Ch3 5 6 Vectors

CH 3 & 5 & 6 Vectors, Newton’s Laws, & Applications of Newton’s Laws Subject

Relevant Equations

Scalars and Vectors

Adding Vectors

Relationships Scalar Vector •Vector is mathematical quantity with both magnitude •A number and direction. with units that •Magnitude=speed and direction = direction of can be motion. positive, •A vector is defined by magnitude and direction negative, or 0. always regardless of its location. Graphically Components •Split into x y •To add vectors A and B, place the tail of B at components and then the head of A. add. •The sum C= A + B is the vector extending •More accurate than from the tail of A to the head of B. graphs. •Negative of a vector is represented by an arrow of the same length as the original vector but pointing in the opposite direction.

Subtracting Vectors •The x unit vector, x is a dimensionless vector of unit length pointing in the positive x direction. •The y unit vector, y is a dimensionless vector of unit length pointing in the positive y direction. rx+ry=scalar components rx+by = vector components.

Unit Vectors

Position, Velocity, Acceleratio n Vectors

Position •Position vector is denoted r. S.I.=m r=xy+yy. •Displacement vector = Δr. rf=ri+Δ r

Velocity

Acceleration

•Vav=Δr/Δt S.I.=m/s •Vav is parallel to Δ r. •V=lim(under Δ t = 0) Δr/Δt. •Velocity vector always points in the direction of a particle motion.

•Aav=Δv/Δt. S.I.=m/s2 •a=lim (under Δt-0) Δ v/Δ t •Acceleration vector always points in one direction other than the direction of motion.

CH 3 Vectors CH 5 Newton’s Laws

Subject Newton's Laws

Relevant Equation s

Relationships

CH 3 & 5 & 6 Vectors, Newton’s Laws, & Applications of Newton’s Laws First (Law of Inertia) •An object at rest stays at rest as long as no net force acts on it. •An object moving with constant velocity continues to move as long as no net force acts on it. •IF net force =0 then velocity is constant.

W=mg S.I.= N W=mgsin Θ or -mgcosΘ W=m(g-a)

Weight

Normal Forces

Second (F=ma)

•Acceleration proportional force. •F=ma. S.I.=N I N=1kg•m/s2

is to

Third (ActionReaction)

•For every force that acts on an object, there is a reaction force acting in a different object that is equal in magnitude and opposite in direction. •Contact forces: Actionreaction force pairs whenever objects are touching each other.

Weight

Apparent Weight

•Weight of an object is the gravitational force exerted on it by the Earth. •W=mg S.I=N •In the x direction: W=mgsinΘ or •in the y direction W=mgcosΘ

•Weight in an elevator when the upward force exerted on your feet by the floor of the elevators changes, hence one feels weightless. •W=m(g-a)

Perpendicular to the surface

CH 6 Applications of Newton’s Law Subject Fricitonal Forces

Relevant Equations

fk=µkN

Relationships

CH 3 & 5 & 6 Vectors, Newton’s Laws, & Applications of Newton’s Laws Kinetic Friction When surfaces slide against one another with finite speed.

Fk=µkN

Static Friction Typically stronger than kinetic friction.

0 ≤ fs which ≤ f , s max friction µ=Fk/FN Force of kinetic fs,max=µsN Coefficient of kinetic

friction between two surfaces is 1.) proportional to the magnitude of normal force 2.) Independent of the relative speed of the surf

Springs and Strings

Hooke's Law: A spring stretched or compressed by the amount x from its equilibrium length exerts a force given by Fx=-

kx

Ex. Ti-mg=0

Translationa l Equilibrium Connected Objects

1)Independent of the area of contact between surfaces 2) Parallel to the surface of contact and in the direction that opposes relative motion

•At any point, tension depends on each situation. •A pulley simply changed the direction of the tension in a string without changing its magnitude.

•Net force -0 therefore acceleration is also = 0. •Set all equations to 0 to solve for variables.

•The string forces of two boxes have the same acceleration. •Treat each box as a separate system. •Write at corresponding equation and try go find variables.

CH 3 & 5 & 6 Vectors, Newton’s Laws, & Applications of Newton’s Laws

•Two factors that affect circular motion are direction and magnitude. Direction Force of the ball is directed toward the center of the circle

Magnitude Force must have magnitude

When the object's mass in the circle with a radius, r, has constant speed, v,

acp=v2/r.

A force must be applied to the object to give it circular motion.

Fcp=macp=2mv2/r. Circular Motion