measuring instrument which can make inside, outside, or depth measurements (tresnainstrument.com). This device basically use two kinds of separate "ruler". The big one measure the "normal" cm ruler with no decimal places, and the second smaller ruler on the below measures the first decimal places, therefore the precision is until the tenth (+- 0.01 cm).
2. Digital balance: A digital scale is a measurement device used to measure the weight or mass of an object or substances (wisegeek.com). The one that we use in this experiment is precise until the ones.

Part 2

1. Spring Scales: a spring fixed at one end with a hook to attach an object at the other. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position.
2. Angle measurement apparatus:  a device that is used to measure angle (shown below)

Spring Scales

Angle Measurement

Procedure:

Part 1

1. Measure all width (diameter), weight, and length of all three cylinders given (steel, cooper, and aluminium) using a caliper and digital balance.

STEEL

COOPER

ALUMINIUM

2. Record all data.
3. Calculate the propagated error in each density measurements.

Part 2

1. You will find in the back of the class, three set up as shown in the picture below.

2. Choose two of the set ups, and write down the number marked on the unknown mass, and record the values found on the spring scales.
3. Measure the angle as appointed in the picture.

unknown mass 1

unknown mass 7

Data Analysis:

Part 1

• Below is the collection of data we got with the device precision included.

• Now, we calculated the density propagated error as show below

• Below is the real density of each cylinder.

Materials	Steel	Cooper	Aluminum
Density	7.75 g/cm3	8.96 g/cm3	2.70 g/cm3

• In comparison the percent error we got is:

•  The value is still within the range of our calculated density, therefore our calculation is "quite accurate".

Part 2

• Below is the data we got from the set up.

Unknown 1	Spring Scales
	F1 = 5.3 N +/- 0.50N	F1 = 7.2 N +/- 0.50N
	Angle
	Θ1 = 28° +/- 0.01π	Θ2 = 42° +/- 0.01π
Unknown 7	Spring Scales
	F1 = 8.0 N +/- 0.50N	F1 = 5.3 N +/- 0.50N
	Angle
	Θ1 = 38° +/- 0.01π	Θ2 = 24° +/- 0.0

• Now, we calculate the mass as shown below.

Conclusions:

• From calculating the propagated error of each measurements, we are most likely to find the "true" value in the bigger range, but as a risk, we are getting more "calculated error".
• The more uncertainties we agreed upon a device, the more calculated error we will make toward the end of calculation.