(1) - Wales High School · A student suspended a spring from a laboratory stand and then hung a...

Figure 1 shows an exercise device called a chest expander. The three springs are identical.

Figure 1

A person pulls outwards on the handles and does work to stretch the springs.

(a) Complete the following sentence.

When the springs are stretched ___________ ___________ energy is stored in thesprings.

(1)

1

(b) Figure 2 shows how the extension of a single spring from the chest expander depends onthe force acting on the spring.

Figure 2

(i) How can you tell, from Figure 2, that the limit of proportionality of the spring has notbeen exceeded?

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(ii) Use data from Figure 2 to calculate the spring constant of the spring.Give the unit.

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Spring constant = ___________ Unit ___________

(3)

(iii) Three identical resistors joined in parallel in an electrical circuit share the total currentin the circuit.

In a similar way, the three springs in the chest expander share the total force exerted.

By considering this similarity, use Figure 2 to determine the total force exerted on thechest expander when each spring is stretched by 0.25 m.

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Total force = ___________ N

(2)

(c) The student in Figure 3 is doing an exercise called a chin-up.

Figure 3


Each time the student does one chin-up he lifts his body 0.40 m vertically upwards.The mass of the student is 65 kg.The student is able to do 12 chin-ups in 60 seconds.

Calculate the power developed by the student.

Gravitational field strength = 10 N/kg

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Power = ___________ W

(3)

(Total 10 marks)

A student investigated how the extension of a spring depends on the force applied to the spring.

The diagram shows the spring before and after a force had been applied.

(a) (i) Complete the following sentence using letters, A, B, C or D, from the diagram.

The extension of the spring is the distance between the positions labelled

___________and ___________ on the metre rule.

(1)

2


(ii) What form of energy is stored in the stretched spring?

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(1)

(b) The results from the investigation are plotted on the following graph.

(i) The graph shows that the student has made an error throughout the investigation.

What error has the student made?

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Give the reason for your answer.

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(2)


(ii) The student has loaded the spring beyond its limit of proportionality.

Mark on the graph line the limit of proportionality of the spring. Label the point P.

Give the reason for choosing your point P.

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(2)

(c) The student uses a different spring as a spring balance. When the student hangs a stonefrom this spring, its extension is 72 mm.

The spring does not go past the limit of proportionality.

Calculate the force exerted by the stone on the spring.

spring constant = 25 N/m

Show clearly how you work out your answer.

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Force = _________________________ N

(2)

(Total 8 marks)


A student wants to calculate the density of the two objects shown in the figure below.

© Whitehoune/iStock/Thinkstock, © Marc Dietrich/Hemera/Thinkstock

Describe the methods that the student should use to calculate the densities of the two objects.

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(Total 6 marks)

3


A student wanted to determine the density of a small piece of rock.

(a) Describe how the student could measure the volume of the piece of rock.

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(4)

4

(b) The volume of the piece of rock was 18.0 cm3.

The student measured the mass of the piece of rock as 48.6 g.

Calculate the density of the rock in g/cm3.

Use the equation:

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Density = _______________________ g/cm3

(2)


The graph below shows the densities of different types of rock.

(c) What is the most likely type of rock that the student had?

Tick one box.

Basalt

Flint

Granite

Limestone

Sandstone

(1)


(d) Give one source of error that may have occurred when the student measured the volumeof the rock.

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(1)

(e) How would the error you described in part (d) affect the measured volume of the rock?

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(1)

(Total 9 marks)

A student carried out an investigation to determine the spring constant of a spring.

The table below gives the data obtained by the student.

Force in N Extension in cm0 0.0

2 3.5

4 8.0

6 12.5

8 16.0

10 20.0

5

(a) Describe a method the student could have used to obtain the data given in the table above.

Your answer should include any cause of inaccuracy in the data.

Your answer may include a labelled diagram..........

(6)

(b) The student measured the extension for five different forces rather than just measuring theextension for one force.

Suggest why.

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(1)


The diagram below shows some of the data obtained by the student.

