CM Consider a system comprising two extended bodies, which have massesM1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole systemis atR-MIRI+M2R2M1M2(This beautiful result means that in finding the CM of a complicated system, you cantreat its components parts just like point masses positioned at their separated centersof mass, even when the component parts are themselves extended bodies.)

Question
Asked Sep 13, 2019
3 views
CM Consider a system comprising two extended bodies, which have masses
M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system
is at
R-MIRI+M2R2
M1M2
(This beautiful result means that in finding the CM of a complicated system, you can
treat its components parts just like point masses positioned at their separated centers
of mass, even when the component parts are themselves extended bodies.)
help_outline

Image Transcriptionclose

CM Consider a system comprising two extended bodies, which have masses M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system is at R-MIRI+M2R2 M1M2 (This beautiful result means that in finding the CM of a complicated system, you can treat its components parts just like point masses positioned at their separated centers of mass, even when the component parts are themselves extended bodies.)

fullscreen
check_circle

Expert Answer

Step 1

Total forces acting on masses m1 and m2 are,

help_outline

Image Transcriptionclose

xt

fullscreen
Step 2

Adding both the equations,

help_outline

Image Transcriptionclose

12 21 d (mu)+(m,v^)=R2+F +(-F12)+F Using Newton's law) dt dt d +F Ext (mi + m2v2)=F dt d (mi + m2v2)= Fo dt bta

fullscreen
Step 3

Upon further simpl...

help_outline

Image Transcriptionclose

d dR, dR |- (m +m) a m2 т dt dt dt d'2 (mR,+m,R.) =(m + md Reu dt dt m tm2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Physics

Kinematics

Related Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: You drive up a long road inclined at 10 degrees for 1.5 miles.  How may meters of elevation increase...

A: Click to see the answer

question_answer

Q: What is 47.905 rounded to three significant figures? I put 48.0 and it was incorrect.

A: The given number is having five significant numbers.The new round of to three significant figures is...

question_answer

Q: How long would it take in seconds to travel a distance of 2000 meters if you are traveling at a spee...

A: Write the expression for time taken, and substitute 2000m for d, and 25m/s for v in the below equati...

question_answer

Q: A point charge of -3.00 μC is located in the center of a spherical cavity of radius 6.60 cm inside a...

A: Given:Charge at the centre of the spherical cavity, Q = -3.00 µCRadius of the spherical cavity, Ri =...

question_answer

Q: Two identical balls are charged to +q and +2q respectively. Draw a free body diagram for the electro...

A: The free body diagram of the electrostatic force on both the balls having charge q and 2q which are ...

question_answer

Q: The resultant vector R = 9A + 5B + 2C where A = 5 i + -2 j + 7 k ; B = 6 i + 8 j + -7 k and C = -6 i...

A: It is given that :

question_answer

Q: You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the s...

A: Consider the first experiment. The weight of the mass must be equal and opposite to the spring force...

question_answer

Q: find the weight density in SI units of a metal block 18.0cm x 24.0cm x 8cm with a mass density of 9....

A: Substitute 9.76 kg for M, 9.8 m/s2 for g, 18.0cm×24.0 cm×8 cm for V in the above equation to find we...

question_answer

Q: Spheres of Charge: A metal sphere of radius 10 cm carries an excess charge of +2.0 μC. What is the m...

A: Electric field is given by,