A crane whose motor has a power input of 5.0 kW lifts a 120-kg load of bricks through a height of 30m in 90s. what is the efficiency of the crane, which is the ratio between its output power and its input power.
To find the efficiency of the crane, we need to calculate its output power and input power.
1. First, let's calculate the output power. Output power is the work done per unit time, which can be calculated using the formula:
Output Power = Work / Time
The work done by the crane can be found using the formula:
Work = Force x Distance
In this case, the force can be calculated using the formula:
Force = Mass x Acceleration
Since the load is being lifted vertically, the acceleration due to gravity (g = 9.8 m/s^2) acts as the upward force opposing gravity's downward force.
Force = Mass x Acceleration = 120 kg x 9.8 m/s^2
Now, we can calculate the work done:
Work = Force x Distance = (120 kg x 9.8 m/s^2) x 30 m
Finally, we can calculate the output power:
Output Power = Work / Time = (Force x Distance) / Time
2. Next, let's calculate the input power. The input power is given as 5.0 kW (kilowatts).
Now, we can calculate the efficiency using the formula:
Efficiency = (Output Power / Input Power) x 100
Substituting the values into the formula, we get:
Efficiency = (Output Power / 5000) x 100
You can now calculate the output power and input power and substitute them into the efficiency formula to find the efficiency of the crane.