A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency is?
(30 / 3000) / 200 = ?
To find the efficiency of a machine, you need to know the input work and output work. In this case, the input work is the work done by the effort and the output work is the work done on the load.
The velocity ratio (VR) is given as 30, which means that for every 30 units of distance the effort moves, the load moves 1 unit of distance. In other words, the distance ratio (DR) is 1/30.
The input work (WI) is calculated by multiplying the effort (E) by the distance moved by the effort (DE):
WI = E x DE
The output work (WO) is calculated by multiplying the load (L) by the distance moved by the load (DL):
WO = L x DL
In this case, the load is 3000N and the effort is 200N. Now we need to find the distance moved by the effort and the load.
The distance moved by the effort (DE) is calculated by multiplying the distance moved by the load (DL) by the distance ratio (DR):
DE = DL x DR
Since the distance ratio (DR) is 1/30, DE = DL/30.
We know that when the effort of 200N is applied, the load of 3000N moves. So we can set up the equation:
200 x DE = 3000 x DL
Substituting DE = DL/30, we get:
200 x (DL/30) = 3000 x DL
Simplifying the equation, we have:
DL/30 = 3000/200
DL/30 = 15
Multiplying both sides of the equation by 30 gives:
DL = 15 x 30 = 450
Now we know that the distance moved by the load (DL) is 450 units.
Substituting the values into the equations for input work and output work, we get:
WI = 200 x DL/30 = 200 x 450/30 = 3000 joules
WO = 3000 x DL = 3000 x 450 = 1350000 joules
The efficiency (η) is calculated by dividing the output work by the input work and multiplying it by 100:
η = (WO / WI) x 100
Substituting the values, we get:
η = (1350000 / 3000) x 100 = 45000
Therefore, the efficiency of the machine is 45000%.