(c) Complete the diagram above by plotting the missing data from the table above.

Draw the line of best fit.

The table above is repeated here to help you answer this question.

Force in N Extension in cm0 0.0

2 3.5

4 8.0

6 12.5

8 16.0

10 20.0

(2)

(d) Write down the equation that links extension, force and spring constant.

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(1)


(e) Calculate the spring constant of the spring that the student used.

Give your answer in newtons per metre.

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Spring constant = ______________________ N/m

(4)

(f) Hooke’s Law states that:‘The extension of an elastic object is directly proportional to the force applied, provided thelimit of proportionality is not exceeded.’

The student concluded that over the range of force used, the spring obeyed Hooke’s Law.

Explain how the data supports the student’s conclusion.

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(2)

(Total 16 marks)


A student suspended a spring from a laboratory stand and then hung a weight from the spring.

Figure 1 shows the spring before and after the weight is added.

Figure 1

(a) Measure the extension of the spring shown in Figure 1.

Extension = ________________________ mm

(1)

6


(b) The student used the spring, a set of weights and a ruler to investigate how the extensionof the spring depended on the weight hanging from the spring.

Before starting the investigation the student wrote the following prediction:

The extension of the spring will be directly proportional to the weight hangingfrom the spring.

Figure 2 shows how the student arranged the apparatus.

Figure 2

Before taking any measurements, the student adjusted the ruler to make it vertical.

Explain why adjusting the ruler was important.

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(2)


(c) The student measured the extension of the spring using a range of weights.

The student’s data is shown plotted as a graph in Figure 3.

Figure 3

What range of weight did the student use?

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(1)

(d) Why does the data plotted in Figure 3 support the student’s prediction?

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(1)

(e) Describe one technique that you could have used to improve the accuracy of themeasurements taken by the student.

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(2)


(f) The student continued the investigation by increasing the range of weights added to thespring.

All of the data is shown plotted as a graph in Figure 4.

Figure 4

At the end of the investigation, all of the weights were removed from the spring.

What can you conclude from Figure 4 about the deformation of the spring?

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Give the reason for your conclusion.

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(2)

(Total 9 marks)


A student investigated the behaviour of springs. She had a box of identical springs.

(a) When a force acts on a spring, the shape of the spring changes.

The student suspended a spring from a rod by one of its loops. A force was applied to thespring by suspending a mass from it.

Figure 1 shows a spring before and after a mass had been suspended from it.

Figure 1

Before After

(i) State two ways in which the shape of the spring has changed.

1. ____________________________________________________________

2. ____________________________________________________________

(2)

7

(ii) No other masses were provided.

Explain how the student could test if the spring was behaving elastically.

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(2)


(b) In a second investigation, a student took a set of measurements of force and extension.

Her results are shown in Table 1 .

Table 1

Force in newtons 0.0 1.0 2.0 3.0 4.0 5.0 6.0

Extension in cm 0.0 4.0 12.0 16.0 22.0 31.0

(i) Add the missing value to Table 1.

Explain why you chose this value.

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(3)

(ii) During this investigation the spring exceeded its limit of proportionality.

Suggest a value of force at which this happened.

Give a reason for your answer.

Force = _________________ N

Reason _______________________________________________________

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(2)


(c) In a third investigation the student:

• suspended a 100 g mass from a spring

• pulled the mass down as shown in Figure 2

• released the mass so that it oscillated up and down

• measured the time for 10 complete oscillations of the mass

• repeated for masses of 200 g, 300 g and 400 g.

Figure 2

Her results are shown in Table 2.

Table 2

Time for 10 complete oscillations in seconds

Mass in g Test 1 Test 2 Test 3 Mean

100 4.34 5.20 4.32 4.6

200 5.93 5.99 5.86 5.9

300 7.01 7.12 7.08 7.1

400 8.23 8.22 8.25 8.2


(i) Before the mass is released, the spring stores energy.

What type of energy does the spring store?

Tick ( ) one box.

