A system of pulleys is used to lift a load of 1000kg.if the efficiency of pulley system is 80%and velocity ratio is 20,find effort required to lift the load...............??
To find the effort required to lift the load, we can use the formula for efficiency:
Efficiency = (Output Work / Input Work) * 100
Efficiency is given as 80%, so we can rewrite the formula as:
0.80 = (Output Work / Input Work) * 100
Let's find the Input Work first. The formula for Work is:
Work = Force * Distance
In this case, the Force is the effort required to lift the load, denoted as E, and the distance is the distance the load is lifted, denoted as D.
So, the Input Work can be calculated as:
Input Work = E * D
The Output Work can be calculated using the Velocity Ratio:
Velocity Ratio = Output Distance / Input Distance
In this case, the Input Distance is equal to the distance the load is lifted, D, and the Output Distance is the length of rope pulled, R.
So, we can rewrite the formula for Output Distance as:
Output Distance = Velocity Ratio * Input Distance
Substituting the values, we get:
Output Distance = 20 * D
Now, the Output Work can be calculated as:
Output Work = Output Force * Output Distance
The Output Force can be calculated using the equation:
Output Force = Load / Number of Pulleys
In this case, the Load is given as 1000kg, and the Number of Pulleys is 1 (assuming there is only one pulley in the system).
So, the Output Force is:
Output Force = 1000kg / 1 = 1000kg
Therefore, the Output Work is:
Output Work = Output Force * Output Distance = 1000kg * (20 * D) = 20000kg * D
Now, let's substitute the values back into the efficiency formula:
0.80 = (Output Work / Input Work) * 100
0.80 = (20000kg * D / (E * D)) * 100
Simplifying the equation:
0.80 = 20000kg / E * 100
0.008 * E = 20000kg
E = 20000kg / 0.008 = 2500000 kg
Therefore, the effort required to lift the load is 2500000 kg.