A load of 500N is raised through 5m by a machine when it's effort E moves simultaneously through a distance of 25m along it's direction. If the machine has efficiency of 80% , calculate
a) Total work done by machine.
b) Value of E
output work = 500 * 5 = 2500 Joules
work in = work out/.8 = 2500/.8 = 3125 Joules
E * 25 = 3125
E= 125 Newtons
Total work done by the machine is 5,625J.
Value of E is 125N.
To calculate the total work done by the machine, we can use the formula:
Work = Force × Distance
Given that the load is raised through a distance of 5m and the force (load) is 500N, we have:
Work = 500N × 5m
Work = 2500 N·m (or Joules)
Therefore, the total work done by the machine is 2500 N·m.
To calculate the value of E (effort), we can use the equation for efficiency:
Efficiency = (Useful work output / Total work input) × 100
Given that the efficiency is 80%, the total work input is 2500 N·m, and the distance E moves is 25m, we have:
80% = (Useful work output / 2500 N·m) × 100
Dividing both sides by 100, we get:
0.8 = Useful work output / 2500 N·m
Multiplying both sides by 2500 N·m, we have:
0.8 × 2500 N·m = Useful work output
Useful work output = 2000 N·m
Therefore, the value of E (effort) is 2000 N·m.
To calculate the total work done by the machine and the value of effort (E), we need to use the formulas for work, efficiency, and mechanical advantage.
a) Total work done by the machine:
The work done by a machine can be determined using the formula:
Work = Load × Distance.
In this case, the load (force) is 500N and the distance is 5m. Therefore, the work done by the machine is:
Work = 500N × 5m = 2500Nm (or Joules).
b) Value of effort (E):
Efficiency of a machine is defined as the ratio of useful work output to the total work input, expressed as a percentage. The formula for efficiency is given as:
Efficiency = (Work output / Work input) × 100%.
We are given the efficiency of the machine as 80%, or 0.8 as a decimal. We can rewrite the efficiency formula as follows:
0.8 = (Work output / Total work input) × 100%.
Since we know the total work input (2500Nm) from part (a), we can rearrange the formula to solve for the work output, which is the product of the effort (E) and the distance it moves:
Work output = Efficiency × Total work input.
Work output = 0.8 × 2500Nm.
Now, we have the work output, but we need to find the value of the effort (E). The formula for mechanical advantage is defined as:
Mechanical Advantage = Load / Effort.
Rearranging the formula, we can solve for Effort:
Effort = Load / Mechanical Advantage.
Effort = 500N / (Work output / Load).
Using the value of the load (500N) and the calculated work output, we can calculate the value of the effort (E):
Effort = 500N / (0.8 × 2500Nm / 500N).
By substituting the values into the formula and simplifying, we can find the value of E:
Effort = 500N / (0.8 × 2500Nm / 500N) = 0.1N.
Therefore, the value of the effort (E) is 0.1N.