Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 5, Problem 30P
To determine

The center of mass of the particles which are positioned at the corners of a square with length of sides measuring 30 cm , as shown in Fig. 5-19.

  Physics Fundamentals, Chapter 5, Problem 30P

Expert Solution & Answer
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Answer to Problem 30P

Position of center of mass =14.14 cm and its x and y coordinate is 10 cmand10 cm .

Explanation of Solution

Given info:

  Mass of particle A =10.0 gm

  Mass of particle B =5.00 gm

  Mass of particle C =20.0 gm

  Mass of particle D =10.0 gm

Length of side of square =30.0 cm

Formula used:

The x and y coordinates, of the center of mass of particles of a system in a two dimensional plane is calculated by the following formula:

  Xcm=x1mA+x2mB+x3mC+x4mDmA+mB+mC+mD

Wherein x1,x2,x3 and x4 the linear horizontal are distances of particles from the origin and mA,mB,mC and mD are the various masses of particles.

Similarly the y coordinates are given by the following formula:

  Ycm=y1mA+y2mB+y3mC+y4mDmA+mB+mC+mD

Wherein y1,y2,y3 and y4 the linear verticals are distances of particles from the origin and mA,mB,mC and mD are the various masses of particles.

The position of center of mass of a particle having x and y coordinate is given by the formula:

  r=X2cm+Y2cm

Wherein r is the position of center of mass of the particle, while X and Y are its coordinates.

Calculation:

As per figure 5-19, the x and y coordinates of position of mass at A is

  (x1,y1)=(0,30.0 cm)

Similarly the x and y coordinates for the position of mass at B, C and D respectively are

  (x2,y2)=(30.0 cm,30.0 cm)

  (x3,y3)=(0,0)(x4,y4)=(30.0 cm,0)

Substituting the various values of masses of particles at points A, B, C and D and also its horizontal distances from origin in the equation:

  Xcm=x1mA+x2mB+x3mC+x4mDmA+mB+mC+mD       =(0×10.0 g)+(30.0 cm×5.00 g)+(0×20.0 g)+(30.0 cm×10.0 g)(10.0 g+5.00 g+20.0 g+10.0 g)       =10 cm

Similarly substituting the various values of masses of particles at points A, B, C and D and also its vertical distances from origin in the equation:

  Ycm=y1mA+y2mB+y3mC+y4mDmA+mB+mC+mD     =(30.0 cm×10.0 g)+(30.0 cm×5.00 g)+(0×20.0 g)+(0×10.0 g)(10.0 g+5.00 g+20.0 g+10.0 g)     =10 cm

The position of center of mass is given by the formula:

  r=X2cm+Y2cm

Substituting Xcm=10 cm; and Ycm=10 cm in the formula:

  r= (10 cm)2+ (10 cm)2r=14.14 cm

Conclusion:

The x and y coordinates of the particles are 10 cmand10 cm , of which its position of center of mass is 14.14 cm

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