EGR 280 Mechanics 7 – Friction

Friction Given a block that rests on a surface with friction. If a force is applied to the block to push it along the surface, a plot of the friction force would look something like: PP W N f P f μsNμsN EquilibriumMotion μkNμkN

In general, we will assume static equilibrium exists and we will solve for the magnitude of the friction force f to hold the block in equilibrium. However, if f must be greater than μ s N for equilibrium, then there cannot be enough friction generated for equilibrium… therefore the block must be in motion and f= μ k N. If f is exactly equal to μ s N, then motion of the block is impending. Examples…

Frictional forces on flat belts Flat or V-belts are often used to transmit torque between shafts Such as with this fan and motor Graphics and problem statements © 2004 R.C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ.

∑Fx = 0; T cos(dθ/2) + μ dN – (T + dT) cos(dθ/2) = 0 ∑Fy = 0; dN – (T + dT) sin(dθ/2) - T sin(dθ/2) = 0 keeping only the 1 st order terms, these equations reduce to μ dN = dT dN = Tdθ

So that: ln(T 2 /T 1 ) = μβ T 2 = T 1 e μβ T 2 >T 1