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)
80d = 60*4 = 240,
d = 3 Ft.
To find the force the fulcrum applies to the beam and the distance to the fulcrum from the 80 lb. child, we can use the concept of torque.
Torque is the product of force and distance from the fulcrum. In the case of a balanced see-saw, the sum of the torques on either side of the fulcrum is equal.
Given:
Weight of the first child = 80 lb.
Weight of the second child = 60 lb.
Distance of the second child from the fulcrum = 4 ft.
Since the see-saw is in equilibrium, the torques on both sides of the fulcrum must balance out:
Torque1 (from the first child) = Torque2 (from the second child)
The torque due to each child is given by the product of their weight and the distance from the fulcrum:
Torque1 = Weight1 * Distance1
Torque2 = Weight2 * Distance2
We can rearrange the equations and solve for Distance1 (the distance of the first child from the fulcrum):
Weight1 * Distance1 = Weight2 * Distance2
Plugging in the given values:
80 lb. * Distance1 = 60 lb. * 4 ft.
To solve for Distance1, we can divide both sides of the equation by 80 lb.:
Distance1 = (60 lb. * 4 ft.) / 80 lb.
Calculating:
Distance1 = 3 ft.
So, the distance from the fulcrum to the 80 lb. child is 3 ft.
To find the force the fulcrum applies to the beam, we can use the torque equation again:
Torque1 = Torque2
Force1 * Distance1 = Force2 * Distance2
The force the fulcrum applies to the beam (Force1) can be found by rearranging the equation:
Force1 = (Force2 * Distance2) / Distance1
Since we know the weight of the children, we can substitute their weights for the corresponding forces:
Force1 = (Weight2 * Distance2) / Distance1
Plugging in the values:
Force1 = (60 lb. * 4 ft.) / 3 ft.
Calculating:
Force1 = 80 lb.
So, the force the fulcrum applies to the beam is 80 lb.