A machine of efficiency 80% or use to rise a load of body of mass 75kg through a vertical height of 3 metre in 30 seconds calculate the power input take ( g =10mls)
If you think g is in m/s, forget it
I will assume g= about 10 m/s^2
work accomplished = weight * distance up = m g h = 75 * 10 * 3
= 2250 Joules
work put in = 2250 / 0.80 = 2812.5 Joules
power = work/time = 2812.5 Joules / 30 s = 93.75 Watts
To calculate the power input, we need to first find the work done to raise the load and then divide it by the time taken.
The work done (W) can be calculated using the formula:
W = m * g * h
where:
m = mass of the load = 75 kg
g = acceleration due to gravity = 10 m/s^2
h = vertical height = 3 meters
W = 75 kg * 10 m/s^2 * 3 meters
W = 2250 Joules
Now, since the machine has an efficiency of 80%, only 80% of the input power will be converted into useful work. This means that the actual work done by the machine is:
Actual work = Efficiency * Input work
Actual work = 0.8 * 2250 Joules
Actual work = 1800 Joules
Finally, we can calculate the power input using the formula:
Power = Work / Time
Time = 30 seconds
Power = 1800 Joules / 30 seconds
Power = 60 Watts
Therefore, the power input required is 60 Watts.
To calculate the power input, we need to use the formulas for efficiency and power.
The formula for efficiency is:
Efficiency = (Useful Output Energy / Total Input Energy) * 100%
And the formula for power is:
Power = Work / Time
Given:
Efficiency = 80% = 0.80 (in decimal form)
Mass = 75 kg
Height = 3 meters
Time = 30 seconds
Acceleration due to gravity = 10 m/s^2
First, let's find the work done to lift the body:
Work = Force * Distance
In this case, the force required to lift the body is the weight of the body, which can be calculated using the formula:
Force = Mass * Acceleration due to gravity
Force = 75 kg * 10 m/s^2 = 750 N
Now, calculate the work done:
Work = Force * Distance = 750 N * 3 m = 2250 Nm
Next, we can calculate the power input using the formula:
Power = Work / Time
Power = 2250 Nm / 30 s = 75 W
Since the efficiency is given as 80%, we can calculate the total input energy as follows:
Efficiency = (Useful Output Energy / Total Input Energy) * 100%
0.80 = (2250 Nm / Total Input Energy) * 100%
Total Input Energy = (2250 Nm / 0.80) * 100% = 2812.5 Nm
Now, we can calculate the power input:
Power Input = Total Input Energy / Time
Power Input = 2812.5 Nm / 30 s = 93.75 W
Therefore, the power input required to lift the load is approximately 93.75 Watts.