A LevelPhysicsAQAExam QuestionsMechanics & MaterialsThe Young Modulus

The Young Modulus (AQA A Level Physics)

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11 mark

Which equation is used to calculate the Young Modulus of a material?

  • E = fraction numerator F L over denominator A increment L end fraction

  • F = kx

  • E = fraction numerator F increment L over denominator A L end fraction

  • k =  F over x

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21 mark

The Young Modulus can be found using the equation, E = fraction numerator s t r e s s over denominator s t r a i n end fraction .

What are the units of stress and strain?

 

stress

strain

A

Pa

N

B

Pa

 no units

C

N

Pa

D

no units

no units

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    31 mark

    The stress-strain graph for carbon is shown.

    Which property of the graph gives the Young Modulus of carbon?

    q3_the-young-modulus_aqa-as-physics-mcq

    • The gradient of the whole graph

    • The gradient of the straight section of the graph

    • The y-intercept

    • The Young Modulus cannot be calculated from the graph

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    41 mark

    A student uses the following apparatus to determine the Young modulus of copper. 

    q4_the-young-modulus_aqa-as-physics-mcq

    The student wishes to plot a stress-strain graph for the copper wire.

    What two additional pieces of apparatus would be required to determine values for stress and strain?

     

    stress

    strain

    A

    micrometer

    metre ruler

    B

    micrometer

    vernier calipers

    C

    digital scales

    vernier calipers

    D

    metre ruler

    micrometer

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      51 mark

      What direct measurements would a student make in an experiment to find the Young Modulus?

      1. diameter of the wire being tested

      2. cross sectional area of the wire being tested

      3. applied load

      4. the amount of mass

      • 1, 2 and 4

      • 2, 3 and 4

      • 1 and 3

      • 1 and 4

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      61 mark

      The graph shows the stress-strain curve for a length of constantan wire.

      What is the ultimate tensile stress (UTS) of the wire?

      q6_the-young-modulus_aqa-as-physics-mcq

      • 475 × 106 MPa

      • 475 × 106 Pa

      • 5.3 × 10–3

      • 5.3 cross times 10–3 m

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      71 mark

      An experiment was carried out to find the Young Modulus of copper, using copper wire.

      The uncertainties in the measurements are given below.

      measurement

      uncertainty

      applied load

       plus-or-minus space 2.0 percent sign

      cross-sectional area

       plus-or-minus space 3.0 space percent sign

      What is the percentage uncertainty in the stress applied to the wire?

      • 6.0 %

      • 1.5%

      • 5.0 %

      • 0.7 %

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      81 mark

      A metal wire that is supported vertically from a hook has a cross sectional area of 0.5  × 10-6 m2.

      Weights totalling 1.5 N are suspended from the wire, which extends by 2.0 %.

      What is the Young Modulus of this wire?

      • 75 kPa

      • 300 kPa

      • 7.5 MPa

      • 150 MPa

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      91 mark

      A student performs the Young Modulus experiment.

      Which line in the table correctly matches up the best choice of equipment for a particular measurement, and the precision of the measurement?

       

      quantity

      instrument

      precision

      A

      original length

      metre ruler

      ± 0.1 mm

      B

      extension

      metre ruler

      ± 1 mm

      C

      diameter

      micrometer

      ± 0.1 mm

      D

      mass

      force meter

      ±0.1 g

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        101 mark

        A student has plotted the graph below, after carefully investigating the extension produced by different loads applied to a wire.

        What calculation based on the graph will give the Young Modulus?

        q10_the-young-modulus_aqa-as-physics-mcq

        • gradient

        • gradient × fraction numerator l e n g t h blank over denominator c r o s s minus s e c t i o n a l blank a r e a end fraction

        • gradient × fraction numerator c r o s s minus s e c t i o n a l blank a r e a over denominator l e n g t h end fraction

        • the area under the line

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        11 mark

        An experiment was carried out to find the Young Modulus of copper, using copper wire.

        The uncertainties in the measurements are given below.

        measurement

        uncertainty

        applied load

         plus-or-minus space 3.0 space percent sign

        diameter of wire

         plus-or-minus space 0.5 space percent sign

        extension

          plus-or-minus space 2.5 space percent sign

        original length of wire

         plus-or-minus space 0.2 space percent sign

        What is the percentage uncertainty in the Young Modulus applied to the wire?

        • 5.1 %

        • 6.7%

        • 0.5 %

        • 9.0 %

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        21 mark

        A metal tube with a thin wall thickness w is shown in the diagram. The thickness of the wall is small when compared to the diameter of the tube.

        q12_the-young-modulus_aqa-as-physics-mcq

        A force T applied parallel to the axis of the tube puts the tube under tension. It is proposed that making the wall thicker would reduce the stress on the tube.

