Force of a Box

1. Apr 27, 2010

COKEDUDE

1. The problem statement, all variables and given/known data
A cube of side l rests on a rough floor. It is subjected to a steady horizontal pull F, exerted a distance h above the floor as shown below. As F increases, the block will either begin to slide, or begin to tip over and thus rotate. Determine the coefficient of static friction so that (a) the block begins to slide rather than tip; (b) the block begins to tip. [Hint: Where will the normal force on the block act if it tips?]

2. Relevant equations
No movement
F< Us
Movement
F>Us

3. The attempt at a solution
I know the higher you push on the cube the more likely the cube is to move or tip over. When you push low on the cube the harder it is to move and less likely it is to tip. How would I derive some kind of formula for this? I don't have any numbers, I just need formulas.

2. Apr 27, 2010

bjd40@hotmail.com

when u pull the box with F consider the torques on the box. one will be due to F and other due to gravity, mg. the box will rotate if the torque due to F is higher. so the limiting value of F can be found by equating the torques. now with that value of F consider the friction, it should not have a maximum value which is greater than F. in that condition the box will slide.
for rolling or tippng F x L must be greater than mg x l/2.