A system of pulleys is used to raise a load of 1000N. When the applied effort of 250N moves through 10m, the load rises through 2m. calculate (i) velocity ratio. (ii) efficiency of the system
To calculate the velocity ratio and efficiency of the system, we first need to understand the concepts involved.
1. Velocity Ratio:
The velocity ratio in a pulley system is the ratio of the distance moved by the effort (input) to the distance moved by the load (output). It indicates how much the effort is magnified or reduced in relation to the load.
2. Efficiency:
Efficiency represents how effectively a system converts input work to useful output work. In a pulley system, it is the ratio of the output work to the input work, expressed as a percentage.
Now, let's calculate the velocity ratio and efficiency using the given information:
Given:
Load (output force, W) = 1000N
Effort (input force, E) = 250N
Distance moved by effort (input distance, DE) = 10m
Distance moved by load (output distance, DW) = 2m
(i) Velocity Ratio:
The velocity ratio is calculated as the ratio of input distance to output distance.
Velocity ratio (VR) = DE / DW
Substituting the given values:
VR = 10m / 2m = 5
The velocity ratio of the pulley system is 5.
(ii) Efficiency:
Efficiency (η) is calculated as the ratio of output work to input work, multiplied by 100 to express it as a percentage.
Efficiency (η) = (output work / input work) x 100
In a pulley system, the output work is equal to the load lifted multiplied by the output distance.
Output work (Wout) = W * DW
Similarly, the input work is equal to the effort applied multiplied by the input distance.
Input work (Win) = E * DE
Now, substituting the given values:
Wout = 1000N * 2m = 2000 Nm (Joules)
Win = 250N * 10m = 2500 Nm (Joules)
Efficiency (η) = (2000 Nm / 2500 Nm) x 100 = 80%
The efficiency of the pulley system is 80%.
Thus, the velocity ratio is 5 and the efficiency is 80%.