Motion

•      Any change in the position of an object.

•      Can be completely described with speed and direction.

 

 

 

Speed: 

•      Instantaneous Speed:  the speed at any instant

•      Average Speed:  distance traveled per unit of time.

•      s = Dd / D t

•      Units - any distance over any time.

Ex. m/s, km/hr, cm/s,

 

Velocity:

•           Speed PLUS direction.

•           A vector quantity

(magnitude + direction)

•           v = Dd / D t, direction

•           Units – any distance over any time, plus, direction.

Ex.  6.5 cm/s, due north

•           Can change velocity by changing speed and/or direction

Speed Problem

    A cat can run 5.0 meters in 3.25 seconds.  What is the cat’s average speed?

List Data        Equation      Solution

d = 5.0 m        s = D d / D t       s = 5.0m / 3.25s

t = 3.25 s                           s = 1.54 m/s

                                                                                        

Velocity Sample Problem

•      A tennis ball flies off the end of a racket and travels 10.0 meters in 0.95s.  What is the velocity of the tennis ball?

List Data       Equation             Solution

d = 10.0 m     v = D d / D t        v = 10.0m / 0.95s

t = 0.95s                         v = 10.53 m/s, across the net

                                                                                                               

 

Velocity Vectors

•      Vector Quantity:  any quantity described by both a magnitude (how much) and direction (which way)

–   Represent with arrow

–   Length represents magnitude
–   Direction represents direction

Resultant Vector

•      Resultant Vector = the algebraic sum of two or more vectors

–   two parallel vectors in the same direction – Add

A boat travels 30 km/hr north in winds traveling 20 km/hr north.  The resulting velocity is 50 km/hr north

 

 

 

A boat travels 45 km/hr north into a wind moving 15 km/hr south.  The resulting velocity is 30 km/hr north.

 

Resultant Vector

•      Resultant Vector = the algebraic sum of two or more vectors

–   two parallel vectors in the same direction – Add

A boat travels 30 km/hr north in winds traveling 20 km/hr north.  The resulting velocity is 50 km/hr north

 

 

 

A boat travels 45 km/hr north into a wind moving 15 km/hr south.  The resulting velocity is 30 km/hr north.

 

Adding vectors that are NOT parallel

•      Parallelogram rule:  Construct a parallelogram with two vectors as adjacent sides with their tails together.  The diagonal of the two vectors is the resultant.

–     For perpendicular vectors the length of the diagonal is calculated as: c2 = b2 + a2

d vs. t graphs

•      Graph the motion

•      use the slope to interpret the relationship between the variables (d & t)

Acceleration

•      Acceleration (a) = Any change in velocity (speed or direction) of an object

              a = vf – vi        =       Dv

                     tf – ti                      Dt

      

vf = final velocity           vi = initial velocity

tf = final time                 ti = initial time

 

Units = distance per time per time - Example:  km/hr/hr = km/hr2

 

•      When direction is not changing a = DS/ Dt  (S = speed)

 

•      Acceleration applies to increasing and decreasing velocity, but deceleration and decreasing accleration are often used to describe slowing down

 

Example:A runner increases her speed from 3m/s to 10m/s in 2 seconds.  Calculate her rate of acceleration.

 

 

Example:  A car goes from 88km/hr to stopped in 4s.

 

Falling Objects

Free-fall:  object falls under the influence of gravity alone.  It is free from all restraints such as air resistance and friction.

 

All objects, regardless of their mass, fall at 9.8 m/s2 near the surface of the earth.

•       For falling objects a =g = 9.8 m/ s2

     

       g = Dv/ Dt => Dv = g Dt

 

If you drop an object in a vacuum, it will be falling at:

      9.8m/s after one second,

      19.6m/s after two seconds,

      29.4m/s after three seconds,                                        etc…

               

 

 

Air Resistance

•      The upward force of air on falling object.

     Depends on the surface area of the object.

 

     Think About:  Falling with vs. falling without a parachute!  Which situation has the most air resistance? 

           

Force

•      A push or a pull.

•      Measured in newtons with a spring scale.

•       1 newton (N) = 1 kg m/s2

•      An apple weighs about 1 newton.

•      Calculate your weight in newtons:

          Weight in pounds = _____       2.2 lbs/kg

          Mass in kg = _____  x  9.8m/s2 =  

          Weight in newtons _____ N

Forces that affect motion

•      Fa          Applied Force –a force exerted on an object       by other objects in it’s environment.

•      Ff          Frictional Force – a force that opposes       motion between the object and the surface it       rests upon

•      Fg          Gravitational Force – the force of attraction       between two objects with mass (ex. Between       an object and the Earth, for example)

•      Fn          Normal Force – the supportive force of the       surface an object rests upon.  It is equal to the force of gravity acting on the object.

                Normal means “perpendicular”

 

     

If forces are balanced…
No Motion

•      No net (unbalance) forces.

If forces are unbalanced…
Motion

If forces are balanced…
No Motion