BCIT Department of Physics MGO-02 - Measurements and Uncertainties

BCIT Department of Physics MGO-02

MGO-02: Measurements and Uncertainties

Learning Objectives

In this lab you will improve your ability to:

Follow a definite set of instructions for the collection and analysis of data.

Analyze and combine experimental uncertainties.

Communicate experimental results in a clear, concise manner.

Analyze precision, accuracy and operational uncertainties.

Experimental Objective

The objective of this experiment is to determine the density of a toonie, including an uncertainty. To achieve this objective we will need to measure the mass and volume of the toonie, paying special attention to the uncertainties in our measurements and calculations.

Equipment

• Computer with Excel • Toonie (two dollar coin) • Ruler • Kitchen scale (preferred, but not required)

Theory

All measurements have uncertainties. These uncertainties depend upon the precision and accuracy of the instruments used, the operational uncertainty of the individual measurements taken, and the constancy of the measured quantities. In this experiment we will practice assessing uncertainties for simple analogue and digital measurements, and then combining these uncertainties when we perform calculations using measured values.

The volume V of a cylindrical object is given by the product of the circular cross sectional area, π????!/4, where ???? is the diameter of the circle, and the height ????:

???? = ( ????????!

4 * ????. (1)

Therefore, a cylindrical object of mass ???? and volume ???? has a density ρ given by:

ρ = m V =

4???? ???? ????!???? .

(2)

MGO-02 BCIT Department of Physics

Procedure and Analysis Record all data in the MGO-02 spreadsheet. Consult L003, as well as Secs. 4 and 5 of the lab manual introduction to review proper uncertainty assessment and propagation.

Complete Table 1. Assume that the accuracy, Δ????, is the same as the precision, Δ????.

Note: If you do not have a kitchen scale, look up a value for the mass (see the instructions in Step 4). Assume that the precision and accuracy are one unit in the last digit of the value you look up.

Use a ruler to measure the diameter, ????, and thickness, ????, of your toonie. ???? and ???? are defined in Figure 1. Repeat these measurements 5 times and record your values in Table 2.

Complete the rest of Table 2. You should perform your calculation using Excel, not a calculator. Note: (1) The operational uncertainty, Δ????, is half the range of measured values; (2) The total uncertainty, Δ????, is determined by adding the precision, accuracy and operational uncertainty in quadrature:

Δu = 8(Δa)! + (Δp)! + (Δo)! . (3)

Measure the mass of your toonie using a kitchen scale and record your measurement in Table 3. If you do not have a kitchen scale, look up a value for the mass of the toonie (Wikipedia is fine). Make sure to note the year your coin was manufactured. If you are looking up the mass of the toonie, make sure you find the mass for the appropriate year, as the composition and therefore the mass has changed since the toonie was first introduced.

Figure 1: A Toonie of diameter d and thickness t.

Complete the rest of Table 3. The total uncertainty is determined by adding the precision and accuracy in quadrature (since we do not have an operational uncertainty for the mass).

Complete Table 4. Note: (1) To enter the value π in Excel use the function PI(). Do not just enter the number 3.14; (2) The uncertainty must be calculated according to the procedure described in Sec. 4 of the lab manual introduction.

Post your density measurement to Piazza. The appropriate discussion thread can be found under Labs → Lab 2.

Worksheet

Complete the MGO-02 worksheet on separate sheets of paper and attach a PDF of your data and analysis tables. See Sec. 9 of the lab manual introduction. Submit your PDF to the appropriate Learning Hub Assignment folder.