Question

# hree children are trying to balance on a seesaw, which consists of a fulcrum rock, acting...

hree children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board 4.2 m long. Two playmates are already on either end. Boy A has a mass of 45 kg, and boy B a mass of 35 kg.

Where should girl C, whose mass is 25 kg, place herself so as to balance the seesaw?

Let us say A is situvated at a postion A , which is a 2.1 m(left) from the center, and B is at 2.1 m (right) from center

The torque produced by A is TA= r x FA , angle beteen r and F is 90 deg ,

rA = 2.1 m ,

F= mA g = 45 * 9.8 = 441 N

TA= 2.1 * 441 = 926.1 Nm

The torque produced by B is Tb= r2 x FB , angle beteen r and F is 90 deg ,

The torque produced by B is TB= rx FB , angle beteen r and FBis 90 deg ,

rB = 2.1 m ,

F= mB g = 35 * 9.8 = 343 N

TB= 2.1 * 343= 720 Nm

The net torque produced by both A and Bi is TA-TB

TA-TB= 926-720 =206 Nm

let the third chidl is located at a distance x from origin to compensate the net torque.

The torque produced by C is TC=r x FC , angle between r and Fc( = 25 * 9.8 = 245 n) is 90 deg , and should banlace the net torque produce by A and B

TC=r X FC =r * 245

206=r * 245

r= 206/245

= 0.84 m

Therefore the third child must be 0.84 m from the center (pivot )