Q.
The $U$ shaped object shown in the figure has outside dimensions of $100 \,mm$ each side and each of its three sides is $20 \,mm$ wide. The respective values of the $X, Y$ and $Z$ coordinates of the center of mass of the object will be close to
AMUAMU 2013
Solution:
object
Mean
X
Y
Z
Left bar
$m_A$
$10\,mm$
$50\,mm$
$3\,mm$
Right bar
$m_B$
$90\,mm$
$50\,mm$
$3\,mm$
Bottom bar
$m_C$
$50\,mm$
$50\,mm$
$3\,mm$
$x_{\min }=\frac{m_{A} x_{A}+m_{B}+x_{B}+m_{c} x_{c}}{m_{s y s}}$
$=\frac{m(10)+m(90)+0.6\, m(50)}{2.6 \,m}$
$=50\, m m$
$ y_{\min }=\frac{m_{A} V_{A}+m_{B} y_{B}+m_{c} y_{c}}{m_{s y s}}$
$=\frac{m(50)+m(50)+0.6\, m(10)}{2.6 \,m} $
$= 41 \,m m$
$z=\frac{m(3 \,m m)+m(3 \,m m)+0.6 \,m(3 \,m m)}{2.6 \,m} $
$z=3 \,m m$
| object | Mean | X | Y | Z |
|---|---|---|---|---|
| Left bar | $m_A$ | $10\,mm$ | $50\,mm$ | $3\,mm$ |
| Right bar | $m_B$ | $90\,mm$ | $50\,mm$ | $3\,mm$ |
| Bottom bar | $m_C$ | $50\,mm$ | $50\,mm$ | $3\,mm$ |
