Center of Mass. Consider motion of object as if all mass located at C of G.
Transcript of Center of Mass. Consider motion of object as if all mass located at C of G.
![Page 1: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/1.jpg)
Center of Mass
![Page 2: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/2.jpg)
Consider motion of object as if all mass located at C of G.
![Page 3: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/3.jpg)
Center of Gravity – Average position of weight
Average position of massCenter of Mass –
![Page 4: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/4.jpg)
C of M does not have to be on the object.
![Page 5: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/5.jpg)
Locating Center of Gravity
![Page 6: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/6.jpg)
Locating Center of Gravity
![Page 7: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/7.jpg)
Center of Gravity = Balance Point
![Page 8: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/8.jpg)
![Page 9: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/9.jpg)
m1 m2 m3 m4
A
ΣτA = m1gx1 + m2gx2 + m3gx3 + m4gx4
CM
(m1+m2+m3+m4)
ΣτA = (m1 + m2 + m3 + m4)g xCM
A
![Page 10: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/10.jpg)
m1gx1 + m2gx2 + m3gx3 + m4gx4
(m1 + m2 + m3 + m4)g xCM=
m1x1 + m2x2 + m3x3 + m4x4 + …
xCM = --------------------------------- m1 + m2 + m3 + m4 + …
![Page 11: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/11.jpg)
Calculating CM 2- dimensions
Platform: 6.0 m x 6.0 m 100. kg500. kg masses @ 3 cornersCM?
![Page 12: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/12.jpg)
Toppling
Object is stable if its CG is above its base of support.
![Page 13: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/13.jpg)
![Page 14: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/14.jpg)
More stability if CG is low andbase of support is wide.
![Page 15: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/15.jpg)
![Page 16: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/16.jpg)
![Page 17: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/17.jpg)
Calculating Angle of Stability
θ
h
b θ
tan θ = h/b θ = tan-1 (h/b)
![Page 18: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/18.jpg)
5.0 cm
8.0 cm
To what angle can the block tip before it topples over?
58º
![Page 19: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/19.jpg)
![Page 20: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/20.jpg)
![Page 21: Center of Mass. Consider motion of object as if all mass located at C of G.](https://reader036.fdocuments.us/reader036/viewer/2022062618/551446755503466d1a8b5ab2/html5/thumbnails/21.jpg)
If CG is underneath base of support, object remains stable.