a system consists of particles of masses 5, 2 and 3g located at (1, 0, -1), (1, 2, 1) and (1, -1, -3) respectively. Find the centre of position of mass.
that would be 5(1,0,-1)+2(1,2,1)+3(1,-1,-3) = (10,1,-12)
To find the center of mass, we need to calculate the weighted average of the positions of the particles, where the weights are the masses of the particles.
Step 1: Calculate the sum of the masses of the particles.
Sum of masses = 5g + 2g + 3g = 10g
Step 2: Calculate the weighted sum of the x-coordinates.
Weighted sum of x-coordinates = (mass1 * x1 + mass2 * x2 + mass3 * x3) / Sum of masses
= (5g * 1 + 2g * 1 + 3g * 1) / 10g
= 10g / 10g
= 1
Step 3: Calculate the weighted sum of the y-coordinates.
Weighted sum of y-coordinates = (mass1 * y1 + mass2 * y2 + mass3 * y3) / Sum of masses
= (5g * 0 + 2g * 2 + 3g * -1) / 10g
= (0 + 4g - 3g) / 10g
= 1g / 10g
= 0.1
Step 4: Calculate the weighted sum of the z-coordinates.
Weighted sum of z-coordinates = (mass1 * z1 + mass2 * z2 + mass3 * z3) / Sum of masses
= (5g * -1 + 2g * 1 + 3g * -3) / 10g
= (-5g + 2g - 9g) / 10g
= -12g / 10g
= -1.2
Therefore, the center of mass of the system is located at (1, 0.1, -1.2).