A machine of velocity ratio required 1000j to raise a load of 500N through the vertical distance of 1.5m
Find the efficiency of the machine
Solution
Work out put = 500x1.5 =170
Work input=1000j
Efficiency= work output/work input x 100
=500/1000 x 100=75%
work out = 500 * 1.5 = 750 Joules
work in = 1000 Joules
so
750/1000 = 0.75 = 75%
To find the efficiency of the machine, we need to know the work input and work output. The work input is the energy or effort put into the machine, while the work output is the useful work done by the machine.
Given:
Effort (work input), W_in = 1000J
Load (work output), W_out = Force x Distance = 500N x 1.5m = 750J
Efficiency (η) is defined as the ratio of the work output to the work input, multiplied by 100%:
η = (W_out / W_in) x 100
Substituting the given values into the formula:
η = (750J / 1000J) x 100 = 0.75 x 100 = 75%
Therefore, the efficiency of the machine is 75%.
To find the efficiency of the machine, we need to calculate the work done by the machine and divide it by the work input.
Efficiency is usually given as a percentage, so we will multiply the result by 100 to convert it into a percentage.
To calculate the work done by the machine, we need to multiply the force exerted by the machine by the distance it moves the load.
Given:
- Force (F) = 500N
- Distance (D) = 1.5m
- Velocity Ratio (VR) = 1000j
We know that the Velocity Ratio (VR) is equal to the ratio of the distance moved by the effort to the distance moved by the load.
So, VR = Distance moved by effort / Distance moved by load
Since the load is moving through a vertical distance of 1.5m, we can determine the distance moved by the effort by dividing 1.5m by the Velocity Ratio (VR):
Distance moved by effort = Distance moved by load / Velocity Ratio
Now, let's calculate the distance moved by the effort:
Distance moved by effort = 1.5m / 1000
Next, we can calculate the work done by the machine using the formula:
Work done = Force × Distance moved
Work done by the machine = Force × Distance moved by effort
Substituting the values:
Work done by the machine = 500N × (1.5m / 1000)
Now, we can calculate the work input:
Work input = Force × Distance moved by load
Work input = 500N × 1.5m
Finally, we can find the efficiency using the formula:
Efficiency = (Work done / Work input) × 100
Substituting the values calculated earlier:
Efficiency = (Work done by machine / Work input) × 100
Now, you can calculate the efficiency of the machine by plugging in the calculated values into the formula.