Centre of Mass of Isosceles Triangle?

[jereldc]

Homework Statement

an isosceles with base=a, height=h. It has uniform density and negligible thickness.

Homework Equations

determine it's centre of mass by integration,using more than one orientation

The Attempt at a Solution

It is a two-dimensional continuous structure. Let the base,a, lie on the X-axis and the Y-axis
be axis of symmetry. Then the COM must lie on the Y-axis. Slice the triangle into strips parallel to the X-axis. Each strip is of width dy, and length l. The mass per strip,dm, is obtained through:

mass=density x area,

p l dy
and the variable of integration is y as it is the axis of symmetry and integration is over 0 and h.

 

[LowlyPion]

Welcome to PF.

You will need to express l in terms y, since l is a function of y.