Sliding And Toppling

Question 1

What range if values will an object slide (begin to slide)

Answer 1

When the friction = the pushing force , then it’s at the POINT OF SLIDING

So above this it begins to slide

Question 2

How to find the range of values when something is on the point of toppling

Answer 2

At point of toppling, the moments are net 0, but the centre of mass acts through the last point , thus the REACTION FORCE IS DIRECTLY UP ON THIS EDGE NOW

Find moments and resolve to find

Question 3

How to find what ranges of mew will allow for the box to topple without sliding?

Answer 3

If you set the friction to = the push force, this will give you the value for which it will be on point of sliding l

But if you set the force applied to the point of TOPPLING, and rearrange for mew, then it reaches the point of sliding but this is also the point of toppling, so a bit of force past this just makes it TOPPLE WITHOUT SLIDING

Question 4

How to derrive how to find when sliding snd topllimg happens for an angle on a slope

Answer 4

Sliding
= do same as before , set friction and weight to 0, and you’ll see that theta = arc tan MEW at point of sliding , so abive this and it slides

Toppling
= set reaction force pointing up at last post of contact, take moments and end up considering the weight components only

End up finding that when theta = arc tan x / y, it’s at point of toppling

So beyond this it tool,es

Question 5

So two cinditons for sliding toppling then? at a slope with angle theta?

Answer 5

Point to sliding theta = arc tan mew

Point of toppling = arctam x/y (parallel to slope)