Question

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?

Answer 1

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 T_A= r x F_{A ,} angle beteen r and F is 90 deg ,

r_A = 2.1 m ,

F= m_A g = 45 * 9.8 = 441 N

T_A= 2.1 * 441 = 926.1 Nm

The torque produced by B is T_b= r₂ x F_{B ,} angle beteen r and F is 90 deg ,

The torque produced by B is T_B= rx F_{B ,} angle beteen r and F_Bis 90 deg ,

r_B = 2.1 m ,

F= m_B g = 35 * 9.8 = 343 N

T_B= 2.1 * 343= 720 Nm

The net torque produced by both A and Bi is T_A-T_B

T_A-T_B= 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 T_C=r x F_{C ,} angle between r and F_c( = 25 * 9.8 = 245 n) is 90 deg , and should banlace the net torque produce by A and B

T_C=r X F_C =r * 245

206=r * 245

r= 206/245

= 0.84 m

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