Sem 2 2014 EDUH 1017 Sports Mechanics L7 1

EDUH 1017Sports Mechanics

Lecture 7Force

Sem 2 2014 EDUH 1017 Sports Mechanics L7

Reminder

• Assignment 1 due in on Friday

• Report instructions have been issued.• Proposal (1 page max) is due on

September 5• Report (1500 words) is due on October

10

2

Sem 2 2014 EDUH 1017 Sports Mechanics L7 3

More on vectors

From last time:• Vectors can be added tip-to-tail

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More on vectors : “Breaking vectors apart”

• Any vector can be broken into two perpendicular components.

• e.g. the vector A can be broken into two components Ax and Ay

• Together the components are equivalent in every way to the original vector – and can be added together again to make the original vector.

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• What is the magnitude (size) of these components?

(where |A| denotes the magnitude of the vector A, etc.)• Multiplying both sides of these equations by |A| yields

sinθ =side oppositeθhypotenuse

=Ay

A

cosθ =side adjacent θhypotenuse

=Ax

A

Ax = Ax = A cosθ and Ay = Ay = A sinθ

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Examples (Hecht Example 2.9 and 2.12)

• A firefighter dashes up a 26 m long ladder, making an angle of 60 degrees with the ground.

• What is the vertical displacement of her feet at the top? • What is the horizontal displacement of her feet at the

top?

• An aircraft in a 45 degree dive is travelling at a constant 800 km/h. Determine its speed in m/s in the vertical direction – i.e. the rate at which the plane is losing altitude.

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Newton’s First Law….

• What makes a person or object accelerate?• It is perhaps contrary to usual experience, but the normal

state of motion is to keep doing what you have been doing• Moving objects tend to keep moving• Stationary objects tend to stay stationary

• This is Newton’s First Law – the “Law of Inertia”“Every body continues in a state of rest or motion in a straight line unless it is compelled to change its motion by external forces exerted upon it.”

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…doesn’t work????

• What we really observe in everyday life is that moving objects tend to slow down and eventually stop. Why?

• Why does a car stop if you take the foot off the accelerator?

• How do I keep a moving object moving?

Forces!

• Newton’s first law does work, but there are usually frictional forces opposing the motion.

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What is Force?

• What is a force?• Naively, perhaps a push or a pull

• What we really see is the effect of a force – e.g. deforming a tennis ball when hit by a racquet

• “Force is an agent of change’• “Force is that which alters motion”

• Force defies a really satisfactory definition“If you insist on a precise definition of force, you will never get it” RICHARD FEYNMANN (Nobel Laureate)

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Force is a vector

• The unit of force is the Newton (N) = kg.m/s2

• Several forces acting at one point on an object act add up and as a single force – force is a vector

• There are 5 horizontal forces in the tug-of-war – the man on the left experiences one large force although there are 4 individual forces

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Examples (Hecht Example 4.1)

• Determine the resultant (i.e. net force) exerted on the stationary elephant by the two clowns. What is the magnitude and direction of the force?

300 N

400 N

θ

EDUH 1017 Sports Mechanics L9Sem 2, 2014

Types of forces

There are two types of forces:• long-range forces – gravity• All other forces are contact forces – pushes or pulls,

friction.We will be talking about identifying forces in lecture 9.

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Gravity as a Force

• Perhaps the most obvious force is gravity – which produces the acceleration due to gravity (g = 9.8m/s2)

• The gravitational force is directed downward – toward the centre of the Earth

• The force of gravity between any two objects is proportional to their masses and inversely proportional to the square of the distance between them

• Is there gravity in space?

Fgravity = GMearth mr2

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Weight – Gravitational Force

• Weight is the downward gravitational force experienced by an object. The weight force is related to the acceleration due to gravity (g = 9.8 m/s2)

• We might say a person’s “weight” is 50 kg. We should say her mass is 50 kg and her weight is 50 kg x 9.8 m/s2 = 490 N

Fgravitation = mg

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Summary

• Force alters motion…but how are force and acceleration related?

• NEXT: Newton’s other laws