speed, velocity, acceleration & newton micro-world macro-world lecture 2
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Speed, velocity, acceleration & Newton
Micro-World Macro-WorldLecture 2
speed
speed = v =distance traveled
elapsed time
50km
v = 50km1 hr = 50km/hr
Hawaii Kai HaleiwaIn one hour
This is the averagespeed over 1 hour.For shorter time intervals it can be higher or lower.
instantaneous speed
Instantaneousspeed = 0 here
& here
Speed determined for very short time intervals
vistantaneous =distance traveled“very short” time
km
km km
Earth’s motion around the Sun
r=1.5x1011m
V = distance
elapsed time = 2 r 2 x 3.14 x 1.5 x 1011m
365 days x 24 hr/day =
1year
= 9.4 x 1011 m8760 hr
=9.4 x 1011 m8.76 x103 hr
= 1.1x108 m/hr = 1.1x105 km/hr 110,000 km/hr
9.48.7
= x 1011-3 m/hr
=10-3 km
Tip of a watch’s minute hand (HW!!)
V = distance
elapsed time = 2 r 2 x 3.14 x 1cm
60 min x 60 s/min =
1hr
= 6.28 cm3600 s
=6.28 cm
3. 6 x103s= 1.7x10-3 cm/s
= 1.7x10-5 m/s
r=1
cm
=10 -2m
Scalars and VectorsSimple numbers:
Speed vTemperature T
Number + direction
Velocity vrelative positions rForce FAcceleration aLibrary
rCam
pusCen
ter
Velocity = speed + direction
r=1.5x1011m
6 months laterspeed = same
different directionv
velocity is a “vector”: a quantity that has both magnitude and direction
Length of the arrow = speedDirection of arrow same asdirection of the motion
Acceleration ( changes in v)
acceleration =change in velocity
elapsed time
a =change in velapsed time
Change in V = 100km/hr
Elapsed time = 3 sec
“This baby goes from 0 to100km/hr in only 3 seconds”
a =change in velapsed time
=100km/hr
3 s = 33 km/hr s
103 m
3600 s=3.6x103s
=33x103m
3.6x103 sxs = 9.1 m/s2
Different ways to change V
v v
Car speeds up
v
Car slows up
vscreech!
a
a
Accelerations (continued)
v
Car turnsv
In all three cases, v changes. Therefore these are all examples of accelerations
a
a & v on a hot wheels track
Free Fall
4.9m
t=0 v0=0
t=1s v1=?
vavg = disttime
4.9m1 s= = 4.9m/s
vavg = v0 + v1
2
0 + v1
2=
v1
2=
v1 = 2vavg = 9.8 m/s
V1 = 9.8 m/s
Free-fall acceleration
acceleration =change in velocity
elapsed time
a = 9.8m/s1s = 9.8 m/s2
9.8m/s
1s
This is called the “acceleration due to gravity” and given the special symbol:
g=9.8m/s2
In this class g10 m/s2 will be close enough for us.
g
Free fall from greater heights
V0 = 0
t = 0s
V1 = 10m/s
t = 1s
5m
V2 = 20m/s
t = 2s
V3 = 30m/s
t = 3s
V4 = 40m/s
t = 4s
15m
25m
35m
5m
20m
45m
80m
Total distance
12
gt2
Upward tossV4 = 0t = 4s
V3 = 10m/st = 3s5m
V2 = 20m/st = 2s
V1 = 30m/st = 1s
V0 = 40m/st = 0
15m
25m
35m
75m
60m
35m
0m
Total height
80m
gt212
v0t
Simple rule for free fallaka: projectile motion
When Earth’s gravity is the only force involved:
actual height = height for no gravity – ½gt2
Horizontal tosst = 0s
t = 1s
5m
t = 2s t = 3s t = 4s
20m
45m
80m
upward toss
t = 0s
t = 1s
5m
t = 2s
t = 3st = 4s
20m
45m80m
Shoot the monkeycommunistdead whiteEuropean male
Very fast horizontal toss
t = 0s
t = 1sx= 8km
5m
t = 2sx=16km
t = 3sx=24km
20m 45m
V=8km/s
Orbital motion is free fall
Artificial satellite
a = g
v = 8 km/s
Turning car
An object free to slide on the dashboard,tries to follow a straight line path
Newton’s 3 laws of motion
Isaac Newton 1642 --- 1727
Alexander Pope:
Nature and nature’s laws lay hid in the night
God said, “Let Newton be,” and all was light.
