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?
Item I The three masses shown in the figure 10 cm 10 cm A O 1 100 g m, In Tap image to zoom are connected by massless, rigid rods. Assume that mi- 17O g and m2 = 310g.

Answer

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,

u

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,

Ση,

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:

u

Here, the system contains three masses. Hence,

mx, =m*+m;*+mexc
m = m +me+mc

Substitute xu+PxPu+ x+x for Ση,χ, and Pu+ 
+ for.

myx, +m3*+mex
Xem =-
m,+mg + mc

Substitute for , for, for , for , for , and 10 cm for .

_(100 g)(0 cm)+(170 g)(0 cm)+(310 g)(10 cm)
100 g +170 g +310 g
= 5.34 cm

Therefore, the x-coordinate of center of mass is 5.34 cm.

Part a

Part a

Answer

The x-coordinate of center of mass is 5.34 cm.


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:

Ση,

Here, the system contains three masses. Hence,

Emy; = mYx+mpy; +mcy

Substitute APu+ 
+ for кша and Pu+ 
+ forin the equation andΣη,solve for.

_ my + y +mcyc.
m+mg + mc

Substitute for , for, for , for , 10 cmfor , and for .

_(100 g)(0 cm)+(170 g)(10 cm)+(310 g)(0 cm)
100 g +170 g +310 g
= 2.93 cm

Therefore, the y-coordinate of center of mass is 2.93 cm.

Part b

Part b

Answer

Therefore, the y-coordinate of center of mass is 2.93 cm.


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,

Answer

Part a

Part a

Answer

The x-coordinate of center of mass is 5.34 cm.

Part b

Part b

Answer

Therefore, the y-coordinate of center of mass is 2.93 cm.

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