Tick ( )

Elastic potential energy

Gravitational potential energy

Kinetic energy

(1)

(ii) The value of time for the 100 g mass in Test 2 is anomalous.

Suggest two likely causes of this anomalous result.

Tick ( ) two boxes.

Tick ( )

Misread stopwatch

Pulled the mass down too far

Timed half oscillations, not complete oscillations

Timed too few complete oscillations

Timed too many complete oscillations

(2)

(iii) Calculate the correct mean value of time for the 100 g mass in Table 2.

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Mean value = __________________ s

(1)


(iv) Although the raw data in Table 2 is given to 3 significant figures, the mean values arecorrectly given to 2 significant figures.

Suggest why.

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(2)

(v) The student wanted to plot her results on a graph. She thought that four sets ofresults were not enough.

What extra equipment would she need to get more results?

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(2)

(Total 17 marks)


Mark schemes

(a) elastic potential11

(b) (i) line is straight

accept line does not curve1

(ii) 400

allow 1 mark for correct substitution of any pair of numbers correctlytaken from the graph e.g.160 = k × 0.40

2

newtons per metre or N/m

if symbols are used they must be correct1

(iii) 300

allow 1 mark for correctly obtaining force on 1 spring = 100N2

(c) 52

allow 2 marks for calculating change in gpe for 1 chin-up as 260 (J)or for 12 chin-ups as 3120 (J)

an answer 4.3 gains 2 marks

allow 1 mark for correct substitution into gpe equation ie gpe = 65 ×10 × 0.4 (× 12)

or

correct use of power equation with an incorrect value for energytransferred

3

[10]

(a) (i) B C

either order1

2

(ii) elastic potential (energy)

accept strain for elastic1

(b) (i) mark both parts together1

measured / recorded the length of the spring (and not extension)

accept measured A–C (and not B–C)

accept did not work out/measure the extension

extension does not equal zero when force = 0

accept line should pass through the origin1


(ii) point marked at 5.5 (N)

accept any point between 5.0 and 5.6 inclusive1

up to that point force and extension are (directly) proportional

accept it’s at the end of the straight part (of the graph line)

accept past that point force and extension are no longer (directly)proportional

accept the line starts to curve1

(c) 1.8

allow 1 mark for correct substitution, ie 25 x 0.072 provided nosubsequent step shown

an answer 1800 gains 1 mark

an incorrect conversion from mm to m with a subsequent correctcalculation gains 1 mark

2

[8]

Level 3 (5–6 marks):Clear and coherent description of both methods including equation needed to calculate density.Steps are logically ordered and could be followed by someone else to obtain valid results.

Level 2 (3–4 marks):Clear description of one method to measure density or partial description of both methods. Stepsmay not be logically ordered.

Level 1 (1–2 marks):Basic description of measurements needed with no indication of how to use them.

0 marks:No relevant content.

Indicative content

For both:• measure mass using a balance• calculate density using ρ = m / V

Metal cube:• measure length of cube’s sides using a ruler• calculate volume

Small statue:• immerse in water• measure volume / mass of water displaced• volume of water displaced = volume of small statue

[6]

3


(a) Level 2: The method would lead to the production of a valid outcome. Key steps areidentified and logically sequenced.

3−4

Level 1: The method would not necessarily lead to a valid outcome. Some relevantsteps are identified, but links are not made clear.

1−2

No relevant content0

4

Indicative content

• part fill a measuring cylinder with water• measure initial volume• place object in water• measure final volume• volume of object = final volume − initial volume

• fill a displacement / eureka can with water• water level with spout• place object in water• collect displaced water• measuring cylinder used to determine volume of displaced water

(b)

1

density = 2.70 (g/cm3)1

an answer of 2.70 (g/cm3) scores 2 marks

(c) limestone1

(d) eye position when using measuring cylinderorwater level in can (at start) not at level of spoutornot all water displaced by stone is collected in container

1

(e) volume would be lower / higher1

[9]


(a) Level 3: The method would lead to the production of a valid outcome. All key stepsare identified and logically sequenced.