         If the tube diameter and the tension remain the same, which wall thickness would half the stress?

        • 4w

        • 2w

        •  square root of 2 w

        • w over 2

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        31 mark

        A steel metal wire has the following properties:

                                                         diameter = 5.0 × 10–4 m

                                                Young modulus = 2.0 × 1011 Pa

                                                              tension = 20 N

        The string snaps and contracts elastically.

        By what percentage does a length l of a piece of the string contract?

        • 1.3 x 10–2 %

        • 1.3 x 10–4 %

        • 5.1 x 10–4 %

        • 5.1 x 10–2 %

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        41 mark

        The Young modulus of a metal wire is dependent on which property?

        • spring constant 

        • ductility

        • ultimate tensile stress 

        • elastic limit

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        51 mark

        The Young modulus E and the force per unit extension k describes the behaviour of a wire under tensile stress.

        For a wire of length L and cross-sectional area A, what is the relationship between E and k?

        • E equals fraction numerator A over denominator k L end fraction

        •  E equals fraction numerator k A over denominator L end fraction

        • E equals fraction numerator k L over denominator A end fraction

        • E equals fraction numerator L over denominator k A end fraction

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        61 mark

        A steel bar, shown in the diagram, has a circular cross-section that is under tension T.

        The diameter of the thinner portion is half the wider portion.

        q16_the-young-modulus_aqa-as-physics-mcq

        What is the value of  fraction numerator bold italic s bold italic t bold italic r bold italic e bold italic s bold italic s bold space bold italic i bold italic n bold space bold italic t bold italic h bold italic e bold space bold italic w bold italic i bold italic d bold italic e bold space bold italic p bold italic o bold italic r bold italic t bold italic i bold italic o bold italic n over denominator bold italic s bold italic t bold italic r bold italic e bold italic s bold italic s bold space bold italic i bold italic n bold space bold italic t bold italic h bold italic e bold space bold italic n bold italic a bold italic r bold italic r bold italic o bold italic w bold space bold italic p bold italic o bold italic r bold italic t bold italic i bold italic o bold italic n end fraction ?

        • 4.0

        • 2.0

        • 0.50

        • 0.25

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        71 mark

        A student wanted to find the young modulus of a wire. The equation for the young modulus E is:

                                                                            E equals fraction numerator 4 F l over denominator pi d squared x end fraction

        The student extended the wire with a known force and made a series of measurements.

        Which measurement has the largest effect on the uncertainty in the value of the calculated Young modulus?

         

        measurement

        symbol

        value

        A

        length of wire before force applied

        l

        2.043 ± 0.002 m

        B

        force applied

        F

        19.62 ± 0.01 N

        C

        extension of wire with force applied

        x

        5.2 ± 0.2 mm

        D

        diameter of wire

        d

        0.54 ± 0.02 mm

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          81 mark

          Which unit cannot be used for the Young Modulus?

          • N m-2 

          • kg m-1 s-2 

          • J m-3

          • kg m s-2

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          91 mark

          The stress-strain graph for carbon is shown.

          q3_the-young-modulus_aqa-as-physics-mcq

          What is the Young Modulus of the carbon?

          • 1 020 Pa

          • 2 200 Pa

          • 2.8 x 106 Pa

          • 2.8 x 109 Pa

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          101 mark

          A steel wire X has a length L and a circular cross-section of radius r. When X hands vertically and a load is attached to the bottom end, it extends by e.

          Another wire Y is made from the same material and has the same load attached to it.

          Which length and radius for Y will produced an extension of begin mathsize 16px style e over 8 end style?

           

          length of Y

          Radius of Y

          A

          16L

          2r

          B

          4L

          0.5r

          C

          0.5L

          2r

          D

          2L

          0.5r

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            11 mark

            A construction site crane has a steel lifting cable with diameter 36 mm and length 27.0 m. The steel used has a Young modulus of 200 GPa.

            Calculate the extension when the crane is used to lift materials with weight 28 kN.

            • 0.37 mm

            • 3.7 mm

            • 3.7 cm

            • 3.7 m

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            21 mark

            Steel has a Young Modulus of 2 × begin mathsize 16px style 10 to the power of 11 end style Pa and a breaking strain of 0.1 %.

            What is the force needed to break a steel wire of diameter 1 mm?

