A machine has a velocity ratio 5and 80% efficiency effort should of needed to left a load of 200N with the aid of machine
To calculate the effort required to lift a load with the aid of a machine, we need to consider the velocity ratio and the efficiency of the machine.
1. Velocity Ratio (VR): The velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load. In this case, the velocity ratio is given as 5.
2. Efficiency (η): The efficiency of a machine measures how effectively it converts the input work (effort) into output work (lifting the load). In this case, the efficiency is given as 80%, which is equivalent to 0.8.
Now, let's calculate the effort required:
Efficiency (η) = Output Work / Input Work
Since the input work is equal to the effort (E) multiplied by the distance moved by the effort (DE) and the output work is equal to the load (L) multiplied by the distance moved by the load (DL), we can write:
η = (L × DL) / (E × DE)
Given:
Load (L) = 200N
Velocity Ratio (VR) = 5
Efficiency (η) = 0.8
We need to find the effort (E).
We know that the distance moved by the effort (DE) is equal to the distance moved by the load (DL) divided by the velocity ratio (VR):
DE = DL / VR
Substituting this into the efficiency equation:
0.8 = (L × (DL / VR)) / (E × DE)
Simplifying the equation:
0.8 = L × DL / (E × DL / VR)
0.8 = VR × L / E
Rearranging the equation to solve for E (effort):
E = VR × L / 0.8
Substituting the given values:
E = 5 × 200N / 0.8
E = 1250N
Therefore, the effort required to lift the load of 200N with the aid of the machine is 1250N.