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Work, energy and power questions
Work is energy in transit, and it has a strict definition that ignores effort entirely: only force along the motion counts. Power is how fast the transfer runs, and one rearrangement of it, P = Fv, explains the top speed of everything with an engine.
19 original questions · 54 marks · the work, energy and power notes · Mechanics
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A force of 20 N moves an object 3.0 m in the direction of the force. Calculate the work done.
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W = Fs = 20 × 3.0 (1)
W = 60 J (1)Define power and state its SI unit.
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Power is the rate of doing work, or of transferring energy: P = work done / time taken (1). Unit: the watt, W, equal to one joule per second (1).State the equations for kinetic energy and for the change in gravitational potential energy near the Earth's surface.
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Kinetic energy = ½mv2 (1); change in gravitational potential energy = mgΔh (1).A shopper carries a bag at constant height across a level floor. State and explain the work done on the bag by the upward force from the shopper's hand.
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The force is vertical and the displacement horizontal, so the angle between them is 90° (1). W = Fs cos 90° = 0: the force does no work on the bag. (1)A kettle transfers energy at a rate of 2.5 kW. Calculate the energy it transfers in 3.0 minutes.
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P = 2500 W and t = 180 s (1). E = Pt = 2500 × 180 = 4.5 × 105 J. (1)State the quantity represented by the area under a force-displacement graph.
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The work done by the force. (1)A force of 50 N pulls a crate 4.0 m along the ground, acting at 30° above the horizontal. Calculate the work done by the force.
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W = Fs cosθ (1)
W = 50 × 4.0 × cos 30° (1)
W = 173.2 J (1)A 2.0 kg object moves at 6.0 m s−1. Calculate (a) its kinetic energy and (b) the distance it travels before stopping if a constant 12 N resistive force acts on it.
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(a) KE = ½ × 2.0 × 6.02 (1)
KE = 36 J (1)
(b) Work done against the force removes this energy: s = KE/F = 36/12 (1)
s = 3.0 m (1)A motor raises a 20 kg load through a height of 5.0 m in 4.0 s at steady speed. Taking g = 9.81 m s−2, calculate the useful output power of the motor.
A machine has an input power of 800 W and a useful output power of 600 W. Calculate its efficiency.
The force needed to stretch a spring increases linearly from zero to 12 N as its extension increases from zero to 80 mm. Determine the work done in stretching the spring.
A sprinter of mass 62 kg accelerates from rest to 9.0 m s−1 in 3.5 s. Calculate the average useful power she develops.
A van of mass 900 kg climbs a straight road at a steady 15 m s−1. The road rises 1.0 m for every 20 m travelled along it. Taking g = 9.81 m s−2, calculate the additional output power the engine must supply against gravity, compared with driving at the same speed on a level road.
A car engine develops a useful output power of 40 kW while the car travels at a steady 25 m s−1. Calculate the driving force provided by the engine.
A 10 kg box is pushed at steady speed a distance of 4.0 m up a slope inclined at 30° to the horizontal, against a constant frictional force of 15 N. Taking g = 9.81 m s−2, calculate (a) the gain in gravitational potential energy, (b) the work done against friction, and (c) the force applied parallel to the slope.
Explain why the efficiency of a real machine is always less than 100%, and where the 'lost' energy goes.
A borehole pump raises 120 kg of water through a vertical height of 15 m every minute; the water leaves the outlet with negligible kinetic energy. The pump's electrical input power is 500 W, and the manufacturer claims an efficiency of at least 65%. Taking g = 9.81 m s−2, deduce whether the pump meets the manufacturer's claim.
A resultant force acts on a 0.50 kg trolley, initially at rest, along a straight track. The force is a constant 6.0 N for the first 2.0 m of travel, then decreases linearly to zero over the next 2.0 m. Determine the speed of the trolley after it has travelled 4.0 m.
Estimate the useful power a student develops against gravity when running up a flight of stairs. State the estimated values you use.
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