A crane lifts a 500 kg load to a height of 10 m in 5 seconds. What is the power output of the crane?
\[ P = \frac{W}{t} \\ W = mgh = 500 \times 9.8 \times 10 = 49000\,J \\ P = \frac{49000}{5} = 9800\,W = 9.8\,kW \]
Power is the rate at which work is done or energy is transferred. It tells us how quickly energy is being used or converted. The formula for power is:
\[ P = \frac{W}{t} \]
Where P = Power, W = Work and t = time
Since work can also be expressed as force times displacement (\(W = Fd\)), power can also be written in terms of force and velocity:
\[ P = Fv \]
Efficiency is a measure of how effectively a system converts input energy into useful output energy. No real system is 100% efficient because some energy is always lost as heat, sound, or friction. Efficiency is calculated as:
\[ \text{Efficiency} = \frac{\text{Useful Output Energy or Power}}{\text{Total Input Energy or Power}} \times 100\% \]
A machine with 80% efficiency means that 80% of the input energy is converted into useful work, while 20% is lost.
A crane lifts a 500 kg load to a height of 10 m in 5 seconds. What is the power output of the crane?
\[ P = \frac{W}{t} \\ W = mgh = 500 \times 9.8 \times 10 = 49000\,J \\ P = \frac{49000}{5} = 9800\,W = 9.8\,kW \]
A machine uses 5000 J of energy to lift an object, but only 3500 J is converted into useful work. Calculate the efficiency of the machine.
\[ \text{Efficiency} = \frac{3500}{5000} \times 100\% = 70\% \]
A hydroelectric turbine receives 8000 J of energy from falling water but produces only 6000 J of electrical energy. Find the efficiency of the turbine.
\[ \text{Efficiency} = \frac{6000}{8000} \times 100\% = 75\% \]
Written by Thenura Dilruk