1. Two children balance a see-saw in horizontal equilibrium. One weighs 80 lb. and the other weighs 60 lb. and is sitting 4ft. from the fulcrum. Find the force the fulcrum applies to the beam and the distance to the fulcrum to the 80 lb. child. (Neglect the mass of the see-saw)

If I recall my highschool physics,

W1 * D1 = W2 * D2
80D1 = 60(4)
D1 = 240/80 = 3

to find the force...you just subtract the two weights?

To solve this problem, we need to analyze the forces involved and apply the principle of torque. Torque is the measure of how effectively a force causes an object to rotate.

Let's assign some variables:
- Let F1 be the force applied by the fulcrum to the beam.
- Let F2 be the force applied by the 80 lb. child.
- Let d1 be the distance from the fulcrum to the 80 lb. child.
- Let d2 be the distance from the fulcrum to the 60 lb. child.

Since the see-saw is in horizontal equilibrium, the sum of the torques on either side of the fulcrum must be equal.

The torque, τ, is calculated as the product of the force and the distance from the fulcrum:
τ = F * d

In this case, for the left side of the fulcrum (where the 80 lb. child is located), the torque is given by:
τ1 = F1 * d1

For the right side of the fulcrum (where the 60 lb. child is located), the torque is given by:
τ2 = F2 * d2

Since the see-saw is in equilibrium, τ1 must be equal to τ2.

We have the following information:
- F2 = 80 lb. (force applied by the 80 lb. child)
- d2 = 4 ft. (distance from the fulcrum to the 60 lb. child)
- F1 = ? (force applied by the fulcrum)
- d1 = ? (distance from the fulcrum to the 80 lb. child)

Using the equation τ1 = τ2, we can set up the equation:
F1 * d1 = F2 * d2

Plugging in the known values, we get:
F1 * d1 = 80 lb. * 4 ft.

To find the force applied by the fulcrum (F1), divide both sides of the equation by d1:
F1 = (80 lb. * 4 ft.) / d1

To find the distance from the fulcrum to the 80 lb. child (d1), rearrange the equation:
d1 = (80 lb. * 4 ft.) / F1

So, to determine the force the fulcrum applies to the beam, you'll need to divide the product of the weight of the 80 lb. child and the distance to the 60 lb. child by the distance to the 80 lb. child. Similarly, to find the distance to the fulcrum to the 80 lb. child, divide the product of the weight of the 80 lb. child and the distance to the 60 lb. child by the force applied by the fulcrum.