Question

A collar brass 50 mm length is mounted on an aluminum bar 80 mm in length (density of brass 8470 kg / m 3 density of aluminum 2800 kg / m 3 ). Find the height to which is the center of mass of the composite body.

Answer 1

here is the data given

Answer 2

You need the volume of the aluminium rod, which is straightforward
\[V = \pi r^2 h\]
r is radius, h is height.
You also need the volume of the collar, so just work out the volume if it were completely solid then subtract the volume of the empty space.
\[V = \pi h(r_{outer}^2 - r_{inner}^2)\]

Then you work out the masses
\[m = \rho V\]

Both centres of mass are on-axis so you can work out the total centre of mass in one dimension
\[c.o.m = \frac{x_1m_1 + x_2m_2}{m_1+m_2}\]
where x is the location of the centre of mass (half the height) of each individual object.

Answer 3

thanks a lot! i was having difficulties, but didn't keep in mind that x1 and x2 are center mass location of each cylinder.