A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency of the machine is?
200 * 30 = 6, 000 N
but we could only lift half of that
100% * (3000/6000) = 50%
To find the efficiency of a machine, we can use the formula:
Efficiency = (Output work / Input work) x 100%
In this case, the output work is the work done on the load, which is given by:
Output work = Load x Distance moved by the load
The input work is the work done by the effort, which is given by:
Input work = Effort x Distance moved by the effort
We are given that the load is 3000N and the effort is 200N. We need to find the distance moved by both the load and the effort.
Velocity ratio (VR) is defined as:
VR = Distance moved by effort / Distance moved by load
Given VR = 30, we can rearrange the equation to find the distance moved by the effort:
Distance moved by effort = VR x Distance moved by load
To find the efficiency, we substitute the values into the formula:
Distance moved by load = Output work / Load
Distance moved by effort = VR x Distance moved by load
Input work = Effort x Distance moved by effort
So the steps to find the efficiency are as follows:
1. Calculate the distance moved by the load: Distance moved by load = Output work / Load = Output work / 3000N
2. Calculate the distance moved by the effort: Distance moved by effort = VR x Distance moved by load = 30 x (Output work / 3000N)
3. Calculate the input work: Input work = Effort x Distance moved by effort = 200N x (30 x (Output work / 3000N))
4. Calculate the efficiency: Efficiency = (Output work / Input work) x 100%
Note: To calculate the efficiency, we need to know the output work. If the output work is not provided in the question, we won't be able to calculate the efficiency.
To determine the efficiency of the machine, you need to know the work done by the effort and the work done on the load. The formula for efficiency is:
Efficiency = (work output / work input) * 100%
To calculate the work done by the effort, you can use the formula:
Work output = effort * distance moved by effort
Similarly, you can find the work done on the load using the formula:
Work input = load * distance moved by load
From the information given, we know the effort applied is 200N and the load is 3000N. The velocity ratio is given as 30.
We can assume that the distance moved by the effort and the distance moved by the load are the same (let's call it 'd') because they are both part of a single system.
Using the formulas, let's calculate the work output and work input:
Work output = effort * distance moved by effort
= 200N * d
Work input = load * distance moved by load
= 3000N * d
Now, we can calculate the efficiency using the work output and work input:
Efficiency = (work output / work input) * 100%
= (200N * d / 3000N * d) * 100%
= (200 / 3000) * 100%
Simplifying the calculation:
Efficiency = (2/30) * 100%
= 6.67%
Therefore, the efficiency of the machine is 6.67%.