# Incline plane + torque problem

## Homework Statement

A tall uniform rectangular block sits on an inclined plane. If Us = .4, does the block slide or fall over as the angle is slowly increased? Also, the block is 3a units tall and "a" units wide.

## The Attempt at a Solution

Just by intuition, I figured that it would tip over, since the static friction is pretty high, but I'm not sure how to prove that.

I initially thought you could say that as the incline increased, the force between the bottom of the block and the incline plane would increase, creating torque on the block. But in this case, there's no opposing torque at the top of the block, so by this logic, it would tip over as soon as there was any incline. Any help would be appreciated. Thanks!

This is a statics problem. You want to analyze the point where nothing is moving (everything is "static") but if you were to increase the incline any further the block would either tip or slide.

Anytime you have to solve a statics problem you should immediately think of two things:
1) Sum of forces equals zero
2) Sum of torques equals zero

Solving every statics you will see will probably go the same way:
* Find an expression for the sum of forces along a particular axis. Set it equal to zero. (Remember to choose your coordinate axes so that most or all forces will be along one axis.)
* Find an expression for the sum of torques. Set it equal to zero.
* Solve the equations that you just wrote down.

So the first step to solving any statics problem involves identifying all the potential sources for torques and/or forces. In this problem the forces are: gravity, friction, normal force.

Thinking of your block slowly tipping over - it will fall when the centre of mass goes just past the point directly over the point of contact. This should be calculable, which gives you an angle. You can then work out the frictional force vs the sliding force.
In the little pic, the red dot represents the CoM.

#### Attachments

• block tipping.jpg
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