Question

Guys please help :0

Answer 1

http://screencast.com/t/4JNH9TpLxpvo

Answer 2

@Vincent-Lyon.Fr

Answer 3

how would i approach a question like this, to make it simple to do

Answer 4

Do you know that the centre of mass of a solid cone is a quarter of the total height away from the base?

Answer 5

If you cannot use these formula, you can use integration. It is not too difficult.

Simply stack elementary discs together, but first put the cone upside down.



Elemental volume of disc is \(dv=\pi \,r^2\,dz\)
Since \(\tan \theta = \dfrac rz=\dfrac RH\)

then \(dv = \pi \dfrac{R^2}{H^2}z^2\,dz\)

So distance of centre of mass from O is

\(a=\dfrac{\int_h^Hz\,dv}{\int_h^H\,dv}=\dfrac{\int_h^Hz^3\,dz}{\int_h^Hz^2\,dz}=\dfrac 34\;\dfrac{H^4-h^4}{H^3-h^3}\)

Work this out with H = 1.2 m and h = 0.8 m
then the distance from larger plane will be b = H - a = 0.174 m

Answer 6

Elemental disc is here: radius r and thickness dz

Answer 7

i hvent learn integration yet, what about the cone formula/?

Answer 8

this looks complicated :/

Answer 9

In order to solve this problem, you need either to be able to integrate, or you need to know 3 formulae:
- volume of a cone of radius R and height H : \(V=\dfrac \pi 3 R^2H\)
- position of the centre of mass of a solid cone : \(z=\dfrac 34 H\)
- composition of centre of mass :

\((m_1+m_2) \,\vec {OG}_{total}=m_1\,\vec {OG}_1+m_2 \,\vec {OG}_2\)

Answer 10

yes i know tht formula "_

Answer 11

but i dont know the centre of mass to the lower body :/

Answer 12

Use the formula this way:

\(M \,\dfrac 34 H=m \,\dfrac 34 h+(M-m) \, a\)

and solve for a, using the formulae above.

Answer 13

can u explain why its M-m and the reason u hve arranged the equation in that way :/ its confusing

Answer 14

with a diagram ?

Answer 15

In order to use formulae (1) and (2), you need full cones.
Then you say:
Big cone = small cone + truncated cone
and apply the last formula.