CP Physics Ch 2 notes

 

SPEED VS VELOCITY

 

I.                   Start simple?

a.       Usually math classes go easy to hard

b.      NOT in physics

c.       Need to understand motion before moving on to other concepts

d.      Math is NOT EASY, but don’t panic

e.       Joke…What means of motion has done more to change the way cities are built than any other?

 

II.                Neglecting Air Resistance

a.       In physics, we will always look at things in them most simple, idealistic situation

b.      We neglect air resistance so that simple relationships will become apparent

c.       AS long as all objects are in the same environment, this idealistic approach works well

 

III.             Demo – Book and paper…which hits the ground first?

 

IV.             Speed

a.       Definition: speed = distance/time

b.      Equation: v = d/t

 

                                                              i.      v = speed (velocity)

                                                            ii.      d = distance

                                                          iii.      t = time

c.       Units = m/s, cm/s, [L]/[T]

d.      Measured with speedometer

e.       Division / = “per” like mph

f.       DEMO –

                                                              i.      walk across floor with 1 meter strides, one per second

                                                            ii.      moving at 1 meter per 1 second = 1m/s

 

V.                Velocity

a.       Definition = speed with direction

b.      This distinction is not as important now as it will be since we are only dealing with straight line motion so the direction will always be the same

 

VI.             Instantaneous vs average speed/velocity

a.       Instantaneous speed = the speed at that instant

b.      Average speed = average speed between two times and/or distance

c.       Question – What type of speed does the speedometer in your car read?

d.      Example – Your speedometer reads 20 mph at the first corner and 40 mph at the second corner.

                                                              i.      What is your instantaneous speed at the first corner?

                                                            ii.      What is your average speed between the first and last corner?

 

VII.          Demo-

a.       Car + ticker timer…convert to km/hr

 

ACCELERATION AND FREEFALL

 

I.                   Acceleration

a.       Definition – change in VELOCITY over time

b.      You FEEL change in motion NOT speed

c.       Question – What are the three controls in a car that make it accelerate?

d.      One undergoes acceleration when executing a curve, even though the speed may not change, the direction changes so the velocity changes

e.       Equation :  a = (vf – vi/t)

                                                              i.      a = acceleration

                                                            ii.      vf = final velocity

                                                          iii.      vi = initial velocity

                                                          iv.      t = time

f.       Units = m/s2

 

II.                Numerical Examples

a.       What is the acceleration of a car that goes from rest to 100 km/hr in 10 s? –check with your neighbor

b.      What is the acceleration of a car that goes from rest to 200 km/hr in 10 s? –check with your neighbor

c.       What is the acceleration of a mechanical part that moves from 0 to 10 m/s in 1 s? – check with your neighbor

d.      Sample problem – A boy on a bicycle is decelerates at –2 m/s2 until he comes to a stop at a stop sign. If it takes him 3 seconds to stop, what was his initial velocity?

G: a =  –2 m/s2, vf = 0, t = 3s

F: vi =?

R: a = (vf – vi)/t

S: at = vf – vi

     vi + at = vf

     vi = vf – at

C: vi = 0 – (–2 m/s2)(3s) = 6 m/s

 

III.             Free Fall

a.       Demo – drop an object from hand

b.      Question – Did it move at a constant velocity or did it accelerate?

c.       Question – What does the statement “An object accelerates at 10m/s2 as it falls” mean?

d.      This is why one wouldn’t hesitate to catch a baseball dropped from a height of 1 meter, but would be quite reluctant to catch the same baseball if it were dropped from an airplane at high altitude.

e.       Check questions:

                                                              i.      If an object is dropped from rest at the top of a cliff, how fast will be falling after 1 second?

                                                            ii.      How fast will it be going after 2 seconds? 10 seconds? T seconds?

IV.             Equation: v = at (for constant acceleration from rest like free fall or down a ramp) .. this is really the same as the acceleration equation…just solved for vf and vi = 0

V.                How far??

a.       Now that we know how fast…how far do object fall each second? Does it stay the same?

b.      Demo – Runner and sprinter

c.       Question – Suppose a falling object is equipped with a speedometer

1.      t = 0s

                                                v = 0 m/s

                                                a = 10 m/s2

d = 0m

 

 

 

2.      t = 1 s

                                                v =       m/s

                                                a =       m/s2

d =      m

 

 

 

3.      t = 2 s

                                                v =      m/s

                                                a =      m/s2

d =      m

d.      We can actually come up with another equation to help with distance:

                                                              i.      vf = at and vavg = (vf + vi)/2

                                                            ii.      vi = 0, so vavg = vf/2

                                                          iii.      substituting à vavg = at/2

                                                          iv.      vavg = d/t = at/2

                                                            v.      so….

                                                          vi.      d = ½ at2

e.       Check Questions:

                                                              i.      How far will a freely falling object fall if it is released from rest after 2 seconds? after 10 s?

                                                            ii.      Consider a rifle fired straight downward from a high-altitude balloon. If the muzzle velocity is 100 m/s and air resistance can be neglected, what is the acceleration of the bullet after one second?

                                                          iii.      Consider a rifle fired straight downward from a high-altitude balloon. If the muzzle velocity is 100 m/s and air resistance can be neglected, what is the velocity of the bullet after one second?

 

           

INTERPRETATION OF GRAPHS

 

I.                   Use motion sensor

a.       walk slowly away

b.      walk slows towards

c.       walk quickly away

d.      don’t move

e.       match graph

f.       make a probably graph

 

II.                How does slope change with motion? What does slope represent?

 

III.             Let’s look at three types of graphs… (look at units)

a.       d vs t    d                                 slope = d/t =

area = dt =

        t

b.      v vs t    v                                 slope = v/t =

area = vt =       

 

                                     t

c.       a vs t                                        slope = a/t =

a                                  area = at =   

 

                    t   

 

IV.             Slope and area are opposites just like addition and subtraction

 

V.                d vs t à v vs t à a vs t = slope

 

VI.             d vs t ß v vs t ß a vs t = area