Download Kinematic Graphs

Newton & Biomechanics
Related to Chapters 3 and 1 in
the text
5/22/2017
Dr. Sasho MacKenzie - HK 376
1
Where does the bottle go?
• A disorderly HK student leaves the Inn and is
walking towards The Pub holding a bottle. In
an attempt to heckle a stop sign for looking
stupid, the bottle slips from his hand. What
path would it follow to its tragic end?
A
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B
Direction of stumble
C
Dr. Sasho MacKenzie - HK 376
2
Newton’s First Law of
Motion
• An object continues to stay at rest or move
in a straight line until an external force
acts on it.
• After release, the bottle continues to move
with the same horizontal velocity as the
student, but without the force of the hand
balancing out the force of gravity, it also
accelerates vertically to the ground.
• Thus following a curved path with
independent horizontal and vertical
velocities.
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Dr. Sasho MacKenzie - HK 376
3
When does the ball have the
greatest speed?
•
During a golf drive, does a golf ball
have the most speed
a) Halfway between when it was
struck and its peak height.
b) About 10 to 20 meters after it has
been struck.
c) The instant it loses contact with the
clubface
5/22/2017
Dr. Sasho MacKenzie - HK 376
4
Newton’s Second Law of
Motion
• The acceleration of an object is proportional
to the net force acting on it. The
acceleration is also in the same direction as
the force.
• F = ma
• The golf ball will accelerate and thus gain
speed until the instant it leaves the clubface.
Air resistance then becomes the dominant
force, and the ball accelerates negatively.
5/22/2017
Dr. Sasho MacKenzie - HK 376
5
Carl (170 lbs) vs. The Bus (50,000 Lbs)
•
Carl decides to take his chances
by crossing the street in front of a
bus. Carl eats pavement because
a) The bus hit Carl with more force
b) Carl didn’t want it bad enough
c) Carl succumbed to a greater
acceleration because of his
reduced mass (inertia)
5/22/2017
Dr. Sasho MacKenzie - HK 376
6
Newton’s Third Law of
Motion
• For every force, there is an equal and
opposite force.
• Carl and The Bus impart equal but opposite
forces on each other.
• Carl eats pavement because he undergoes
a greater acceleration due to his smaller
inertia.
• a = F
m
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Dr. Sasho MacKenzie - HK 376
7
Clean and Jerk…example question
• What force is required to lift a
100 kg weight off of the ground
with an acceleration of 5 m/s/s?
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Dr. Sasho MacKenzie - HK 376
8
Newton’s Law of Universal
Gravitation
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Dr. Sasho MacKenzie - HK 376
9
What is gravity
• It is a force
• The force of attraction between two objects
• The force of gravity produces an
acceleration of about 9.81 m/s/s on all
objects in free fall “near” the earth’s
surface (if air resistance was neglected).
• This force is directed towards the center of
the earth and therefore so is the
acceleration
5/22/2017
Dr. Sasho MacKenzie - HK 376
10
Newton’s Law of Universal
Gravitation
1. All objects attract each other with a force
that is inversely proportional to the square
of the distance between them.
2. This force is proportional to the mass of
the two bodies under consideration.
F = G m1m2
r2
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F is the force of gravity, G is the
gravitational constant, m1 and m2 are object
masses, and r is the distance between the
centers of mass of the objects.
Dr. Sasho MacKenzie - HK 376
11
Gravitational Force = Weight
• The earth’s gravitational force acting
on an object, is the object’s weight.
For an object close to the earth’s surface, the variables
G, m2, and r become constant so we can replace them
in the equation with, g, which is equal to 9.81 m/s/s.
1.
F = G m1m2
r2
2.
F = m1 * G
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m2
r2
3.
4.
g = G
m2
r2
= 9.81 m/s/s
F = m1g = mg = W
Dr. Sasho MacKenzie - HK 376
12
Earth Parameters
• Mass = 5.9763 x 1024 kg =
– 6,000,000,000,000,000,000,000,000 kg
•
•
•
•
Radius at Equator = 6378.245 km
Average Radius = 6370.949 km
Radius at Pole = 6356.775 km
Angular Velocity = 360/24 hrs =
0.0042/s = 0.00007 rad/s
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Dr. Sasho MacKenzie - HK 376
13
Gravity related question
• Relative to a stationary point in space
what is our linear velocity due to the
earth’s rotation if we are sitting at the
equator?
• What about at the North Pole?
• Where is the traveler?
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Dr. Sasho MacKenzie - HK 376
14
Bob
Beamon
at the
Mexico
City
Olympics
in 1968
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Beamon's world record (8.90 m;
29 ft. 2½ in.) stood for 23 years,
and was named by Sports
Illustrated magazine as one of the
five greatest sports moments of
the 20th century. Beamon’s world
record was finally broken in 1991
when Mike Powell jumped 8.95 m
(29 ft. 4-3/8 in.) at the World
Championships in Tokyo, but
Beamon's jump is still the Olympic
record and 40 years later remains
the second longest of all time.
At an altitude of 2240 m (7349 ft), Mexico
City's air had less resistance than air would
have at sea level. What about gravity?
Dr. Sasho MacKenzie - HK 376
15
Bob
Beamon at
the Mexico
City
Olympics
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Dr. Sasho MacKenzie - HK 376
16