Overview
This lecture covers the concept and applications of friction in statics, building on previous equilibrium concepts, including dry friction, friction laws, angle of friction, angle of repose, and their practical uses in problems such as blocks, ladders, belts, wedges, and screw jacks.
Review of Previous Concepts: Equilibrium
- Equilibrium occurs when net forces and moments on a body are zero.
- Three equilibrium equations: sum of forces in x, sum in y, and sum of moments equals zero.
- Sometimes more unknowns than equations exist, requiring additional free-body diagrams (FBD).
Introduction to Friction
- Friction is the force that opposes relative motion between two surfaces in contact.
- Two types: dry friction (no lubrication) and wet friction (with lubrication).
- Dry friction is the focus in engineering mechanics.
Laws of Dry Friction (Coulomb’s Laws)
- Friction force is directly proportional to the normal load: ( F \leq \mu N ).
- Friction is independent of the contact area (idealization).
- Kinetic friction is assumed independent of velocity (idealization).
Static and Kinetic Friction
- Static friction: maximum value before motion starts, ( F_{max} = \mu_s N ).
- Kinetic friction: remains constant once body starts moving, ( F_k = \mu_k N ).
- If applied force < ( F_{max} ), friction equals applied force and there’s no motion.
- Friction transitions from static to kinetic at the point of impending motion.
Friction Angle and Angle of Repose
- Friction angle (( \phi )): the angle such that ( \tan \phi = \mu ).
- Angle of repose: maximum incline angle at which a body remains at rest; numerically equals friction angle.
Common Friction Problems
- Free body diagrams (FBD) are essential for analyzing friction questions.
- Always check if motion will occur by comparing applied force to ( \mu N ).
- Key to solving is setting up equilibrium equations and resolving forces.
Applications of Friction
Block and Incline Problems
- Calculate forces parallel and perpendicular to contact surface.
- Minimum force needed to move a body is ( F = \mu N ).
Ladder Problems
- Smooth wall: only normal force at the wall, both normal and friction at the floor.
- Ladder slips at minimum angle when static friction is fully used.
Belt Friction
- For a rope/belt wrapped around a peg: ( T_{max}/T_{min} = e^{\mu \theta} ), where ( \theta ) is in radians.
- The direction with greater tension is where the motion tends to occur.
Wedge Problems
- Wedges convert small input forces into larger lifting forces using friction.
- FBDs must account for normal and frictional forces at contact surfaces.
Screw Jack
- Force to lift: ( P = W \tan(\phi + \theta) ), to lower: ( P = W \tan(\phi - \theta) ).
- ( \theta ) is the helix angle; ( \phi ) the friction angle.
- For self-locking, ( \phi > \theta ).
Key Terms & Definitions
- Friction force (( F )) — The force resisting sliding between surfaces.
- Normal force (( N )) — The perpendicular contact force between surfaces.
- Coefficient of friction (( \mu )) — Ratio of friction force to normal force.
- Static friction — Friction when there is no relative motion.
- Kinetic friction — Friction when surfaces are sliding.
- Friction angle (( \phi )) — Angle where ( \tan \phi = \mu ).
- Angle of repose — Inclination angle where an object just starts to slide.
- Helix angle (( \theta )) — Angle of a screw thread to its axis.
Action Items / Next Steps
- Practice DPP problems given in the app.
- Review and complete the screw jack assignment.
- Join the Telegram group for discussion and doubt resolution.
- Prepare for next class on Trusses and Frames.