2. speed
speed = v =
distance traveled
elapsed time
50km
v =
50km
1 hr
= 50km/hr
Hawaii Kai Haleiwa
In one hour
This is the average
speed over 1 hour.
For shorter time
intervals it can be
higher or lower.
4. Earth’s motion around the Sun
r=1.5x1011m
V =
distance
elapsed time =
2 p r 2 x 3.14 x 1.5 x 1011m
365 days x 24 hr/day
=
1year
=
9.4 x 1011 m
8760 hr
=
9.4 x 1011 m
8.76 x103 hr
= 1.1x108 m/hr = 1.1x105 km/hr 110,000 km/hr
9.4
8.7
= x 1011-3 m/hr
5. Tip of a watch’s minute hand (HW!!)
V =
distance
elapsed time =
2 p r 2 x 3.14 x 1cm
60 min x 60 s/min
=
1hr
=
6.28 cm
3600 s
=
6.28 cm
3. 6 x103s
= 1.7x10-3 cm/s
= 1.7x10-5 m/s
6. Scalars and Vectors
Simple numbers:
Speed v
Temperature T
Number + direction
Velocity v
relative positions r
Force F
Acceleration a
Library
r
7. Velocity = speed + direction
r=1.5x1011m
v
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
8. Acceleration ( changes in v)
acceleration =
change in velocity
elapsed time
a =
change in v
elapsed time
9. Change in V = 100km/hr
Elapsed time = 3 sec
“This baby goes from 0 to
100km/hr in only 3 seconds”
a =
change in v
elapsed time
=
100km/hr
3 s
= 33 km/hr s
103 m
3600 s
=3.6x103s
=
33x103m
3.6x103 sxs = 9.1 m/s2
14. 4.9m
t=0 v0=0
t=1s v1=?
vavg = dist
time
4.9m
1 s
= = 4.9m/s
vavg =v0 + v1
2
0 + v1
2
= v1
2
=
v1 = 2vavg = 9.8 m/s
V1 = 9.8 m/s
15. Free-fall acceleration
acceleration =
change in velocity
elapsed time
a =
9.8m/s
1s
= 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
16. 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
1
2
gt2
17. Upward toss
V4 = 0
t = 4s
V3 = 10m/s
t = 3s
5m
V2 = 20m/s
t = 2s
V1 = 30m/s
t = 1s
V0 = 40m/s
t = 0
15m
25m
35m
75m
60m
35m
0m
Total
height
80m
gt2
1
2
v0t -
18. Simple rule for free fall
aka: projectile motion
When Earth’s gravity is the only force
involved:
actual height = height for no gravity – ½gt2
27. Alexander Pope:
Nature and nature’s laws lay hid in the night
God said, “Let Newton be,” and all was light.
28. 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.
32. 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.
34. inversely proportional to mass
a
a
Large mass
Small acceleration
small mass
Large acceleration
Bowling
ball
Beach
ball
35. “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),
36. Units again! (we cant avoid them!)
Mass: basic unit = 1kilogram = 1kg
mass of 1 liter (1.1 quarts) of water
This much
water!
10cm
10cm
10cm
37. Net force
Tip-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).
39. 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/m
combine:
set proportionality
constant = 1: a = F/m
multiply
both sides
by m
40. Weight = Force of gravity
a = g
M
Bowling
ball
m
Beach
ball
a = g
F1 = 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
41. Weight is proportional to mass
Newton’s 2nd law: F=ma
If gravity is the only force: F = W
a = g
W = mg
weight
“gravitational”
mass
acceleration
due to gravity
42. 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
mgg
Newton’s 2nd law:
Experiment
shows: mg = mi
44. What is your mass?
Weight = force of
Earth’s gravity on you
W=mg
W
a=g
F=ma
m=
W
g
Suppose I
jump off
a tqble
45. Mass & weight
!!!!!
Convert to Newtons:
W = 85 kg x 9.8m/s2 = 833 N
kg m/s2
Units of N =
Kgf =“kilogram force” = 9.8 N
kg is a unit of mass, not force
46. 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
