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LINEAR KINETICS (Part 1) Readings: McGinnis Chapters 1 and 3

FORCE:

Definitions... • effect of one body on another • a push or pull applied to an object • that needed to change the state of motion

(i.e., velocity) of an object (i.e., that which causes acceleration)

Remember...

CAUSE → EFFECT FORCE → ACCELERATION

Characteristics of force: • Force is a vector quantity

Magnitude and direction • A third, unique, characteristic:

Point of application (especially important relative to torque)

Thus, to completely understand influence of a net force, we must have knowledge of all three characteristics.

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INERTIA: Natural property of a body to resist a changes

in its state of motion (i.e., state of motion defined by velocity, ∆ state of motion = ______________).

MASS: Quantity of matter of which a body is

composed Mass...

direct measure of a body’s resistance to change in _______ motion (i.e., an object’s inertia w.r.t. (with respect to) linear motion).

e.g., more difficult to change the motion of a large object (i.e., large mass) than a small object

large mass (e.g., shot) vs. small mass (e.g., tennis ball)—it takes more effort (i.e., _____) to produce a given change in motion (i.e., ___________) for the larger mass

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NEWTON'S 1ST LAW OF MOTION:

A special case of Newton's 2nd Law... essentially a statement of the principle of inertia:

In the absence of a net force (i.e., ΣF = 0)... the state of motion of an object (i.e., velocity) will not change.

i.e., A stationary object will remain motionless and a body in motion will continue to move in a straight line with the same speed...

IF the NET force acting on it is zero.

Examples?

Body at rest will stay at rest... Body in motion will continue to move with

the same speed in the same direction...

unless ...

a net force acts on body.

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i.e., to speed up or slow down an object’s motion, and/or to change an object’s direction of motion (acceleration), an object’s inertia must be “overcome.”

Examples of Inertia

1. Bag of groceries on car seat. Slam on

brakes of car.

What happens? Objects (groceries, passengers, car, etc.) retain their state of motion unless a net force acts of them.

Forces acting on the car?

...on the body?

2. Standing in the back of a pickup truck that

takes an unexpected turn. What happens?

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Forces acting on the body?

...on the truck?

Relate to the centripetal/centrifugal force controversy...

Let’s tie the concepts of inertia, mass, force, and acceleration together... NEWTON'S 2ND LAW OF MOTION: Sum of all mass or acceleration forces acting object’s inertia on object... (i.e., net force)

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A quantitative example... What average force must a baseball catcher apply to an 80 mph (35.8 m/s) pitch in order to stop it?

What do we need to know? What forces are involved?

Ball mass? 4.5 ounce weight = 0.13 kg mass

“Impact” time?

Ball acceleration? vf = vi = ∆t =

a =

ΣF = ma =

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Consider... Meaning of negative force? Average vs. instantaneous force? The effect of ∆t on F?

Some important interpretations of ΣF = ma:

• Cause (ΣF) and effect (a) relationship

probably the most important concept in this class!

• a directly proportional to ΣF

(bigger F produces greater a... i.e., more rapid change in velocity)

• a is in the same direction as ΣF

• To produce a given a, it takes a larger ΣF

for a larger object (i.e., higher mass requires higher force for the same effect)

NEWTON'S 3RD LAW OF MOTION

Action-Reaction...describes how objects interact with one another:

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If one body exerts a force on a second body, the second exerts back on the first a force of equal magnitude but opposite in direction.

e.g., impact between a tennis ball and racquet: Is this an action-reaction pair?

A confusing principle to many:

1. Where you find force, you will always find two interacting bodies or objects. According to action-reaction, there is never just a single force but always a pair of forces.

impact

ball

racquet face

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2. If action and reaction forces are of equal

magnitude but opposite in direction, do they cancel each other (i.e., result in ΣF = 0)?

___!! They _______ cancel each other.

Action and reaction forces affect the motion of different bodies. They influence the acceleration of different objects.

e.g., Tennis ball and racquet.

Action force applied to the ball by the racquet accelerates ball. Reaction force applied to racquet by the ball accelerates the racquet.

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3. The label “action-reaction” tends to suggest

that the action and reaction forces do NOT occur simultaneously, but rather occur sequentially... Correct?

Example: Bouncing on a trampoline. Is this an example of action-reaction?

Simultaneous or sequential action-reaction forces?

_________! Action-reaction forces act

____________, not ______________!

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Example: Push-off during running Effect of reaction force (GRF)? Tends to accelerate body CM upward and forward:

Effect of action force (our push against the ground)?

Negligible acceleration of earth. Why?

Earth’s huge mass

GRF

our push againstthe ground

earth

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Let’s see just how big earth’s mass is...

