Sliding Toppling Systems

Question 1

HOW TO PROVE SOMETHING IS IN EQUILIBRIUM IF ON A SLOPE (2 things to do)

Answer 1

1) prove that the weight force acting down is < than the MAX FRICTION , therefore it won’t slide
- alternatively say angle is too small for it to slide, so won’t slide

2) find angle at which it will topple
- if it doesn’t meet this angle it won’t topple

Therefore EQUILBKRUM

Question 2

When using toppling equation x / y, what is x and y?

(Tan theta toppling = x/y)

Answer 2

X and y is the CENTRE OF MASS distances relative to anywhere

NOT THE WIDTH AND HEIGHT !

Question 3

Remember what’s the centre of mass of a triangle ?

Answer 3

1/3 the way from a corner to centroid

If it’s symmetry, always use the bototm to the top

Question 4

If two things toppling at same time, what does this imply about centre of masses?

Answer 4

This mean angle of topple is the same

Thus tan theta constsnt so centre of mass 1 = centre of mass 2

Question 5

Want to topple without sliding?

Slide without topple?

Answer 5

Set the sliding force to be greater than toppling, this means it will never reach sliding and always topple

Set topple grewter than slide , this mean it will slide then toppled

Now remember how to find slide = equate friction to other direction firce, this is point of sliding
And how to find topple, = equate moments at last point of contact , where reaction force goes through this point, and find force

Question 6

If you want a shape to topple by decreasing angle other side, or increasing angle so normal how to do

Answer 6

Remmeber this is possible, just position last point fo contact and use same formula for centre of mass, and remember if you go LESS THAN THIS angle it will topple right way, but go higher than normal topple left wards

Thud you get a minimum angle and a max angle in whcih ti doesn’t toplle