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DP IB Physics: SL

Topic Questions

Home / IB / Physics: SL / DP / Topic Questions / 2. Mechanics / 2.3 Work, Energy & Power / Structured Questions


2.3 Work, Energy & Power

Question 1a

Marks: 4

A box of mass 5.8 kg with initial speed 7.2 m s–1 begins to move up a smooth incline.

q1a_work-energy-_-power_ib-sl-physics-sq-medium

The box is momentarily brought to rest after colliding with a spring of spring constant 210 N m–1. It stops a vertical distance of 0.65 m above its initial position.

(a)       

(i)
Calculate the initial energy of the box
   

(ii)
Determine an equation for the final energy of the box when it collides with the spring
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    Question 1b

    Marks: 3
    (b)
    Hence, or otherwise, calculate the amount by which the spring is compressed.
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      Question 1c

      Marks: 3

      There is now a constant frictional force of 16 N opposing the motion of the box as it moves along the slope uphill part of its path. The incline is at an angle of 22º from the horizontal.

      (c)
      Calculate the magnitude of the work done on the box as it travels uphill.
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        Key Concepts
        Work Done

        Question 1d

        Marks: 3
        (d)
        Hence, or otherwise, calculate the new amount by which the spring is compressed.
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          Question 2a

          Marks: 3

          Some cargo ships use kites working together with the ship’s engines to move the vessel.

          q2a_work-energy-_-power_ib-sl-physics-sq-medium

          The tension in the cable that connects the kite to the ship is 350 kN. The kite is pulling the ship at an angle of θ to the horizontal. The ship travels at a steady speed of 3.9 m s–1 when the ship’s engines operate with a power output of 5.7 MW.

          (a)
          Calculate the angle θ if the work done on the ship by the kite when the ship travels for 5 minutes, before the engines are cut off, is 355 MJ.
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            Key Concepts
            Work Done

            Question 2b

            Marks: 3
            (b)
            When the ship is travelling at 3.9 m s–1, calculate the power that the kite provides.
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              Key Concepts
              Power

              Question 2c

              Marks: 3
              (c)
              Hence calculate the percentage of the total power required by the ship that the kite provides.
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                Key Concepts
                Efficiency
                Power

                Question 2d

                Marks: 3

                The kite is taken down and no longer produces a force on the ship. The resistive force F that opposes the motion of the ship is related to the speed of the ship by

                 F = kv

                where k is a constant.

                (d)
                Show that, if the power output of the engines remains at 5.7 MW, the speed of the ship will decrease to about 3.5 m s–1. Assume that k is independent of whether the kite is in use or not.
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                  Question 3a

                  Marks: 3

                  The arrangement shown below is used to test golf club heads.

                  q3a_work-energy-_-power_ib-sl-physics-sq-medium

                  The shaft of a club is pivoted and the centre of mass of the club head is raised by a height h before being released. The club head then falls back to the vertical position where it strikes the ball.

                  (a)
                  Calculate the maximum speed of the club head achieved when h = 75 cm.
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                    Question 3b

                    Marks: 3
                    (b)
                    Explain why, in reality, the speed of the ball will not be the same as the maximum speed of the club head.
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                      Question 3c

                      Marks: 3

                      The optimal launch angle for a projectile, such as a golf ball, is 45º. Another experiment is carried out with a golf club that has a shaft 1.14 m long.

                      q3c_work-energy-_-power_ib-sl-physics-sq-medium

                      (c)
                      Calculate the maximum speed this club head achieves just before it hits the ball.
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                        Question 3d

                        Marks: 3

                        The golf club head has a mass of 200 g and has a power of 460 mW just before it hits the ball.

                        (d)
                        Show that time taken for the golf club swing is about 1.4 s.
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                          Key Concepts
                          Power

                          Question 4a

                          Marks: 3

                          A motor is used to lift a 50 kg mass from rest up a vertical distance of 18 m in 0.3 minutes.

                          (a)
                          Calculate the minimum power requires to the lift the mass.
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                            Key Concepts
                            Power
                            Work Done

                            Question 4b

                            Marks: 2
                            (b)
                            Explain why the power of the motor is only a minimum.
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                              Question 4c

                              Marks: 3

                              A different motor is used to lift an identical mass through the same distance in the same amount of time with an overall efficiency of 38 %. The mass experiences a resistive force of 170 N.

                              (c)
                              Calculate the work required from the motor.
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                                Key Concepts
                                Work Done

                                Question 4d

                                Marks: 3
                                (d)
                                Hence, determine the average power input to the motor.
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                                  Key Concepts
                                  Power
                                  Efficiency

                                  Question 5a

                                  Marks: 3

                                  The top speed of a car with a mass of 1400 kg whose engine is delivering 490kW of power is 530 km h–1.

                                  (a)
                                  Calculate the force from the engine on the car.

                                  Assume that air resistance is negligible.
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                                    Key Concepts
                                    Power

                                    Question 5b

                                    Marks: 4

                                    The car now travels at a new constant velocity up a hill of incline 25º.

                                    (b)
                                    Determine the decrease in velocity from the previous motion of the car as it travels up the hill with the same power.
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                                      Key Concepts
                                      Power

                                      Question 5c

                                      Marks: 3

                                      The car engine cuts off whilst travelling up the incline.

                                      (c)
                                      Assuming there are no resistive forces, calculate the distance travelled by the car from when the engine cuts off to when it has a gravitational potential energy of 110 kJ. 

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                                        Question 5d

                                        Marks: 3

                                        A spring in the car’s suspension system has the following force–displacement graph.

                                        q5d_work-energy--power_ib-sl-physics-sq-medium

                                        (d)
                                        Using the area under the graph, show that the spring constant of the spring is about 49 kN m-1.
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