Sample Skills Test Solutions

7/29/2019 Sample Skills Test Solutions

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Sample Skills Test 24/5/2013 S.3

PHYSICS 1

Sample Laboratory Skills Test

SOLUTIONS

(Test is in Lab Manuals and there is an extra Question 7 at end)

Question 1Estimate the length of the Sydney Harbour Bridge that lies between the pylons. Give your

answer in metres and a justification for your answer.

To answer this type of question you need to consider extreme values and then "zoom in" to an

appropriate answer.

1 mm < distance < 100 km

1m < distance < 10 km

10 m < distance < 5 km100 m < distance < 1 km

200 m < distance < 1 km

(1 mark for above argument)

Estimate of distance between pylons of Sydney Harbour Bridge is 600 m.

(1 mark for numerical answer)

Another approach is to consider how long it would take to drive across that section of the

Bridge. So driving at 60km/hr 1km/min a reasonable estimate is that it would take between

30 and 60 seconds. This corresponds to 500 1000m.

Question 2The weight of a box was recorded as 1200 N. How many significant figures are in this

value?

W = 1.200 x 103 N (4 sf)

W = 1.20 x 103 N (3 sf)

x 3 N (2 sf)

The correct answer is 2, 3 or 4 significant figures - the way the number is expressed is

ambiguous.

(2 marks)

Question 3

The dimensions of A4 paper are 2.10x10

2

mm by 2.97x10

2

mm. The paper was quoted bythe manufacturer to be 8.0x101

g.m-2

. What is the mass of a single page of the A4 paper?

Your answer has to be expressed in grams and to the correct number of significant

figures.

1 mm = 10-3 m

Area, A = (2.10x10-1)( (2.97x10-1) m2

A = 6.237x10-2 m2

Surface density (mass/area)

m / A = 8.0x101 g.m-1

m = (8.0x101)( 6.237x10-2) g = 4.9895 g

m= 5.0 g (2 sf)(2 marks)


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Question 4

Pat, whose weight is (650 35) N, is lying on Bondi beach with (0.3 0.1) m2of Pats

body in contact with the beach. How much pressure does Pat exert on the sand? The

uncertainties shown are standard errors of the mean (SEM). Your answer needs to

include the value of the pressure and the SEM.

W= 650 N

E(W) = 35 N

A = 0.3 m2

E(A) = 0.1 m2

Pressure = force / area

P= W / A

P= 650 / 0.3

P= 2166.667 Pa

Uncertainties are SEMs.E(P) / P= { [E(W)/W]

2 + [E(A)/A]2 }0.5

E(P) = P{ [E(W)/W]2 + [E(A)/A]

2 }0.5

E(P) = 2166.667 { [35/650]2 + [0.1/0.3]2 }0.5 = 731 Pa

P= (2.2 0.7) x 103

PaThe uncertainty is generally expressed to one significant figure. The uncertainty then

determines the number of decimal places in the value of the quantity.

(2 marks)

Question 5

You want to measure the density of a liquid. The volume measurement is 2.43x10-4 m3

and the uncertainty is estimated to be 5%. The mass of the liquid is 3.10x10-4

kg and

its uncertainty is estimated to be 1%. What is the density of the liquid and its

uncertainty expressed as a percentage and value?

V= 2.43x10-4 m3

E(V) = (5/100)

m = 3.10x10-4 kg

E(m) = (1/100)

Density = mass / volume = m / V

= (3.10x10-4) / (2.43x10-4) = 1.2757 kg.m-3

Since the uncertainties quoted are percentages

E() / = E(m)/m + E(V)/V

E()= { E(m)/m + E(V)/V} = (1.2757)(5/100 + 1/100 ) = 0.0765

= (1.28 0.08) kg.m-3

Note: uncertainty usually quoted as a single digit.

Note: Value and its uncertainty are expressed to the same number of decimal places.(2 marks)


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Question 6 (modified question and data)An object of weight Wnewtons is suspended vertically on a spring. The length x in metres of

the spring depends on the weight of the object via the equation:

W k x

where k is the spring constant of the spring (a measure of the stiffness of the spring). A First

Year student makes the following measurements of the extension of a spring for objects of a

range of weights.

DATA

Weight (N) 0.2 1.1 3 4.6 6 7.1

Length (m) 0.06 0.26 0.38 0.62 0.88 0.94

(a) Graph this data using an appropriate scale and labels, choosing carefully which

variables are plotted on each axis.

(b) Draw the line of best fit and determine its slope.(c) Draw either a line of maximum (or minimum) acceptable slope and determine its

slope.

(d) From the slope of the line of best fit determine the value of the spring constant kof the

spring and give its units.

(e) Using your line of maximum (or minimum) acceptable slope determine the uncertainty

in your measurement of the spring constant.

(f) Write down your value of the spring constant and its uncertainty using an appropriate

number of significant figures.

Solution

Graph is as follows:


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Slope is determined by

2 1

2 1

.y yrise

Sloperun x x

Select points ,x y on the line for which the slope is required. The selected points are

unlikely to be data values and are usually selected for at least some convenient values (e.g. thevalues associated with length =0m and length=1.0m in the above graph.

Lines of maximum or minimum acceptable fit are somewhat subjective when done manually.

But a key issue is that the lines must be a somewhat reasonable fit to the data. Many students

select lines that are extreme and could not even vaguely be thought of as a fit to the data.

Uncertainty in the slope is best determined from:

max min

2

Slope SlopeSlope

But could be determined from

max best fitSlope Slope Slope or minbest fitSlope Slope Slope .

Results for the above data are:

Best Fit Slope 7.7 N.m-1

Min Fit Slope 6.5 N.m-1

Max Fit Slope 8.9 N.m-1

Delta Slope +/- 1.2 N.m-1

F k x

Slope of line is k so therefore17.7 1.2 N.m .k

Question 7 (this is from the REG/FND Excel Exercise done in Week 2 of first semester).

Combining Estimates of UncertaintiesA common situation is when two or more types of measurement are made and you want to

find out the uncertainty in a derived quantity. For example, suppose you measure the mass

m of an object and also its volume V . Both measurements have an uncertaintyin this case

m and V and you want to find the uncertainty in the calculated density. This type of

calculation is described in detail on pages A9-11. The table on page A10 is particularlyvaluable.

We now wish to calculate the density of the object from the equation

m

V

and to estimate the uncertainty in the density of the object.

Let us do an example in which (1050 30 kg)m and 3(0.98 0.05 m )V .

The uncertainty in the density is calculated from Table A10 as:


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m V

m V

.

We can set this up in Excel using formula to do the calculations and the following columns.

m V m V m

m

V

V

Cells shaded in grey contain data that you enter while the others are derived from Excel

formulae.

The object will float in water if its density is less than that of fresh water3

1000 kg.mw

.

From your results, will the object float?

Solution

Data is:

Mass (kg) Volume (m3) Density (kg/m3) m (kg) V (m3)

1050 0.98 1071 30 0.05

Calculated values are:

m / m V / V / (kg/m3)

0.029 0.051 0.080 85

Results are:31071 85 kg.m

which is consistent with a value smaller than 10003

kg.m and a value larger than1000

3kg.m .

Hence it is not possible to say whether the object will float or sink!

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