Center of Mass. Consider motion of object as if all mass located at C of G.

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.