Speed, velocity,
acceleration & Newton
Micro-World Macro-World
Lecture 2
speed
distance traveled
speed = v =
elapsed time
Hawaii Kai Haleiwa
In one hour
50km
v = 1 hr = 50km/hr
50km
This is the average
speed over 1 hour.
For shorter time
intervals it can be
higher or lower.
instantaneous speed
Speed determined for very short time intervals
vistantaneous
distance traveled
=
“very short” time
Instantaneous
speed = 0 here
& here
km
km
km
Earth’s motion around the Sun
r=1.5x1011m
V =
distance
elapsed time =
1011
9.4 x
m
=
8760 hr
= 1.1x108 m/hr
=
2pr
1year
11m
2
x
3.14
x
1.5
x
10
=
365 days x 24 hr/day
9.4 x 1011 m
8.76 x103 hr
= 1.1x105 km/hr
=
9.4 x 1011-3 m/hr
8.7
 110,000 km/hr
Tip of a watch’s minute hand (HW!!)
V =
=
distance
elapsed time =
6.28 cm
3600 s
=
2pr
1hr
=
6.28 cm
3. 6 x103s
= 1.7x10-5 m/s
2 x 3.14 x 1cm
60 min x 60 s/min
= 1.7x10-3 cm/s
Scalars and Vectors
Simple numbers:
Number + direction
Speed v
Temperature T
Velocity v
relative positions r
Force F
Acceleration a
Library
r
Velocity = speed + direction
v
r=1.5x1011m
velocity is a “vector”:
a quantity that has both
magnitude and direction
Length of the arrow = speed
Direction of arrow same as
direction of the motion
Acceleration ( changes in v)
change in velocity
acceleration =
elapsed time
a =
change in v
elapsed time
Change in V = 100km/hr
Elapsed time = 3 sec
a=
change in v
elapsed time
103 m
=
100km/hr
= 33 km/hr s
3s
3600 s
=3.6x103s
=
33x103m
2
=
9.1
m/s
3
3.6x10 sxs
“This baby goes from 0 to
100km/hr in only 3 seconds”
Different ways to change V
v
v
Car speeds up
v
Car slows up
a
v
a
Accelerations (continued)
v
a
In all three cases, v changes.
Therefore these are all examples of accelerations
a & v on a hot wheels track
Free Fall
t=0
4.9m
v0=0
4.9m
dist
vavg =
= 1 s = 4.9m/s
time
0
+
v
v
+
v
1 = v1
1 =
vavg = 0
2
2
2
v1 = 2vavg
t=1s
= 9.8 m/s
v1=?
V1 = 9.8 m/s
Free-fall acceleration
9.8m/s
change in velocity
acceleration =
elapsed time
1s
9.8m/s
ga =
1s
= 9.8 m/s2
This is called the “acceleration due to gravity”
and given the special symbol:
g=9.8m/s2
In this class g10 m/s2 will be close enough for us.
Free fall from greater heights
t = 0s
V0 = 0
5m
5m
t = 1s
V1 = 10m/s
Total
distance
15m
20m
t = 2s
V2 = 20m/s
1 gt2
2
25m
t = 3s
45m
V3 = 30m/s
35m
t = 4s
V4 = 40m/s
80m
Upward toss
t = 4s
t = 3s
80m
V4 = 0
V3 = 10m/s
5m
75m
15m
t = 2s
Total
height
V2 = 20m/s
60m
v0t - 1 gt2
25m
V1 = 30m/s
2
35m
t = 1s
35m
t=0
V0 = 40m/s
0m
Simple rule for free fall
aka: projectile motion
When Earth’s gravity is the only force
involved:
actual height = height for no gravity – ½gt2
Horizontal toss
t = 0s
t = 1s
t = 2s
t = 3s
t = 4s
5m
20m
45m
80m
upward toss
t = 3s
t = 2s
20m
t = 0s
t = 1s
5m
45m
t = 4s
80m
Shoot
dead white
communist
the European
monkey
male
Very fast horizontal toss
t = 0s
V=8km/s
t = 1s
x= 8km
5m
t = 2s
x=16km
20m
t = 3s
x=24km
45m
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
a
Small force
Small acceleration
Large force
Large acceleration
inversely proportional to mass
a
a
Beach
ball
Bowling
ball
small mass
Large mass
Large acceleration
Small acceleration
“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
10cm
10cm
This much
water!
10cm
Net force
Tip-to-tail method
for adding vector
Net force
is the vector
from the tail of the 1st to
the tip of the 2nd. (0 in
this case).
Slide tail of one to tip
of the other (keep
directions fixed)
Tip-to-tail method
Net force points
down the hill
Slide tail of one to tip
of the other (keep
directions fixed)
Newton’s 2nd law  F=ma
a is proportional to F:
a  F
direction of a
= direction of F:
a  F
a is inversely
proportional to m:
a  1/m
combine:
set proportionality
constant = 1:
a  F/m
a = F/m
multiply
both sides
by
m
Weight = Force of gravity
Free-fall acceleration of a beach ball
& a bowling ball are the same: a=g
Beach
ball
m
F1 = ma
Bowling
ball
M
a=g
F2 = Ma
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
nd
2
law: F=ma
If gravity is the only force: F = W
a=g
W = mg
weight
“gravitational”
mass
acceleration
due to gravity
Two different aspects of mass
Weight: W = m
mggg
Newton’s 2nd law:
a =
F
m
m
i
Experiment
shows: mg = mi
Force of gravity is
proportional to
“gravitational” mass
Inertia; resistance
to changes in state
is proportional to
“inertial” mass
Units of Force
F=ma
m
kg 2
s
Unit of force: 1 Newton = 1N = 1 kg m/s2
1 pound =1lb = 4.5 N
What is your mass?
Suppose I
jump off
a tqble
Weight = force of
Earth’s gravity on you
F=ma
a=g
W
W=mg
W
m= g
!!!!!
Mass & weight
kg is a unit of mass, not force
Convert to Newtons:
W = 85 kg x 9.8m/s2 = 833 N
Units of N = kg m/s2
Kgf =“kilogram force” = 9.8 N
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 push
on the canoe
reaction: the
canoe pushes
me forward
Action Reaction
I push on the bus
v= 0
F
But I accelerate
v
Newton:
The bus exerted an “equal but opposite” force on me.
Look again
All forces come in pairs!
-F
F
This force causes me
to accelerate backwards
This force tries to accel.
the bus forward
Air-filled balloon
reaction: air
pushes on balloon
action: balloon
pushes on air
recoil
reaction: equal but
opposite force on the gun F1
Produces a recoil
action: gun exerts
force F2 on bullet
making it accelerate
Rocket propulsion
reaction: rocket
gets pushed
in the opposite
direction
action: rocket engine
pushes exhaust
gasses out the rear