Physics Lesson 6.2.3 - Centre of Mass of Three Collinear Objects

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Welcome to our Physics lesson on Centre of Mass of Three Collinear Objects, this is the third lesson of our suite of physics lessons covering the topic of Determining the Centre of Mass in Objects and Systems of Objects, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Centre of Mass of Three Collinear Objects

When we have three collinear objects, the centre of gravity of the system is determined at the same way as for two distant objects described above. It is better to choose the reference point on the left of the first object, so that all three objects are on its right and as such, we can take all x-coordinates for the individual centres of mass as positive. Then, the equation (1) written for three objects shown below, is used.

xC = x1 × m1 + x2 × m2 + x3 × m3/m1 + m2 + m3

Example 3

Three objects are placed at the same line as shown below.

Physics Tutorials: This image provides visual information for the physics tutorial Determining the Centre of Mass in Objects and Systems of Objects

What is the position of the centre of mass of this system? All distances are calculated from the origin.

Solution 3

Using the equation (1) for three objects,

xC = x1 × m1 + x2 × m2 + x3 × m3/m1 + m2 + m3

we obtain after the substitutions,

xC = 3 × 2 + 6 × 8 + 1 × 14/2 + 6 + 1
= 68/9 m
= 7.56 m

Therefore, the centre of mass of the system is slightly on the left of the second object.

You have reached the end of Physics lesson 6.2.3 Centre of Mass of Three Collinear Objects. There are 4 lessons in this physics tutorial covering Determining the Centre of Mass in Objects and Systems of Objects, you can access all the lessons from this tutorial below.

More Determining the Centre of Mass in Objects and Systems of Objects Lessons and Learning Resources

Centre of Mass and Linear Momentum Learning Material
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6.2Determining the Centre of Mass in Objects and Systems of Objects
Lesson IDPhysics Lesson TitleLessonVideo
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6.2.1Centre of Mass of a Regular Non-Homogenous Object
6.2.2Centre of Mass of a System Composed by Two or More Distant Objects
6.2.3Centre of Mass of Three Collinear Objects
6.2.4Centre of Mass of Three non-Collinear Objects

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