            • 158 N

            • 628 N

            • 15 800 N 

            • 62 800 N

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            31 mark

            The graph shows the behaviour of a copper alloy when it is stressed.

            q23_the-young-modulus_aqa-as-physics-mcq

            Which of the following shows a second line for a material which;

            • is brittle,

            • has a Young modulus lower than the copper alloy

            • fractures at a strain of 2.6 x begin mathsize 16px style 10 to the power of negative 3 end exponent end style?

            q23-2_the-young-modulus_aqa-as-physics-mcq

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              41 mark

              Two springs are connected in series as shown. The values of the spring constants are different, where k1 = 25 N cm−1 and k2 = 35 N cm−1.

              q24_the-young-modulus_aqa-as-physics-mcq

              The spring has a circular cross-sectional area of 707 mm2 and before the 50 N load is placed, the combination have a length of 5.0 cm.

              What is the young modulus of the material that the spring is made from?

              • 104 GPa

              • 104 kPa

              • 10.4 kPa

              • 104 MPa

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              51 mark

              An A Level Physics student carries out an investigation into the Young Modulus of a copper wire and plots her graph as shown.

              q25_the-young-modulus_aqa-as-physics-mcq

              How would the graph be different if she repeated the experiment, first with thinner wire, and then using thicker wire?

               

              thinner wire

              thicker wire

              A

              limit of proportionality would be at a higher force

              steeper gradient

              B

              limit of proportionality would be at a lower force

              steeper gradient

              C

              steeper gradient

              limit of proportionality would be at a lower force

              D

              shallower gradient

              limit of proportionality would be at a lower force

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                61 mark

                A popular playground ride is a rocking horse on a spring, as shown. The toy is designed to be used by children aged between 2-5 years old.

                When the child sits on the horse, the spring should compress a little but not too much for play to be both fun, and safe.

                q26_the-young-modulus_aqa-as-physics-mcq

                Clinical data from childcare professionals suggests that 2 year old children have average weight of 12.0 kg, while five-year old children average 19.0 kg.

                Which spring constant would be most suitable?

                • 1.15  Nstraight m to the power of negative 1 end exponent

                • 1.03 X 103 Nstraight m to the power of negative 1 end exponent

                • 1 020 X 106 Nstraight m to the power of negative 1 end exponent

                • 10 X 108 Nstraight m to the power of negative 1 end exponent

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                71 mark

                The system below shows a composite rod made from two different materials.

                The dimensions and Young Modulus for each rod are as follows:

                For Rod 1

                For Rod 2

                • diameter, d1 = 1.0 cm,

                • diameter, d2 = 0.5 cm,

                • length, l1 = 4.0 cm,

                • length, l2 = 3.0 cm,

                • Young modulus, E1= 20 GPa.

                •  Young modulus, E2 = 40 GPa

                q27_the-young-modulus_aqa-as-physics-mcq

                What is the ratio of fraction numerator e x t e n s i o n space R o d space 1 over denominator e x t e n s i o n space R o d space 2 end fraction?

                • 1 third

                • 2 over 3

                • 3 over 2

                • bold 1

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                81 mark

                The supporting cable of a suspension footbridge if the cable has a diameter of 55 mm, and it exerts an upwards force on the footpath of 5.2 kN.

                If the Young Modulus of the steel the cable is made from is 2.0 GPa, and the maximum strain the cable can withstand before breaking is 5.0 %, then what is the breaking stress?

                 

                operating stress / Pa

                breaking stress / Pa

                A

                2.2

                1.00 x 108

                B

                2.2 x 106

                1.00 x 108

                C

                2.2

                1.00 x 106

                D

                2.2 x 106

                1.00 x 106

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                  91 mark

                  A uniform, heavy chain of Young Modulus, E, length, L, mass per unit length, μ, cross-sectional area, A is supported by a thin rope with negligible mass.

                  q29_the-young-modulus_aqa-as-physics-mcq

                  Find an expression for the extension, ΔL, when the chain is fully suspended above the ground.

                  • fraction numerator mu g L over denominator 2 A E end fraction

                  • fraction numerator 2 mu g L over denominator A E end fraction

                  • fraction numerator mu g L to the power of 10 over denominator 2 A E end fraction

                  • fraction numerator mu g L over denominator A E end fraction

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                  101 mark

                  A copper wire of length 1.80 m and cross-sectional area of 1.6 x 10 to the power of negative 8 end exponentm2 is put under a tensile stress of 2.45 N. The length of the wire increases by 2 mm.

                  The experiment has been done using the following equipment:

                  • metre ruler to measure length

                  • vernier scale with precision of 0.1 mm to measure extension

                  • micrometer to measure diameter of the wire

                  What is the Young Modulus of copper? You can assume the value for applied force is correct. 

                  • (1.4 ± 0.06) x 108 Nstraight m to the power of negative 2 end exponent

                  • (1.4 ± 0.09) x 108 Nstraight m to the power of negative 2 end exponent

                  • (1.4 ± 0.06) x 1011 Nstraight m to the power of negative 2 end exponent

                  • (1.4  ± 0.09) x 1011 Nstraight m to the power of negative 2 end exponent

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