2.3 Work, Energy & Power

Some cargo ships use kites together with the ships engine to move heavy pieces of cargo. 

The tension in the cable that connects the kite to the ship is 475 kN. The kite is pulling on the ship at an angle of θ to the horizontal plane of the ship's deck. The ship travels at a steady speed of 14.76 km hr⁻¹ when its engines operate with a power output of 5.9 MW. The work done by the engines is 0.365 GJ when turned on for 0.09 hours. 

The ship continues its journey using both the engine and the kite to maintain the same constant speed. After 0.09 hours with the engine on, the ship drives into a spring net erected between two rocky outcrops. Upon impact, the net force from the ship acts parallel to the direction of extension of twelve identical springs in the net and the ship comes to a complete stop with the springs in the net extended. The ship has a mass of 2200 metric tonnes. 

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. 

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. 

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: 

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.

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. 

(ii)

Hence, or otherwise, show that k = 

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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