1st Law: Law of Inertia
A body at rest tends to stay at rest, a body in motion tends to keep moving along at a constant speed and in a straight-line path unless interfered with by some external forces.
example
Motorcycle crash dummy
Another example(watch the ladder)
2nd Law: F=ma
The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.The direction of the acceleration is in the direction of the applied force.
Directly proportional to Force
a
Small forceSmall acceleration
a
Large forceLarge acceleration
inversely proportional to mass
aa
Large massSmall acceleration
small mass
Large acceleration
Bowling ball
Beachball
“Inertial” mass
“Inertial” mass, mi, is the resistance
to changes in the state of motion
Objects with large
mi are hard to get
moving (& once started, hard
to stop),
Objects with small mi
easier to get moving
(& easier to stop),
Units again! (we cant avoid them!)
Mass: basic unit = 1kilogram = 1kg mass of 1 liter (1.1 quarts) of water
This muchwater!
10cm
10cm
10cm
Net forceTip-to-tail method for adding vector
Slide tail of one to tip of the other (keep directions
fixed)
Net force is the vector from the tail of the 1st to the tip of the
2nd. (0 in this case).
Tip-to-tail method
Slide tail of one to tip of the other (keep directions
fixed)
Net force points down the hill
Newton’s 2nd law F=ma
a F
a 1/m
a is proportional to F:
direction of a = direction of F: a F
a is inversely proportional to m:
a F/mcombine:
set proportionalityconstant = 1: a = F/m
multiply both sides
by m
Weight = Force of gravity
a = g
M
Bowling ballm
Beachball
a = gF1 = ma F2 = Ma
Free-fall acceleration of a beach ball& a bowling ball are the same: a=g
Bowling ball has more inertia: M > m
Force of gravity must be larger on the bowling ball
by a factor that is proportional to mass
Weight is proportional to mass
Newton’s 2nd law: F=ma
If gravity is the only force: F = W a = g
W = mgweight
“gravitational”mass
accelerationdue to gravity
Two different aspects of mass
Weight: W = m
g
Force of gravity is proportional to “gravitational”
mass
a =
F
m
Inertia; resistance to changes in
state is proportional to “inertial” mass
mi
mg
gNewton’s 2nd law:
Experiment shows: mg =
mi
Units of Force
F=ma
kgms2
Unit of force: 1 Newton = 1N = 1 kg m/s2
1 pound =1lb = 4.5 N
What is your mass?Weight = force of Earth’s gravity on you
W=mg
W
a=g
F=ma
m=Wg
Suppose I
jump offa tqble
Mass & weight!!!!!
Convert to Newtons:
W = 85 kg x 9.8m/s2 = 833 N
kg m/s2Units of N=
Kgf =“kilogram force” = 9.8 N
“weight” =
85 kg
kg is a unit of mass, not force
“my weight”
Newton’3rd Law: action-reaction
Whenever one object exerts a force on a second object, the second object exerts an equal in magnitude but opposite in direction force on the first.
action: I pushon the canoe
reaction: the canoe pushes
me forward
Action Reaction
I push on the bus
F
v= 0
But I accelerate
Newton: The bus exerted an “equal but opposite” force on me.
v
Look again
F
-F
All forces come in pairs!
This force causes meto accelerate backwards
This force tries to accel.the bus forward
Air-filled balloon
action: balloonpushes on air
reaction: airpushes on balloon
recoilaction: gun exertsforce F2 on bullet
making it accelerate
reaction: equal butopposite force on the gun F1
Produces a recoil
Rocket propulsion
action: rocket enginepushes exhaust
gasses out the rear
reaction: rocketgets pushed
in the oppositedirection