Question

Three particles are placed in the xy plane. A 50-g particle is located at (3, 4) m, and a 40-g particle is positioned at ( 2, 6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at (3, -6)?

Answer 1

To find the position of the 20-g particle for the center of mass to be located at (3, -6), we can use the formula for the center of mass and solve for the unknown position of the particle.

Step-by-step explanation:

To find the position of the 20-g particle for the center of mass of the three-particle system to be located at (3, -6), we need to consider the mass and position of each particle. Let's call the 20-g particle P3.

The center of mass is calculated using the formula: x_cm = (m1 * x1 + m2 * x2 + m3 * x3) / (m1 + m2 + m3) and y_cm = (m1 * y1 + m2 * y2 + m3 * y3) / (m1 + m2 + m3).

Substituting the known values, we get:

x_cm = (50 * 3 + 40 * 2 + 20 * x3) / (50 + 40 + 20) = 3

y_cm = (50 * 4 + 40 * 6 + 20 * y3) / (50 + 40 + 20) = -6

Solving these equations, we find that the 20-g particle must be placed at (-7, -12) m to achieve the desired center of mass.