Plank against wall

Imagine a plank placed against a wall. The wall is rough and the floor the plank is against is frictionless. Will the plank fall and why?

Easy Math Editor

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Comments

Well, the outcome of the experiment can depend on several things. First thing I immediately noticed is that even when the ground has friction, the answer is indeterminable. it depends on how much friction there is and what angle the plank is to the floor. So what I think the answer to this question is $\boxed{\text{indeterminable}}$ .

Daniel Liu - 8 years ago

Apply the concept of torque.

Siddharth Kumar - 8 years ago

I guess it all depends upon the mass of plank and the coefficient of friction of the rough wall. Considering there is no friction on the floor, the force of friction on the wall must be greater than the weight of the plank due to gravity. If it happens, the plank will not fall,else,IT WILL.

Avinash Trivedi - 8 years ago

A similar problem is in HC Verma

Siddharth Kumar - 8 years ago

If you consider the torque around point A (where the plank touch the wall), you'll see there is only the torque of P (plank weight) -> it will fall due to the unbalance

Ruslan Vu - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$