Mechanical Equilibrium An object in mechanical equilibrium is stable, without changes in motion

Learning hint Read the chapters quickly but read then more than once!!! Physics and most other sciences are best learned by going over the same material many, many times!!!

Objectives: Distinguish between force and net force (2.1) Describe the equilibrium rule and give examples (2.2) Distinguish between support force and weight (2.3) Give examples of moving objects that are in equilibrium (2.4) Determine the resultant of a pair of parallel or non-parallel vectors (2.5)

Key Terms Force Net force Vector Vector quantity Scalar quantity a push or a pull Net force combination of all pushes and pulls on an object Vector An arrow that represents magnitude (how much) and in what direction Vector quantity A quantity that needs both magnitude and direction Scalar quantity A quantity that that can be described by magnitude only. (time, area, volume)

2.1 Force A push or pull A force is needed to change an object’s state of motion Net force is the sum of forces acting on an object

Weight and Tension Is the force of gravity on any object Fg = mgg It is measured in newtons 2lbs = 9 newtons Both are measures of force If we hang an object by the rope we used earlier there would be several forces acting on the system. Force on: Object due to gravity Object due to rope Rope due to object – this is called tension

Force Vectors Vector Vector quantity Scalar quantity An arrow that represents magnitude (how much) and in what direction Vector quantity A quantity that needs both magnitude and direction Scalar quantity A quantity that that can be described by magnitude only. (time, area, volume) Scalar quantities can be manipulated according to the rules of math Vector quantities have special math rules!!

2.2 Mechanical Equilibrium An object which has no change in motion SF = O This is the Equilibrium rule Forces acting up must = the forces acting down S = Sum of F = force

Support Force 2.3 If something is still there must be another force besides gravity in order to have SF=0 This force will be opposite to gravity Support force = Normal force Support force is the up force that balances the weight of the object Support force = + Force of Gravity = - A scale gives you your weight when you step on it b/c it is your mass combined with gravity are in the downward direction & the scale & floor forces are in the upward direction Support force and your weight have the same magnitude

2.4 Equilibrium for Moving Objects Just b/c an obj. is moving doesn’t mean it is not in equilibrium Once in motion if SF=O then it is in equilibrium Hockey puck on ice Bowling ball rolling at constant velocity A change in motion means that an obj is not in equilibrium Friction is a contact force btwn objects that slide or tend to slide against each other

2.4 continued Two types of mechanical equilibrium Static equilibrium – to have no motion at all A book on a table Dynamic equilibrium – unchanging speed in a straight line Airplane – once in flight Hockey puck Parachutist – no wind and once the chute is opened

2.5 Vectors If you are evenly on two scales then your weight will be divided evenly between the two scales Combining is easy if parallel (//) Add if in the same direction Subtract if opposite Resultant = sum of 2 or more vectors Non // vectors use parallelogram rule

Parallelogram Rule Create a parallelogram where the vectors are adjacent side. The diagonal of the parallelogram gives you the resultant of the two forces (R) A square is a special case b/c the 2 adjacent sides will have the same magnitude sq. root of 2 = 1.414 therefore we multiply the magnitude of one of the adjacent vectors by this number to obtain the resultant.

Applying the Parallelogram Rule Violet is in equilibrium There are 3 forces acting on her Tension in Lt rope Tension in Rt rope Weight Tension in each rope is more than half her weight As the angle btwn the ropes increases the tension increases The R vector must = the FV downward Tension Tension Weight

When ropes are at different angles There will more tension on the rope that is closer to being vertical. (see figure 2.13)