Mechanics Flashcards
Point of toppling / sliding on a slope in terms of theta?
Theta = arctan mew (for slide)
Theta = arctan (x/y) for topple
Why?
- slide the weight = friction, so rearranging it gives that
- topple the moments about the last point of contact must be 0 (or anywhere Tbf). The reaction acts through the last point of contact, and so reaction and friction are ignored due to no perp distance. Only consider moments of weight. Alternatively centre of mass acts through last point of contact, and use gerometry to work out theta
2 things to consider in a couple?
Resuktsnt force = 0
Couple = sum of all moments
Coeffeicmt of restitution limits?
Must be positive
Can position of centre if mass change / reaction force?
Centr of mass for same system in any orientation will be the SAME position, however it acts through different points!
Thus reaction force changes based on orientation . At point of toppling, throuhbj the last point of contact
What takes dominance toppling or sliding
So if value for toppling and sliding is the same
Toppling
If same = topple
COM of a triangle?
2/3 if the way along the median FROM THE VERTEX
- so draw point from triangle to mid point of oppsite side
- then add 2/3 of the length to find coodeidnates
Easiest way to do this is find the y length of coordinate to midpoint, multiply by 2/3, and same for x and add on!
MUCH EASY FORMULA FOR TRIANGLE CENTE OF MASS IF KNOW ALL THE POINTS
AVERAGE X , AVERAGE Y
IMPORTANT, when finding toppling for COM shapes, what angle do you take when drawing right angle triangle after finding centee if mass?
Top right ine
Draw it out on a ledge and work out thes and you’ll see why!
Don’t lack, always arctan x /y
Centre of mass of circle, parallelogram
Midpoint , a/2 b/2
Triangle = average of all points, else 2/3 away etc to midpoint if line (coodinetsted to make it easier)
