The efficiency to machine is 75% , if this machine raises a load of 150kg , through a vertical height of 20m,calculate the workdone by the labourer using the machine (g=10m/s square) ?
weight = force = m g = 150 * 10
work = force * distance = 150 * 10 * 20 = 30,000 Joules work out
= .75 work in
so
work in = 30,000/.75 Joules
(150 * 20 * g) / .75 ... Joules
To calculate the work done by the laborer using the machine, we first need to find the input work done by the machine. This can be calculated using the efficiency of the machine.
Given:
Efficiency of the machine (η) = 75% = 0.75
Load lifted (m) = 150 kg
Vertical height (h) = 20 m
Acceleration due to gravity (g) = 10 m/s^2
The input work (W_input) done by the machine can be calculated using the formula:
W_input = W_output / η
Where:
W_output is the output work done by the machine, which is equal to the work done to lift the load.
The work done to lift the load against gravity can be calculated using the formula:
W_output = m * g * h
Substituting the given values:
W_output = 150 kg * 10 m/s^2 * 20 m
= 300,000 J
Now, substituting the value of W_output into the formula for input work:
W_input = 300,000 J / 0.75
= 400,000 J
Therefore, the work done by the laborer using the machine is 400,000 J.
To calculate the work done by the laborer using the machine, we need to first calculate the work done by the machine itself and then divide it by the efficiency of the machine.
Work Done by the Machine:
The work done by lifting an object against gravity is given by the formula:
Work = Force * Distance
In this case, the force is equal to the weight of the load being lifted, which is given by:
Force = mass * acceleration due to gravity
So, Force = 150 kg * 10 m/s^2 = 1500 N
The distance is equal to the vertical height through which the load is raised, which is given as 20 m.
So, Distance = 20 m
Now, the work done by the machine is given by:
Work = Force * Distance = 1500 N * 20 m = 30,000 J (Joules)
Efficiency of the Machine:
The efficiency of a machine is defined as the ratio of useful work done by the machine to the total energy input. In this case, the efficiency is given as 75%, which can be written as 0.75.
So, Efficiency = 0.75
Finally, we can calculate the work done by the laborer using the machine as follows:
Work done by the laborer = Work done by the machine / Efficiency
= 30,000 J / 0.75
= 40,000 J (Joules)
Therefore, the work done by the laborer using the machine is 40,000 Joules.