Define power.
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Power is the rate of doing work; or the rate of energy transfer.
Power
Machine A does 5000 J of work in 20 s. Machine B does 5000 J of work in 50 s. Explain which machine has the greater power and why.
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Machine A has the greater power; because both machines do the same amount of work; but Machine A does it in a shorter time; therefore the work done per unit time is greater for Machine A.
A motor does 12 000 J of work in 40 s. Calculate the power of the motor.
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Equation used: $$P=\frac{W}{t}$$ Given: $$W=12 000\text{ J}$$ $$t=40\text{ s}$$ Substituting: $$P=\frac{12 000}{40}$$ $$P=300\text{ W}$$
A pump operates at a power of 500 W. Calculate the time it takes the pump to do 75 000 J of work.
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Equation used: $$P=\frac{W}{t}$$ Rearranging for time: $$t=\frac{W}{P}$$ Given: $$W=75 000\text{ J}$$ $$P=500\text{ W}$$ Substituting: $$t=\frac{75 000}{500}$$ $$t=150\text{ s}$$
A light bulb transfers 9000 J of energy in 2.0 minutes. Calculate the power of the bulb.
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Converting time to SI units: $$t=2.0\times 60$$ $$t=120\text{ s}$$ Equation used: $$P=\frac{\Delta E}{t}$$ Given: $$\Delta E=9000\text{ J}$$ $$t=120\text{ s}$$ Substituting: $$P=\frac{9000}{120}$$ $$P=75\text{ W}$$
An electric motor operates at a constant power of 400 W. The motor does a total of 60 000 J of work. State and explain what happens to the power if the same work is done in half the time.
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The power doubles. Because power equals work done divided by time ($P=W/t$); if $W$ stays the same and $t$ is halved; then $P$ must double, since power is inversely proportional to time for constant work done.