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DP IB Physics: HL

Topic Questions

Home / IB / Physics: HL / DP / Topic Questions / 6. Circular Motion & Gravitation / 6.1 Circular Motion / Structured Questions


6.1 Circular Motion

Question 1a

Marks: 2

A proton of mass m moves with uniform circular motion. Its kinetic energy is K and its orbital period is T .

(a)
Show that the orbital radius r is given by: 

r equals square root of fraction numerator K T squared over denominator 2 pi squared m end fraction end root
[2]
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    Question 1b

    Marks: 3

    The proton moves in a clockwise circle of circumference 1.25 mm. The net force on the proton is 65 fN. 

    (b)
    Determine the linear speed of the proton.
    [3]
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      Key Concepts
      Centripetal Force

      Question 1c

      Marks: 3
      (c)
      Calculate the proton's orbital frequency. 
      [3]
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        Question 1d

        Marks: 3
        (d)

        (i)
        State the mechanism by which protons are made to travel in circular paths.
        [1]
        (ii)
        Comment on the work done on the proton by this mechanism.
        [2]
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          Question 2a

          Marks: 3

          A small ball is attached to a string and moves in a horizontal circular path. It completes one revolution every 2.5 s, with the string at an angle θ to the vertical.

          sl-sq-hard-6-1-q2a

          (a)
          Calculate the orbital radius if θ = 12°. 

          You may wish to use the following data: 
          tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction
          [3] 
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            Key Concepts
            Centripetal Force

            Question 2b

            Marks: 2
            (b)
            Show that the length of the string l is given by: 

            l equals fraction numerator g over denominator omega squared space cos space theta end fraction
            You may wish to use the following data: 
            tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction

            [2]
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              Question 2c

              Marks: 2

              The equation in part (b) seems to suggest that the length of the string l is dependent on the angle it makes to the vertical, θ.

              (c)
              Comment on the relationship between the length of the string l and the angle it makes to the vertical, θ
              [2]
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                Question 3a

                Marks: 3

                A marble rolls from the top of a bowling ball of radius R

                sl-sq-6-1-hard-q3a

                (a)
                Show that when the marble has moved so that the line joining it to the centre of the sphere subtends an angle of θ to the vertical, its speed v is given by: 

                v equals square root of 2 g R left parenthesis 1 minus cos space theta right parenthesis end root
                [3]
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                  Question 3b

                  Marks: 4
                  (b)
                  Deduce that, at the instant shown in the image in part (a), the normal reaction force N on the marble from the bowling ball is given by:

                  N equals m g left parenthesis 3 space cos space theta space – space 2 right parenthesis
                  [4]
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                    Key Concepts
                    Centripetal Force

                    Question 3c

                    Marks: 2
                    (c)
                    Hence, determine the angle θ at which the marble loses contact with the bowling ball. 
                    [2]
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                      Question 4a

                      Marks: 3

                      The 'loop-the-loop' is a popular ride at amusement parks, involving passengers in cars travelling in a vertical circle. 

                      sl-sq-6-1-hard-q4a

                      The loop has a radius of 8.0 m and a passenger of mass 70 kg travels at 10 m s–1 when at the highest point of the loop. 

                      (a)
                      Calculate, at the highest point:

                      (i)
                      the centripetal acceleration of the passenger,
                      [1]
                      (ii)
                      the force that the seat exerts on the passenger.
                      [2]
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                        Question 4b

                        Marks: 3
                        (b)
                        Stating any assumptions required, calculate the speed of the passenger at the point marked 'exit from loop' in part (a). 
                        [3]
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                          Question 4c

                          Marks: 2

                          Operators must ensure that the speed of the vehicle carrying passengers into the loop-the-loop is above a certain value. 

                          (c)
                          Suggest a reason for this, and determine the minimum required speed. 
                          [2]
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                            Question 5a

                            Marks: 3

                            A popular trick to impress young observers is to swing a bucket of water in a vertical circle. If the bucket is swung fast enough, no water spills out. 

                            (a)
                            Estimate the minimum linear speed v required to swing a bucket in a vertical circle, such that no water spills. 
                            [3]
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                              Question 5b

                              Marks: 4

                              When the bucket of water is stirred with a spoon in uniform circular motion near the rim, the level of water in the bucket is observed to change from a flat horizontal dashed line to a curved solid line, as shown.

                              sl-sq-6-1-hard-q5b

                              (b)
                              By considering the circular motion of a fluid particle in the water, explain this observation using relevant physical principles. 
                              [4]

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