1. 12.1 Static equilibrium
Static equilibrium: No net torque, no net force and no motion.
Static equilibrium
12.2 Sample problem: a witch and a duck balance

2. Rotational Equilibrium
Objects in translational equilibrium (no unbalanced forces) may still be subject to torques that produce rotary motion.
The second condition of equilibrium in a given plane is the sum of all the clockwise torques must equal the sum of all counterclockwise torques about any pivot point.
For an object to be in translational and rotational equilibrium both conditions must be met.

3. 12.3 Center of gravity
Center of gravity: The force of gravity effectively acts at a single point of an object called the center of gravity.
When a body is symmetric and uniform, you can calculate its center of gravity by locating its geometric center.
You can empirically determine the center of gravity of any object by dangling it.
Center of gravity

4. Examples
12.4 Sample problem: a leaning ladder 12.5 Interactive checkpoint: fishing 12.6 Sample problem: isometric training 12.7 Interactive problem: achieve equilibrium 12.8 Sample problem: a rock climber 12.9 Interactive checkpoint: wine holder

5. Coupled Forces
Couple – Two forces of equal magnitude act in opposite directions in the same plane but not on the same point. Example: Compass needle not pointing north and south.
Torque of a couple is the product of one of the forces and the perpendicular distance between them.
Couples cannot be balanced by a single applied force, it requires another couple.

6. 12.10 Elasticity
Objects whose size and shape are changed by opposing forces are elastic if they are able to return to their original size and shape after the forces are removed.
Elastic Limit – The change produced by the applied forces is permanent. The molecular forces are overcome and the shape is permanently changed. You have exceeded its yield strength.
At that rupture point, you have exceeded the material’s ultimate strength.
Elastic

7. 12.11 Stress and strain
Stress- the ratio of the internal force (F), that occurs when a substance is changed, to the area (A) over which the force acts (N/m2)
Strain- The relative deformation produced in a body under stress. Fractional change in dimension due to stress.
Ratio of the change in length to the original length is elongation strain.
Ratio of change in volume to original volume is the volume strain

8. Stress & strain cont…
A stress-strain graph plots the minimum stress required to achieve a certain amount of strain. Near the end, the curve flattens and its slope decreases. Less stress is required to generate a certain strain. The material has become ductile.
Materials which reach the rupture point without becoming stretchy; they are called brittle.
Stress and strain

9. Hooke’s Law
The amount of elongation in elastic solids is directly proportional to the deforming force if the elastic limit is not exceeded.
Hooke’s Law – within certain limits strain is directly proportional to stress.
Young’s Modulus (Y) is the ratio of stress to strain and is a constant for a given substance.

10. 12.12 Tensile stress: A stress that stretches
Tensile strength is the force per unit of cross-sectional area applied perpendicularly to the cross section that is required to break a rod or wire of that material (N/m2)
Tensile strength is one way to measure cohesion
Which has greater tensile strength copper or silver?
Tensile stress

11. 12.13 Volume stress
Volume stress: A stress that acts on the entire surface of an object, changing its volume.
Tensile stress results in a change along a single dimension of an object. A volume stress is one that exposes the entire surface of an object to a force. The force is assumed to be perpendicular to the surface and uniform at all points.
Volume strain is measured as a fractional change in the volume of an object. The modulus of elasticity that relates volume stress and strain is called the bulk modulus, and is represented with the letter B.
Volume stress

12. 12.14 Shear stress Shear stress: A stress that creates a “slant.”
Stress equals force divided by surface area. With a shearing force, the area is computed from the surface parallel to the force being applied.
S represents the shear modulus that relates stress and strain. Like other moduli, the shear modulus has units of newtons per square meter.
Shear stress

13. 12.15 Interactive checkpoint: stress and strain
Example
12.15 Interactive checkpoint: stress and strain

14. Kinetic Theory of Matter
Phases of matter describe the way that particles group together in matter
Solid – Particles tightly grouped in a fixed pattern or crystal lattice.
Liquid – Particles are still close together but free to move about (flow).
Gas – particles are far apart and moving at high speed
Vapor – refers to a gas that should be a liquid at normal temperature and pressure
Gases and liquids are both fluids

15. Kinetic Theory of Matter cont…
Two postulates of kinetic theory of matter
The molecules of a substance are in constant motion. The speed of which is dependent on the kinetic energy (temperature).
Collisions between the particles are perfectly elastic (unless the particles react chemically).

16. Forces Between Molecules
Solids have the strongest forces between molecules and the least relative movement.
Liquids have weaker forces of attraction and greater movement
Gases are assumed to have no attraction for other particles and can move freely (occupy about 1000 X more space than an equal mass of liquid).
Like gravity attractive forces decrease as distance between molecules increases. However if the molecules get too close the force of repulsion increases
Solids and liquids do not compress but gases do.

17. Cohesion and Adhesion
Cohesion – attraction between the same kind of molecules.
Holds solids together
Short range force
Adhesion – attraction between different kinds of molecules.
Cohesion and adhesion depend on the nature of the molecules

18. Ductility and Malleability
Ductility – the ability of a metal to be drawn through a die and made into wire. 1 g of platinum can be drawn into a wire 600 km long.
Malleability – the ability of a metal to be hammered or rolled into sheets.
Both malleability and ductility depend on the shared sea of electrons that surrounds the nuclei of metals. This can deform while maintaining cohesion between atoms.