Finding the Centroid of Combined Shapes

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To find the centroid of the combined triangle and rectangle, first calculate the centroids of each shape: the triangle's centroid is at (1.3, 2) and the rectangle's centroid is at (4, -2). The next step involves treating each shape as a point mass located at its centroid, factoring in their areas to determine their relative masses. The combined centroid cannot simply be found by averaging the centroids unless the shapes have equal mass; instead, use the formula for the center of mass of multiple particles. Understanding the mass distribution is crucial for accurately calculating the centroid of the combined shape.
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Hi guys, would really appreciate some help with this question, so far I've only been doing really simple c.o.g questions and I'm lost with this one.

A triangle has its vertices at the coordinates (0,0),(0,4) and (6,0). A rectangle has its vertices at the coordinates (0,0),(8,0),(8,-4) and (0,-4). Determine the coordinates of the centroid of the combined shape.


Ok I started out by finding the center of gravity of each separate shape

rectangle (4,-2)
triangle (1.3,2)



But I don't know where to go after this. Can anyone give me some pointers on how to solve this?
 
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If you had two point masses at different points, could you find their combined center of mass? (I hope so.) Same thing here: For the purpose of calculating the center of mass, think of each shape as a point mass located at that shape's center of mass.
 
So am i right in thinking that I just find the midpoint between the center of gravity of the triangle and rectangle to get the midpoint of the whole shape?

My brain is working slowly today have been doing maths and physics since mid day almost 9 straight hours :(
 
haddow64 said:
So am i right in thinking that I just find the midpoint between the center of gravity of the triangle and rectangle to get the midpoint of the whole shape?
It would only be the midpoint if they have the same mass.

My brain is working slowly today have been doing maths and physics since mid day almost 9 straight hours
I know that feeling all too well. Hang in there.
 
Ok so I take moments about the vertical and horizontal edges.

How would I do this? Really stuck here and its the last question I have to do so any help would be really appreciated.
 
Do you know the mass of each piece? (Or are you to assume they are of uniform density? If so, their areas will be proportional to their masses.)

Given the masses (or at least the relative masses) you treat this using the definition of the center of mass of several particles. Read this for a review: http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html"
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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