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Newton & Biomechanics

Related to Chapters 3 and 1 in the text

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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?

CBADirection of stumble

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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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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

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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.

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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 forceb) Carl didn’t want it bad enoughc) Carl succumbed to a greater

acceleration because of his reduced mass (inertia)

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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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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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Newton’s Law of Universal Gravitation

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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

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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

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.

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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.

F = G m1m2 r2

1.

g = G m2 = 9.81 m/s/s r2

3.

F = m1 * G m2 r2

2.4.

F = m1g = mg = W

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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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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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Bob Beamon at the Mexico

City Olympics in 1968

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?

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Bob Beamon at the Mexico

City Olympics