Physics and Measurements

1
Physics and Measurements

• Physics depends on accuracy of measurement
• Accuracy depends on the instruments used
• Significant figures in measures and calculations
  are necessary

2
Measures and Standards

• Physics needs units for distance, time, mass, and
  angle
• Distance standard meter
• Time standardsecond
• Mass standardkilogram
• Angle standard radian
• This unit equals 180o/p or about 57.3o
• This unit is used for rotation, degrees of angle
  are used for directional heading

3
Metric System/Unit Conversions

• Same metric prefixes and conversions are used as
  in previous courses--see p5 in S/F
• Unit Conversions are done in the same manner as
  in Chemistry--by unit analysis--examples on next
  slide

4
How many centimeters are in one foot?
30.48 cm
How many minutes are there in one and one-half
days?
2160 min
An automobiles speed is 30 mi/hr. Change to cm/s.
1300 cm/s
Hwk p18 ff MC 1,3,4 Pb 1,3,15,16, 20, 39, 47,
48
5
Motion

• Occurs Everywhere in Everything
• Describing motion involves RATE
• Measures of rates of motion
• Speed Velocity Acceleration
• Motion is Relative
• Motion is always dependent on from Where it is
  being measured
• Objects moving together at the same rate have no
  relative motion

6
Study of Motion

• Mechanics is the general study
• Kinematics is the description of the position and
  motion of objects as a function of time. It
  concentrates on displacement, speed, velocity,
  acceleration, and time. It is not concerned with
  cause.
• Dynamics is the study which is concerned with
  causes of motion

7
Displacement

• Defined as the change in position, xf-xi
• Displacement also involves direction as it is a
  vector quantity. It is possible to travel a
  great deal of distance and yet have no
  displacement.
• Vectors have direction associated with them,
  quantities with no assigned direction are
  scalars.

8
Motion on the Earths Surface

• Speed
• What is it?--distance covered
• in time
• Examples of measurements
• meters/sec mi/hr light years/ century
  radians/sec
• Instantaneous--speedometer measurement
• Average speed Total distance
• Total
  time

9
Two students taking a trip of three hours travel
100 km in the first two hours at constant speed.
They then traveled 80 km in the last hour. What
was their average speed for each segment? What is
the average speed for the whole trip?
Segment 1 x100 km t 2 hours speed x/t
100/2 50 km/hr
Segment 2 x 80km t 1 hour Speed 80/180
km/hr
Overall x180 km t 3hours Speed 180/360
km/hr
10
Velocity

• Different from speed
• Constant -- straight line motion-- no change of
  direction
• Changing velocity-- examples
• Falling object gets faster as it falls
• Car rounding a curve at constant speed
• Earth in orbit around the sun

11
Average Velocity

• Depends upon displacement, the measure of how far
  from a starting point an object has moved
• Depends upon how much time has elapsed
• v D x / D t where D is the change in either
  position or time
• It may not be the same as the average speed which
  depends on total distance, rather than position

12
A pigeon flies starts at JFKHS and travels as
follows a. 50 km east in one hour b. 50 km west
in one hour What velocity does the pigeon have in
each case?
First determine the positive direction, which
arbitrarily is east. Therefore the pigeon is
travelling 50km in one hour, thus a velocity of
50km/hr. Travelling west, the only difference is
the direction and the sign, thus -50km/hr.
If the pigeon starts 10km east of JFK, flies 20km
further east and then to 30km west of JFK, all in
one hour, what is its average velocity and its
average speed?
Velocity Displacement is measured from the
starting point, thus from 10 it flew to 30, and
then to -30, using JFK as the zero point. So the
total displacement is -30 -10-40km and velocity
is -40 km/hr. Speed however is total distance
divided by time 20km 60km 80km, thus 80 km/hr.
13
Graphical Representations

• Both displacement and velocity can be represented
  on graphs
• A displacement/time graph will have slope equal
  to the velocity
• In a nonlinear graph, instantaneous velocity at
  any point can be discovered by calculating the
  slope of the tangent line at that point p30 S/F

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Distance from Speed or Velocity

• Since speed and velocity are involved with
  distance/time, distance would then be v(t) or
  speed x time.
• Using the equation, Dx/Dt v, Dx vDt
• Knowing that Dx xf - x0 , the equation can be
  rearranged to x x0 vDt

16
Traveling down I-5 south of Sac at 166
km/hr(youre speeding!!), you see an accident
ahead and apply the brakes. If you come to a
stop in12 seconds, how far do you travel?
t12 sec v0 166 km/hr vf 0 km/hr
0.0461 km/sec
v 1/2 (0.0461 0) 0.02305 km/sec x
0.02305(12) 0.2766 km 0.2766km
277m gt 280 m
17
Homework!!!

