A moto of a crane is lifting a 100 kg load 20m high using 25 kj of electrical energy. calculate the efficiency
eff= powerout/powerin * 100
To calculate the efficiency, we need to find the useful work output and the total work input.
The useful work output is the work done on the load by the crane's motor to lift it to a height of 20m. Work is calculated as the product of force and distance. Here, the force is the weight of the load, which is given as 100 kg, and the distance is the height through which it is lifted, 20m. Therefore, the useful work output is:
Useful work output = force x distance = 100 kg x 9.8 m/s^2 x 20 m = 19600 kg•m^2/s^2
The total work input is the electrical energy consumed by the crane's motor, which is given as 25 kJ. However, we need to convert the electrical energy to work by multiplying it by 1000 since 1 kJ equals 1000 J. Therefore, the total work input is:
Total work input = 25 kJ x 1000 J/kJ = 25000 J
Now, we can calculate the efficiency using the formula:
Efficiency = useful work output / total work input
Efficiency = 19600 kg•m^2/s^2 / 25000 J
Efficiency = 0.784
So, the efficiency of the crane in lifting the 100 kg load 20m high using 25 kJ of electrical energy is approximately 0.784 or 78.4%.