ΣF = ma

5 billion participants gather for World Vertical Jump Games

Typical peak force in VJ

4 BW ≈ 2000 N If all participants jump simultaneously:

ΣF = (5×109)·(2000 N) = __________

earth’s mass (me) = 6×1024 kg

ae = ΣF / me = (1×1013) / (6×1024 kg)

aearth = ____________ m/s2 ... ______!

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NEWTON’S LAW OF GRAVITATION

A fundamental physical principle that describes the concept of gravity...

Any two particles of matter (any bodies or objects) attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance separating them (i.e., distance between their centers): G = gravitational constant = 6.7×10-11 N·m2/kg2

e.g., Like it or not, there is a force of attraction

between you and the person sitting next to you.

However, this force is so small that you don’t notice it.

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When one of the objects is the earth (with its huge mass), the force of attraction (i.e., gravity) is very significant.

e.g., students sitting 1.5 m apart

e.g., attraction between earth and student

r)m m(G = F 2

21g

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WEIGHT:

An object’s weight represents the force of attraction between the earth and the object

Question: Is earth’s gravitational attraction (i.e., force) the same for all objects on or near the surface of the earth?

____...

this force is dependent on the mass of the earth AND the mass of the object close to the earth.

Simplified relationship for the link between weight and mass on earth:

r)m m(G = F 2

21g

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where ag = g (i.e., acceleration due to gravity, 9.8 m/s2) is equivalent to:

PRESSURE

Force applied to an object is rarely applied at a single point, usually distributed over an area:

“force per unit of area”

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Consider: Lying down vs. standing Force? Pressure?

What changes; what stays the same?

Other Examples...

Atmospheric pressure Rock in shoe

Pressure: an important factor related to injury

protection

e.g., impact situations:

Advantageous to spread force over as large an area of contact as possible

Protective equipment: helmets, boxing gloves, protective padding

Landing techniques: parachuting, high jumping, pole vaulting

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Example problem: Which situation would exert more pressure on your stomach (1) a woman in high heels standing on one foot on your stomach, or (2) an elephant standing on your stomach?

What do you need to know?

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MOMENTUM – “_______________” Any object in motion has _____ and a

quantifiable ________.

units of measurement: ________ Momentum: especially useful in collisions...

Collision outcome directly related to momentum of the colliding bodies just before impact.

The greater the momentum of a body (not just mass and not just velocity), the bigger the effect it will have on other objects it collides with.

e.g., auto collision

two football players

tennis racquet and ball

head or foot and soccer ball

boxing glove and boxer’s head

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In impact/collision situations in sport, we often want to manipulate the momentum of at least one of the colliding objects to produce some desired outcome of the collision:

e.g., baseball: home run vs. bunt

Link to kinetics...

One way to describe the effect of a net force is by the ____________ of momentum produced by the force (an alternative way of expressing Newton’s 2nd law):

Time is a critical factor in this relationship... one final rearrangement:

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IMPULSE Product of average net force and the time over which it is applied.

One interpretation of the equation...

We can produce the same change in momentum with many combinations of force and time...

large force over a ______ time small force over a ______ time

GRF

time

1 BW

0

Squat down NetForce

Vert.

mv = vm - mv = t F if ∆∆

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“Spreading an impact out over time”

e.g., catching an egg

landing from a vertical jump (refer to “impact plots” from lab)

function of a bike helmet INERTIA/MOMENTUM vs. FORCE

A common misconception is that a moving body possesses force.

You cannot possess ______; rather you can only apply force to others. What you do possess is _______ and (if you are moving) __________.

The rate at which your momentum changes equals the resultant force applied to you from the outside.

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In other words, since acceleration (__) is the rate of change of velocity (__), (resultant) force (___) is the rate of change of momentum (___).

If there is no _____________, then there is no change in ____________

IMPACTS AND THE PRINCIPLE OF CONSERVATION OF MOMENTUM

When two bodies collide with each other, we can treat the two bodies as a ________ and examine their total momentum.

Newton’s First Law can be restated to predict what will happen to the “system:”

In the absence of _______ forces acting on a system, the total momentum of the system remains constant (in both ________ and _________ ).

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Example #1: A 100 kg running back carries the ball forward with a speed of 9 m/s. He is hit head on in the air at the goal line by a 130 kg defensive back running in the opposite direction at 7 m/s. Who has more momentum? Which direction will the combined bodies move after impact?

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Example #2: Two ice skaters collide on the ice. A man (mass 75 kg) moving forward at a speed of 7 m/s runs into a stationary woman (mass 55 kg). If they cling to each other to keep from falling down, how fast and in which direction do they move as a unit (assuming “frictionless” ice)?