The length of the lever is 2 m. At its ends, weights of 20 N and 140N are balanced. Find the length of the reach of the lever.

We are not given a drawing, but it is not difficult to find it on the Internet.

We write down briefly given:

F1 = 20 H;

F2 = 140 H.

To find:

x -? y -?

Decision:

The given forces F1 and F2 in relation to the pivot point of the lever create torques (M).

To calculate the moment of force for both arms of the lever, we apply the formulas:

M1 = F1 * x and M2 = F2 * y.

Since the lever is at rest, then

M1 = M2 and we can equate expressions

F1 * x = F2 * y.

F2 / F1 = x / y.

Substitute the known values ​​and get the equality:

140/20 = 7 = x / y.

Thus, we get the value x = 7y.

The length of the entire arm is x + y, then it is 7y + y = 8y.

On the other hand, we can write as the length of the lever 2 = 8y.

That is, y = 0.25 m, and x = 7y = 7 * 0.25 = 1.75 m.