Unizor - Physics4Teens - Mechanics - Statics - Problems
Channel: Zor Shekhtman on UNIZOR Education
Date: 03/10/2018

Unizor - Physics through a Looking Glass of Mathematician

Notes to a video lecture on http://www.unizor.com

Problems on Equilibrium

Problem 1

Two point-objects of mass M and m are hanging at two opposite ends of a weightless rod of length L.
At what point on a rod should we fix a thread, so the system of a rod with two weights is hanging on this thread in equilibrium?
Does this state of equilibrium imply that a rod is horizontal?

Answer
At distance m·L /(M+m) from the end with object of mass M.

Problem 2

An object of weight W is positioned on a flat surface. The coefficient of static friction is μ.
What is the minimum pulling force P to be applied to a rope, attached to this object, to start pulling it forward, if the angle between a rope and a horizontal flat surface is φ?

Answer

P = μ·W / [cos(φ)+μ·sin(φ)]

Problem 3

Consider the following illustration to this problem.
A person of weight W stands on a platform of weight P. Pulleys and ropes are arranged as on this illustration.
What is the force F a person should apply to a rope to keep the whole system in equilibrium?

Answer
F = (P+W)/4

Problem 4

A ladder is standing at some angle to the floor. It's in equilibrium, that is it's not slipping down to the floor. What holds it is the static friction between it and the floor.
If the ladder stands almost vertically, the static friction is greater and it easily holds the ladder in the position. As we move the bottom of a ladder away from the vertical, there will be a point when static friction will no longer could hold the ladder in place and the ladder would slip down to the floor.
What is the smallest angle the ladder would hold if the coefficient of static friction is μ?

Answer

φ = arctan[1/(2μ)]
Interestingly, the answer does not depend on the weight or the length of the ladder.