• S/F p45ff CQ 5,8
• P 2, 3, 7, 11, 13

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Acceleration

• Rate of rate, how fast something changes
  velocity
• Change of Velocity Acceleration
• Elapsed Time
• Can be positive, negative, or directional
• Straight line is most commonly investigated, but
  circular and rotational acceleration are also
  possible
• v must be the average velocity, especially if the
  velocity changes v 1/2(v0 vf)

19
Acceleration Problems
A bicyclist starts from rest and increases her
speed to 2.0 m/s in 5.0 s. What is her average
acceleration?
a vf - v0 / t t 5.0 s v0 0 (from rest)
vf 2.0 m/s
a 2.0 / 5.0 0.40 m/s2
A motorcyclist starts from rest and accelerates
at 4.0 m/s2 for 12s. What is the riders velocity
after 12 s?
a vf - v0 / t t 12 s a 4.0 m/s2 v0
0 m/s
4.0 (vf - 0) / 12 48 vf - 0 vf
48 m/s
20
Instantaneous Acceleration

• Just as instantaneous velocity can be determined
  in a displacement/time graph, instantaneous
  acceleration can be found on a velocity/time
  graph
• The slope of the tangent to that graph at any
  point will give instantaneous acceleration see
  p32 S/F

21
A sprinter quickly accelerates to maximum
velocity over time. Determine instantaneous
acceleration at t 0.5, 1.5, and 2.5 seconds.
a .4/.50.8 m/s2
a 1.25/.5 2.50 m/s2
a 3.0/.50 6.0 m/s2
22
Constant Acceleration

• Equations relating t, a, x, v0, vf
• when you dont need t
• vf2 v02 2ax
• when you dont need a
• x ( t)
• when you dont need vf
• x v0t 1/2 at2
• when you dont need x
• vf v0 at

23
A Lockheed L-1011 at rest begins accelerating at
2.3 m/s2 and continues for 34s until it lifts
off. How far does it go before lifting off?
KNOWN a, t, v0 UNKNOWN x UNNECESSARY vf
Use x v0t 1/2 at2 x 0(34)
(.5)(2.3)(34)2 x
1329.4---gt 1300 m (2 sigfigs)
A drag racer travels one-quarter mile in 10s from
a standing start. What is the acceleration in
ft/s2?
KNOWN x, t, v0 UNKNOWN a UNNECESSARY vf
Use x v0t 1/2 at2 0.25 mi 0(10)
(.5)a(10)2 a 0.25/50 0.0050 mi/s2 (5280
ft/mi)(.0050 mi/s2) 26 ft/s2
24
A car going 90 km/hr has to stop suddenly to
avoid hitting a rabbit 50 m away. If the brakes
can apply deceleration of 7.5 m/s2 , will
the bunny hop away unharmed?
KNOWN a, vf , v0 UNKNOWN x UNNECESSARY t
Use vf2 vi2 2ax vf0 m/s a -7.5 m/s2
v0 90 km/hr (90 km/hr)(1000
m/km)(1hr/3600s) 25 m/s 02 (25)2 2(-7.5)x
-625 -15x x 42 m Elil-Hrair-Rah lives to
see another day.
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Motion in Free Fall

• Speed in Free Fall
• Falling with no or negligible air resistance,
  affected only by gravity
• Increases speed at approximately 10 meters/sec
  each second
• This acceleration is termed g
• Accurate value 9.8 m/sec2
• Normally given negative sign to denote decrease
  in positive or increase in negative velocity
• Instantaneous speed in free fall v g t

26
Motion in Free Fall (cont)

• Speed in Free Fall
• An object first propelled upward has same
  acceleration as one falling
• Upward g slows object
• Downward g speeds object

27
Free Fall Problems
At Paramounts Great America in Santa Clara, the
Drop Zone ride drops riders 30 meters down before
braking to a stop. How long to the riders fall
and how fast are they going before braking?
Pt1 KNOWN a, x, v0 UNKNOWN t
UNNECESSARY vf a g9.8 m/s2 v0 0 m/s
x 30 m
Use x v0t 1/2 at2 30(0)t (.5)(9.8)t2
304.9 t2 t
t 2.5s
Pt 2 KNOWN a, x, t , v0 UNKNOWN vf Use
vf v0 at vf 0 (9.8)(2.5) 24 m/s
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Air Resistance

• What is it?
• Air has substance and thus viscosity
• Air resistance is friction with the air
• Without it, gravity affects all objects the same
• Feather and hammer dropped on moon hit at the
  same time
• Crumpled paper falls as fast as a ball

29
Equations for Free Fall

• Velocity at any instant
• v g Dt
• Distance at any instant
• d 1/2 g (Dt)2
• Time for falling a distance

30
Homework!!

• S/F p45ff CQ 12,13, 15
• P 18, 24, 32, 38, 42, 50, 60