An 18 kg mass is placed st one end of a steel bar that is 1 m long. A 35 kg mass is placed at the other end. Where should the fulcrum be placed to balance the bar?

mass x distance on one side = mass x distance on the other side

let the distance be x m from the heavier mass
35x = 18(1-x)
35x = 18 - 18x
53x = 18
x = 18/53 = .3396

the fulcrum should be appr 34 cm from the heavier load.

check:
34(35) = 1190
66(18) = 1188 , close enough for 2 digit accuracy.

To determine where the fulcrum should be placed to balance the bar, we need to consider the principle of moments or torque. Torque is the rotational force generated by applying a force at some distance from a pivot point.

In this scenario, we have two masses placed at different distances from the fulcrum. The torque exerted by a mass can be calculated by multiplying the mass by the distance from the fulcrum. The total torque on the bar must be zero for it to be in equilibrium.

Let's denote the distance of the 18 kg mass from the fulcrum as x and the distance of the 35 kg mass from the fulcrum as (1 - x), where x is a fraction representing the position of the fulcrum along the bar.

Now, we can calculate the torque exerted by each mass:

Torque by the 18 kg mass = (18 kg) * x
Torque by the 35 kg mass = (35 kg) * (1 - x)

For equilibrium, the sum of torques should be zero:

(18 kg) * x = (35 kg) * (1 - x)

Let's solve this equation to find the position of the fulcrum:

18x = 35(1 - x)
18x = 35 - 35x
18x + 35x = 35
53x = 35
x = 35 / 53

Using a calculator, we find that x ≈ 0.6604.

Therefore, the fulcrum should be placed approximately 0.6604 meters from the end where the 18 kg mass is located to balance the bar.