5−6

Level 2: The method would not necessarily lead to a valid outcome. Most steps areidentified, but the method is not fully logically sequenced.

3−4

Level 1: The method would not lead to a valid outcome. Some relevant steps areidentified, but links are not made clear.

1−2

No relevant content0

5

Indicative content

set up a clamp stand with a clamp

hang the spring from the clamp

use a second clamp and boss to fix a (half) metre ruler alongside the spring

record the metre ruler reading that is level with the bottom of the spring

hang a 2 N weight from the bottom of the spring

record the new position of the bottom of the spring

calculate the extension of the spring

measure the extension of the spring

add further weights to the spring so the force increases 2 N at a time up to 10 N

for each new force record the position of the bottom of the spring and calculate /measure the extension

possible source of inaccuracy

not fixing the ruler in position but simply holding the ruler next to the spring

not clamping the ruler vertical

misjudging the position of the bottom of the spring

parallax error

allow any other sensible suggestion that could reasonably lead to inaccuracy in thedata

allow a description that would increase accuracy

repeating the measurements is insufficient


(b) to identify any anomalous resultsallow calculate an average for the spring constant

orto reduce the effect of random error

allow (more) accurate

to obtain an average is insufficientto be able to draw a graph is insufficient

1

(c) both points plotted correctly1

correct line of best fit drawn

to pass through (0,0) and (10,20)1

(d) force = spring constant × extensionallow F = ke

1

(e) extension = 0.2allow 0.035 / 0.08 / 0.125 / 0.16

1

10 = k × 0.2

force value must match extensionthis mark may be awarded if e is in cm

1

allow correct transformation of their chosen valuesthis mark may be awarded if e is in cm

1

k = 50

an answer 0.5 scores 3 marks1

an answer of 50 scores 4 marks

(f) the line is straightallow the line does not curve

1

and passes through the origin

this mark is dependent on scoring the first mark

allow a correct description of direct proportionality for 2marks

ignore the line shows they are directly proportional1

[16]


(a) accept any value between 12 (mm) and 13 (mm) inclusive16

(b) to reduce the error in measuring the extension of the spring

accept length for extension throughout1

as the ruler at an angle would make the measured extensions shorter1

(c) 1 (N) to 6 (N)

accept from 0 (N) to 6 (N)1

(d) gives a straight line through the origin1

(e) any practical technique that would improve the accuracy of length measurement eg

use a set square1

to line up the bottom of the spring with the ruler scale

or

attach a horizontal pointer to the bottom of the spring (1)

so that the pointer goes across the ruler scale (1)1

(f) the spring has been inelastically deformed1

because it went past its limit of proportionality

accept elastic limit for limit of proportionality1

accept it does not go back to its original length when the weightsare removed

[9]

(a) (i) any two from:

• length of coils increased• coils have tilted• length of loop(s) increased• increased gap between coils• spring has stretched / got longer• spring has got thinner

2

7

(ii) remove mass

accept remove force / weight1


observe if the spring returns to its original length / shape (then it is behavingelastically)

1

(b) (i) 8.0 (cm)1

extension is directly proportional to force (up to 4 N)

for every 1.0 N extension increases by 4.0 cm (up to 4 N)

evidence of processing figures eg 8.0 cm is half way between 4.0 cm and 12.0cm

1

allow spring constant (k) goes from to1

(ii) any value greater than 4.0 N and less than or equal to 5.0 N1

the increase in extension is greater than 4 cm per 1.0 N (of force) added

dependent on first mark1

(c) (i) elastic potential energy1

(ii) misread stopwatch1

timed too many complete oscillations1

(iii) 4.3 (s)

accept 4.33 (s)1

(iv) stopwatch reads to 0.01 s1

reaction time is about 0.2 sorreaction time is less precise than stopwatch

1

(v) use more masses1

smaller masses eg 50 g

not exceeding limit of proportionality1

[17]


(1) - Wales High School · A student suspended a spring from a laboratory stand and then hung a...

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