Work, Energy & Power (DP IB Physics: HL): Exam Questions

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

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.   

(i) Calculate the initial energy of the box

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

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Hence, or otherwise, calculate the amount by which the spring is compressed.

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.

Calculate the magnitude of the work done on the box as it travels uphill.

Hence, or otherwise, calculate the new amount by which the spring is compressed.

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

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.

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.

When the ship is travelling at 3.9 m s^–1, calculate the power that the kite provides.

Hence calculate the percentage of the total power required by the ship that the kite provides.

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 v of the ship by

 F = kv

where k is a constant.

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.

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

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.

Calculate the maximum speed of the club head achieved when h = 75 cm.

Explain why, in reality, the speed of the ball will not be the same as the maximum speed of the club head.

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.

Calculate the maximum speed this club head achieves just before it hits the ball.

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

Calculate the minimum power requires to the lift the mass.

Explain why the power calculated in (a) is a minimum value.

A packing company have a contraption involving an inclined plane and a spring. It is used to pack and seal their boxes. 

A box of mass 4800 g with an initial speed 21.96 km h⁻¹ begins to move up a smooth incline.

The box is momentarily brought to rest after colliding with a spring of spring constant 195 N m⁻¹. It stops a vertical distance of 230 mm above its initial position. 

Calculate the compression of the spring in mm. 

A golfing team are conducting investigations into the optimum angles at which golfers should hold their clubs to swing for the ball. 

Golf club A is held at an angle of 30° to the vertical at the pivot and golf club B at an angle of 45°. Both golf clubs are 1.05 m long and have the same mass. 

Compare the maximum speeds of the club heads just before they hit the ball. 

Show that the time of swing for golf club A is 0.21 s when the time of swing for golf club B is 0.23 seconds. 

Assume no additional force is applied to the golf clubs apart from their weight during the swing. 

An object is at rest at the top of a straight slope that makes a fixed angle with the horizontal at a distance h above the ground. 

The object is released and slides down the slope from A to B with negligible friction. Assume that the potential energy is zero at B. 

Sketch and explain a graph showing:

(i) The variation of gravitational potential energy of the object along the slope, label P.

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(ii) The variation of kinetic energy of the object along the slope, label K.

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(iii) The variation of kinetic energy of the object along the slope when there is a frictional force between the object and the surface, label F. 

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In a theme park ride, a cage containing passengers falls freely a distance of x m from A to B and travels in a circular arc of radius 25 m. from B to C. The force required for circular motion on a passenger of mass 63.25 kg is 0.064 × 10² kN.

The equation for calculating centripetal force on an object moving in an arc is: 

$F=\frac{m{v}^2}{r}$

Brakes are applied at C after which the cage with its passengers travels 70 m along an upward sloping ramp and comes to rest at D. The track, together with relevant distances, is shown in the diagram. CD and makes an angle θ with the horizontal. 

The total mass of the cage and passengers is 3.556 × 10² kg. The average resistive force exerted by the brakes between C and D is 4.4 × 10³ N.

Calculate the angle of the ramp to the horizontal, θ.

The diagram below shows a projectile launcher with a spring in both a compressed and uncompressed position. When the spring is compressed, in preparation for launching the projectile, the plate is held in place by a pin at three different positions, P, Q and R.  When the pin is released the sphere is launched. 

A student hypothesises that the spring constant of the spring inside the launcher has the same value for different compression distances. 

The student plans to test the hypothesis by launching the sphere using the launcher.

(i) State a physics principle or law that can be used in designing and conducting an experiment to test this hypothesis.

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(ii) Hence, or otherwise, show that k = $\frac{2mgh}{x^2}$

Measurements can be made with equipment usually found in a school laboratory using the principle or law stated in part (i).

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For the investigation outlined in part (a):

(i) Suggest the quantities, their symbols and the equipment used to measure each. 

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(ii) Describe the best procedure that can be used to test the hypothesis.

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Assess how the experimental data can be analysed to confirm or dispel the hypothesis.