Pls show me the steps how to work this physics question:A pulley system of 4 pulleys is used to raise a loan of mass 50kg vertically,if its effeciency is 80%,determine the minimum effort required to raise the load(g=10ms-2)?
the weight is 500N
80% efficiency means that 1/.8 = 1.25 the weight is needed.
To determine the minimum effort required to raise the load in this pulley system, we need to consider the efficiency of the system and the weight of the load.
Let's break down the problem into steps:
Step 1: Understand the concept
Efficiency is defined as the ratio of output work to input work. In this case, output work refers to the work done in lifting the load, and input work refers to the work done by the effort force.
Efficiency (η) = (Output work / Input work) * 100%
Step 2: Calculate the output work
The output work refers to the work done in lifting the load. In this case, the load is raised vertically, so the work done is given by:
Output Work = Force * Distance
= Weight of the load * Height
= m * g * h
where m is the mass of the load, g is the acceleration due to gravity (10 m/s^2), and h is the height lifted.
Step 3: Calculate the input work
The input work refers to the work done by the effort force. In this case, the minimum effort force required is the force needed to lift the load vertically. Therefore, the input work is equal to the output work.
Input Work = Output Work
Step 4: Calculate the minimum effort force
Since η = (Output Work / Input Work) * 100%, and Input Work = Output Work:
η = (Output Work / Output Work) * 100%
η = 100%
Since the efficiency is given as 80%, the actual input work is equal to 80% of the output work. Therefore, the minimum effort force can be calculated as:
Minimum Effort Force = (Input Work / Distance)
= (0.80 * Output Work) / Distance
Step 5: Solve the problem
Substituting the values given in the question:
m = 50 kg (mass of the load)
η = 0.80 (efficiency)
g = 10 m/s^2 (acceleration due to gravity)
Substituting these values into the equation, we can calculate the minimum effort force. However, the height (h) is not provided in the question. You need to know the height to complete the calculation.
Once you have the height, substitute all the known values into the equation, and calculate the minimum effort force.