center of mass. consider motion of object as if all mass located at c of g
TRANSCRIPT
Center of Mass
Consider motion of object as if all mass located at C of G.
Center of Gravity – Average position of weight
Average position of massCenter of Mass –
C of M does not have to be on the object.
Locating Center of Gravity
Locating Center of Gravity
Center of Gravity = Balance Point
m1 m2 m3 m4
A
ΣτA = m1gx1 + m2gx2 + m3gx3 + m4gx4
CM
(m1+m2+m3+m4)
ΣτA = (m1 + m2 + m3 + m4)g xCM
A
m1gx1 + m2gx2 + m3gx3 + m4gx4
(m1 + m2 + m3 + m4)g xCM=
m1x1 + m2x2 + m3x3 + m4x4 + …
xCM = --------------------------------- m1 + m2 + m3 + m4 + …
Calculating CM 2- dimensions
Platform: 6.0 m x 6.0 m 100. kg500. kg masses @ 3 cornersCM?
Toppling
Object is stable if its CG is above its base of support.
More stability if CG is low andbase of support is wide.
Calculating Angle of Stability
θ
h
b θ
tan θ = h/b θ = tan-1 (h/b)
5.0 cm
8.0 cm
To what angle can the block tip before it topples over?
58º
If CG is underneath base of support, object remains stable.