a farm machine has a velocity ratio of 12 and an actual mechanical advantage of 10.calculate the work input of the machine if it raises an 80kg load by 6m
Efficiency= MA/VA= 10/12
workinput*efficiencey=workout
workinput*10/12=80*9.8*6
solve for work input.
To calculate the work input of a machine, we need to use the formula:
Work Input = Work Output / Efficiency
First, let's find the work output. The work output is given by the product of the load (force) and the distance it is moved:
Work Output = Force * Distance
In this case, the load is a mass of 80 kg and it is raised by a distance of 6 m. To calculate the force needed to raise this load, we can use the formula:
Force = Mass * Acceleration due to gravity
Acceleration due to gravity (g) is approximately 9.8 m/s^2. Therefore:
Force = 80 kg * 9.8 m/s^2 = 784 N
Now, we can calculate the work output:
Work Output = Force * Distance = 784 N * 6 m = 4704 N·m (or Joules)
The next step is to find the efficiency of the machine. Efficiency is usually given as a percentage and can be calculated using the formula:
Efficiency = (Work Output / Work Input) * 100
Since we are given the actual mechanical advantage, we can find the efficiency using the formula:
Efficiency = (Velocity Ratio / Actual Mechanical Advantage) * 100
In this case, the velocity ratio is 12 and the actual mechanical advantage is 10:
Efficiency = (12 / 10) * 100 = 120%
Now, we can calculate the work input using the formula mentioned at the beginning:
Work Input = Work Output / Efficiency
Work Input = 4704 N·m / 120% = 4704 N·m / 1.2 = 3920 N·m (or Joules)
Therefore, the work input of the machine is 3920 N·m (or Joules) when it raises an 80 kg load by 6 m.