What is the x-coordinate of the center of mass?

A.) What is the x-coordinate of the center of mass?
B.) What is the y-coordinate of the center of mass? General guidance

Concepts and reason

The concept required to solve this problem is center of mass. Use the equation for the x-component of the center of mass and calculate the x-component of the center of mass of the given system. Use the equation for the y-component of the center of mass and calculate the y-component of the center of mass of the given system.

Fundamentals

The x-coordinates of the center of mass of the given system is, Here, is the x-coordinate of center of mass, is the mass of particle, and is the x-coordinate of particle.

The y-coordinates of the center of mass of the given system is, Here, is the y-coordinate of center of mass and is the y-coordinate of particle.

Step-by-step

Step 1 of 2

(a)

The equation for the x coordinate of center of mass system is as follows: Here, the system contains three masses. Hence, Substitute for and for . Substitute for , for , for , for , for , and for . Therefore, the x-coordinate of center of mass is .

Part a

Part a

The x-coordinate of center of mass is .

The x-coordinate of the mass at the point A is at the origin. Hence, The mass at the point B is along the y axis. Hence, Step 2 of 2

(b)

The equation for the y coordinate of center of mass system is as follows: Here, the system contains three masses. Hence, Substitute for and for in the equation and solve for . Substitute for , for , for , for , for , and for . Therefore, the y-coordinate of center of mass is .

Part b

Part b

Therefore, the y-coordinate of center of mass is .

The y-coordinate of the mass at the point A is at the origin. Hence, The mass at the point C is along the x axis. Hence, Part a

Part a

The x-coordinate of center of mass is .

Part b

Part b

Therefore, the y-coordinate of center of mass is .