Page 94 - Physics Coursebook 2015 (A level)

Cambridge International AS Level Physics
WORKED EXAMPLE
Summary
■■ The work done W when a force F moves through a displacement s in the direction of the force:
W=Fs or W=Fscosθ
where θ is the angle between the force and the
displacement.
■■ A joule is defined as the work done (or energy transferred) when a force of 1 N moves a distance of 1 m in the direction of the force.
■■ The work done W by a gas at pressure p when it expands:
W=pΔV
where ΔV is the increase in its volume.
■■ When an object of mass m rises through a height h, its gravitational potential energy Ep increases by an amount:
Ep = mgh
■■ The kinetic energy Ek of a body of mass m moving at speed v is:
Ek=12mv2
■■ The principle of conservation of energy states that, for a closed system, energy can be transformed to other forms but the total amount of energy remains constant.
■■ The efficiency of a device or system is determined using the equation:
efficiency = useful output energy × 100%
total input energy
■■ Power is the rate at which work is done (or energy is transferred):
P=WtandP=Fv
■■ A watt is defined as a rate of transfer of energy of one joule per second.
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7 A person who weighs 500 N runs up a flight of stairs in 5.0 s (Figure 5.19). Their gain in height is 3.0 m. Calculate the rate at which work is done against the force of gravity.
Step 1 Calculate the work done against gravity: workdoneW=F×s=500×3.0=1500J
Step2 Nowcalculatethepower: power P = W = 1500 = 300 W
t 5.0
500 N
3m
So, while the person is running up the stairs, they are doing work against gravity at a greater rate than their average power – perhaps three times as great. And, since our muscles are not very efficient, they need to be supplied with energy even faster, perhaps at a rate of 1 kW. This is why we cannot run up stairs all day long without greatly increasing the amount we eat. The inefficiency of our muscles also explains why we get hot when we exert ourselves.
Figure 5.19 Running up stairs can require a high rate of doing work. You may have investigated your own power in this way.