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The rigidly connected unit consists of a 2. 5-kg circular disk, a 2. 5-kg round shaft, and a 3. 4-kg square plate. determine the z-coordinate of the mass center of the unit.

Respuesta :

The answer is 127.31 mm.

Now

consider that The disk

and we know that The given data

[tex]$\begin{aligned}&m_{1}=2.5 \mathrm{~kg} \\&m_{2}=2.5 \mathrm{~kg} \\&m_{3}=3.4 \mathrm{~kg}\end{aligned}$[/tex]

Then The distance is

[tex]$\begin{aligned}&z_{1}=0 \mathrm{~mm} \\&z_{2}=\frac{230}{2}=115 \mathrm{~mm}\end{aligned}$[/tex]

and The

[tex]$z_{3}=230 \mathrm{~mm}$[/tex]

so, find the z-coordinate of the mass centre

[tex]$\bar{z}=\frac{m_{1} z_{1}+m_{2} z_{2}+m_{3} z_{3}}{m_{1}+m_{2}+m_{3}}$[/tex]

put the value.

[tex]$\begin{aligned}&\bar{z}=\frac{(2 \cdot 5) \times 0+(2.5) \times 115+(3.4) \times 230}{2.5+2.5+3.4} \\&\bar{z}=\frac{0+287.5+782}{8.4} \\&\bar{z}=\frac{1069 \cdot 5}{8.4} \\&\bar{z}=127.31 \mathrm{~mm}\end{aligned}$[/tex]

What is mass centre?

  • A location established in relation to an object or set of objects is the center of mass.
  • It represents the system's average location as weighted by each component's mass.
  • The center of mass for straightforward stiff objects with homogeneous density is found at the centroid.

To learn more about center of mass visit:

https://brainly.com/question/8662931

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