Three children acrobats are standing still on a circular horizontal platform of radius 4 m suspended at the center.The origin of the xy - Cartesian coordinate system is in the center of the circular platform.A 30-kg child is located at (1 m,2 m),and a 40-kg child is located at (-1 m,- 2 m).Assuming the children stand still on their positions,where must a 20-kg child acrobat be located so that the center of mass of the system consisting of the three children is at the origin and the platform is balanced?
A)(-0.5 m,2 m)
B)(-0.5 m,-2 m)
C)(-0.5 m,1 m)
D)(-0.5 m,-1 m)
E)Equilibrium impossible in this configuration.

Question

Quizplus · Accepted Answer

The center of mass (COM) of a system is given by the weighted average of the positions of its components. For the COM to be at the origin with the given masses and positions, the position of the third child must balance the system such that the sum of the moments (mass times position) about the origin is zero for both x and y coordinates. The positions of the first two children create a moment that must be balanced by the third child's position. By calculating the required position that balances the moments created by the 30-kg and 40-kg children, we find that the 20-kg child must be positioned at (-0.5 m, -1 m) to achieve equilibrium.

Three Children Acrobats Are Standing Still on a Circular Horizontal