A 10kilow walts electric motor is used to raise a 400kg load of bricks to a height of 60meters.The efficiency of the motor 80%.what is the input energy?
Work = F*h = Mg*h = 400*9.8 * 60 = 235,200 J. = Output energy.
Input energy = Output/Eff. = 235,200/0.8
= 294,000 J.
To find the input energy, we first need to calculate the output power.
The output power is equal to the work done per unit time, given by the formula:
Output Power = Work Done / Time
In this case, the work done is equal to the potential energy gained by raising the load of bricks to a height of 60 meters, which can be calculated using the formula:
Work Done = mgh
where:
m = mass of the load (400 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height (60 meters)
Work Done = 400 kg * 9.8 m/s^2 * 60 meters
Now, let's calculate the output power:
Output Power = Work Done / Time
However, we don't have the time information in the given question. But we can use the efficiency of the motor to find the input power.
Efficiency = (Output Power / Input Power) * 100
Given that the efficiency is 80%, we can rearrange the formula to solve for the input power:
Input Power = Output Power / (Efficiency/100)
Now we can calculate the input power:
Input Power = (Work Done / Time) / (Efficiency/100)
Since we don't have the value for time, we can assume any value for time. Let's assume it takes 10 seconds to raise the load of bricks to a height of 60 meters.
Work Done = 400 kg * 9.8 m/s^2 * 60 meters
Output Power = Work Done / Time = (400 kg * 9.8 m/s^2 * 60 meters) / 10 seconds
Input Power = Output Power / (Efficiency/100)
= [(400 kg * 9.8 m/s^2 * 60 meters) / 10 seconds] / (80/100)
Let's calculate the input power:
Input Power = [(400 * 9.8 * 60) / 10] / (0.8)
Input Power ≈ 17640 W
Therefore, the input energy is approximately 17640 watts (W).