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DP IB Physics: HL

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1.1 Measurements in Physics

Question 1a

Marks: 2

A simple pendulum oscillates in simple harmonic motion. It can be assumed that there are no energy losses in the system.

(a)
Prove dimensionally that the work-energy principle applies for this system.
[2]
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    Key Concepts
    SI Units

    Question 1b

    Marks: 4
    (b)
    Complete the following table by giving the SI base units. Then estimate the order of magnitude for each of the physical quantities.
    [4]
        

    Physical Quantity

    SI Base Unit

    Order of Magnitude

    Acceleration of freefall Earth (g)

     m s−2

     

    Stephan-Boltzmann constant (σ)

     

    10−7

    Speed of a β particle

     

     

    Specific heat capacity of water (c)

     

     

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      Question 1c

      Marks: 2

      The density, ρ, and pressure, p, of a gas are related by the expression:

       x equals square root of fraction numerator gamma space p over denominator rho end fraction end root

      where x and γ are constants.

      (c)
      Given that the constant γ is dimensionless
       
      (i)
      Determine the unit of x.
      [1]
      (ii)
      Suggest what quantity is being represented by the symbol x.
      [1]
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        Key Concepts
        SI Units

        Question 2a

        Marks: 3
        (a)
        Identify the quantity with the SI base units of m3 kg−1 s−2.
        [3]
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          Key Concepts
          SI Units

          Question 2b

          Marks: 4
          (b)
          Convert the following measurements to the appropriate unit, and express to an appropriate number of significant figures.

             

             90 000 GW = ____________ mW

              45.1 hF = _____________ fF

             0.60 pm = _____________ km

          214 minutes = _____________ ms

          [4]

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            Question 2c

            Marks: 2

            A sheet of silver has a thickness of 0.671 µm. A silver atom has a radius of 172 pm.

            (c)
            Estimate the number of layers of atoms in this sheet to the nearest thousand.
            [2]
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              Question 3a

              Marks: 3
              (a)
              Identify the variable that has the SI base units kg m2 s−3 A−2.
              [3]
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                Key Concepts
                SI Units

                Question 3b

                Marks: 2
                (b)
                Explain why potential difference is not defined as current × resistance.
                [2]
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                  Key Concepts
                  SI Units

                  Question 3c

                  Marks: 3
                  (c)
                  Convert 0.01 kWh into PeV.
                  [3]
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                    Question 4a

                    Marks: 4

                    Tensile stress (σ) is defined as the force applied per unit cross-sectional area on a material. The tensile strength is the maximum amount of tensile stress a material can be subjected to before fracturing, meaning that it is equivalent to the tensile stress at the breaking point.

                     

                    The humerus bone is approximately cylindrical and has a tensile strength of 0.17 GPa and a diameter of 20 mm.

                     

                    (a)
                    Calculate the maximum force on the humerus bone before it fractures.
                    [4]
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                      Question 4b

                      Marks: 4

                      The femur bone is the strongest bone in the body. It has a tensile strength of 0.135 kN mm2.

                       

                      (b)
                      Calculate the tensile strength of the femur bone in GPa.
                      [4]
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                        Question 4c

                        Marks: 2
                        (c)
                        Calculate the number of cubic millimetres (mm3) in 23 km3.
                        [2]

                         

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                          Question 5a

                          Marks: 2
                          (a)
                          Estimate the time it takes light to cross the nucleus of a hydrogen atom.
                          [2]
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                            Key Concepts
                            Orders of Magnitude

                            Question 5b

                            Marks: 3
                            (b)
                            Estimate the order of magnitude with an appropriate SI unit and correct prefix for the following quantities.
                               
                            (i)   Mass of an aeroplane.
                            [1]
                            (ii)   Current through an LED.
                            [1]
                            (iii)   Time between two heartbeats.
                            [1]

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                              Key Concepts
                              Orders of Magnitude

                              Question 5c

                              Marks: 3

                              1 u is the atomic mass unit and a common unit used in nuclear physics.

                               

                              (c)
                              Show that its value in kg is approximately equal to the mass of a proton in kg.
                              [3]
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                                Question 5d

                                Marks: 4

                                The cross-sectional area of nuclei are commonly measured in the units barn, which are represented by the symbol b. 1 barn = 100 fm2

                                (d)
                                Calculate the value of a nano barn (nb) in m2.
                                [4]
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