Any machine or mechanism that is created by man is called upon to perform some useful work. To make it, you should spend energy. The question of the ratio of spent and useful work will be considered on the example of determining the efficiency of the lever.
About Leverage
A lever is any simple mechanism that serves to convert power in magnitude and direction. It consists of a beam and a support, in the general case has two shoulders. Strength has an effect on each of the shoulders. Both forces seek to turn their shoulders in opposite directions. Therefore, one of them always does work against the other.
The lever allows you to win on the road or in strength, while there will be a loss in strength or in transit, respectively. The main leverage formula that describes the balance of his shoulders is listed below:
F / R = d R / d F.
Here, the force F does the work against the weight of the load R, acting on a shoulder of length d F. The load is on a shoulder of length d R. The formula reflects the inverse proportionality between the relations of forces and shoulders.
The next moment. When the shoulders begin to move, one of them rises to a height of h 1 , the other falls to a height of h 2 . Since the angle of rotation of the shoulders will be the same, then, in the absence of other forces, the formula above can be rewritten as follows:
F / R = h 1 / h 2 .
Further, this formula will be used to determine the efficiency of the lever.
Efficiency of a simple mechanism
Recall that work in physics is a quantity equal to the product of force and the path during which it acted:
A = F * l.
The efficiency of any mechanism characterizes the effectiveness of its work. It can be calculated by the following formula:
Efficiency = A p / A s * 100%.
Where A p - useful work performed by the mechanism, A s - the work that had to be spent.
Throughout history, mankind has been trying to create mechanisms in which A s = A p , but no one has been able to achieve this equality. The work spent is always greater than the value of A p .
Using the formula for the lever obtained in the previous paragraph, we can write the formula for determining the efficiency of the lever:
And n = R * h 1 ; A s = F * h 2 ;
Efficiency = A p / A s * 100% = R * h 1 / (F * h 2 ) * 100%.
If we take into account the corresponding expression for the lever, then it may seem that the efficiency for it will be 100%. Nevertheless, this is not so, since friction in the axis of rotation and friction against air constantly exist. As a result of these processes, the work expended is partially spent on heating the environment and lever parts, so the efficiency of the mechanism is always less than 100%.
The task of determining efficiency
Suppose that the force F = 18 N applied to the lever led to the lifting of a load of 3 kg to a height of 0.3 meters. Given that the shoulder of the application of force F fell by 0.6 meters in this case, calculate the efficiency of the lever.
We calculate the useful and expended work:
And n = R * h 1 = m * g * h 1 = 3 * 9.81 * 0.3 = 8.829 J;
And s = F * h 2 = 18 * 0.6 = 10.8 J.
As can be seen, A s > A p . The efficiency of the lever is equal to:
Efficiency = A p / A s * 100% = 8.829 / 10.8 * 100% = 81.75%.
This efficiency value can be increased if grease is applied in the axis of rotation of the lever.