Statics

[started] 1/25/17

Friction

Direction: Opposes relative motion between two surfaces
Magnitude:
- Kinetic friction $f_k=\mu_k N$
- Static friction, matches external force up to maximum $f_s \leq \mu_s N$

Concept: Friction points opposite to relative velocity
Problem: A thin slab of mass $m$ rests centered on two cylinders of radius $r$ rotating with angular velocity $\omega$ in opposite directions. What force $F$ is required for the slab travel with velocity $v_0$ across the cylinders? The coefficient of friction is $\mu$ .

Concept: Reaction force angle
The reaction force $R$ is the net force of friction $f$ and the normal force $N$ . The reaction angle $\varphi=\arctan(\frac{f}{N})$ is the angle between the reaction force and normal force. Once the interaction between two surfaces is determined, the reaction angle does not change.
Problem: A force $F$ is applied at an angle $\theta$ from the hortizontal to move a block across the ground wih constant velocity. At what angle is the force minimized? The coefficient of friction is $\mu$

Concept: Self-locking
Occurs when the applied force $F$ to displace an object contributes to the normal force $N$ and friction $f$ . There is a critical angle $\theta$ beyond which the object will not move no matter how much force is applied.
Problem: A rod of length $l$ rests vertically on the ground. A rope is attached to the top end and the ground, making an angle $\theta$ with the verticle. If a force $F$ is applied horizontally on the rod, how far from the bottom does it need applied to be for the rod to self-lock? The coefficient of friction is $\mu_0$ .

Kevin S. Huang