A light platform with a coordinate system drawn on it is supported at the center.A 5-kg mass is placed at .A 3-kg mass is placed at .Where should a 2-kg mass be placed such that the system is in equilibrium?

Question

A light platform with a coordinate system drawn on it is supported at the center.A 5-kg mass is placed at  .A 3-kg mass is placed at  .Where should a 2-kg mass be placed such that the system is in equilibrium?

Quizplus · Accepted Answer

For the system to be in equilibrium, the center of mass of the system should be at the center of the platform, which is (0,0) in the given coordinate system. We can find the center of mass of the system by taking moments about the origin.

Let's call the unknown position of the 2-kg mass (x,y). Taking moments about the origin, we get:

5kg * (-2) + 3kg * 3 + 2kg * x = 0    (for the x-coordinate)
5kg * 0 + 3kg * (-4) + 2kg * y = 0    (for the y-coordinate)

Solving these equations simultaneously, we get x = 1.2 and y = 2.4. Therefore, the 2-kg mass should be placed at (1.2, 2.4) for the system to be in equilibrium. This corresponds to answer choice D.

A Light Platform with a Coordinate System Drawn on It