A system consist of particles of masses 5, 2 and 3g located at (1, 0, -1) ( 1, 2, 1) and ( 1, -1, -3) respectively. find the center of position mass involved
for each coordinate (x,y,z) find the weighted average of all the masses times their distances. For example,
Mx = (5*1 + 2*1 + 3*1)/3 = 10/3
do My and Mz similarly
To find the center of mass of a system of particles, you need to calculate the weighted average of their positions, where the weights are the masses of the particles. Here's how you can do it step by step:
1. Assign variables to the given positions and masses:
Particle 1: mass = 5g, position = (1, 0, -1)
Particle 2: mass = 2g, position = (1, 2, 1)
Particle 3: mass = 3g, position = (1, -1, -3)
2. Calculate the weighted sum of the x, y, and z coordinates separately. The weighted sum is calculated by multiplying each coordinate by its respective mass and then adding them up.
For the x-coordinate:
(5g * 1) + (2g * 1) + (3g * 1) = 5g + 2g + 3g = 10g
For the y-coordinate:
(5g * 0) + (2g * 2) + (3g * -1) = 0g + 4g - 3g = 1g
For the z-coordinate:
(5g * -1) + (2g * 1) + (3g * -3) = -5g + 2g - 9g = -12g
3. Calculate the total mass of the system by summing the masses of the individual particles.
Total mass = 5g + 2g + 3g = 10g
4. Divide the weighted sum of the coordinates (from step 2) by the total mass (from step 3) to get the center of mass.
Center of mass = (10g / 10g, 1g / 10g, -12g / 10g)
= (1, 0.1, -1.2)
Therefore, the center of mass of the system with the given particles is located at (1, 0.1, -1.2).