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Mechanics Road Map

Kinematics

How things move

Classical Mechanics

Dynamics

Mechanics

Why things move

Quantum Mechanics

What the *#&! Is going on with those electrons!!!

Infant stage

Wave vs particle

Quantum tunnelling

Schrödinger's cat

Introduction to Forces

Forces cause things to move.

Forces can push or pull

Forces do not need contact in order to exist.

The unit for force is a Newton ( N ) and can be thought of as the amount of force that is needed to accelerate 1 kg of mass at 1 m/s2

Fundamental Forces

All forces can be derived from a single, or combination of what are known as the four fundamental forces.

From strongest to weakest they are:

Strong Nuclear

Holds atomic nuclei together

Strong Electromagnetic

Holds electrons within an atom

Weak Nuclear & Electromagnetic

Contact forces such as touch, or non-contact forces such as a magnet.

Gravity

Causes objects to fall

“DO NOT COPY TABLE”

(Table can be found on pg 128 of text)

Forces can change an object’s inertia.

Inertia: Inertia is the natural tendency of an object to remain in its current state of motion. The amount of an object’s inertia is directly related to its mass.

Mass: The quantity of matter an object contains.

(A.K.A. The amount of stuff in an object)

Gravitational influence: the property of matter that determines the strength of the gravitational force. This is what causes weight to exist and will be discussed in grater detail in grade 12.

“DO NOT COPY TABLE”

(Table can be found on pg 127 of text)

Units of Measurement

“DO NOT COPY TABLE”

Length

Foot

Meter

Mile

Kilometre

Speed

Mile per Hour

Kilometre per Hour

Volume

Gallon

Litre

Temperature

Fahrenheit

Celsius

Weight

Pound

Newton

Force

Pound

Newton

Mass

Slug

Kilogram

Mass vs Weight

Despite common misconception Mass and weight are two totally different quantities.

Mass is the amount of stuff in an object

Weight is the gravitational force exerted on an object by Earth’s (or any other planets) gravitational field, and can be found with the following formula. Where g, on Earth at sea level is always equal to -9.8 m/s2

Example

Try calculating your own weight, in Newton’s, keeping in mind that mass is measured in kilograms not pounds. However here on Earth at sea level 1 kg of mass has 2.2 lbs of weight.

Example

Find the weight of a 2.26 kg bag of sugar.

The value of g is –9.81 m/s2 “on earth, at sea level”, but what about when your not at sea level or, not even on earth for that matter?

As it turns out the farther away from the center of the earth, you are, the smaller the value of g.

For example g would be smaller on top of a mountain and bigger at the bottom of the deepest ocean.

“DO NOT COPY TABLE”

(Table can be found on pg 132 of text)

Likewise the value of (g) on other planets is different as well, this concept will be looked at in depth in grade 12.

The two main quantities involved, are the mass and radius of the planet.

Example:

Calculate the weight of a 4 kg spherical chicken on the surface of the moon.

Example:

If Mr. Harper has a weight of 1256 N, on earth, find his mass. What would his mass and weight be on the moon?

Mass and Weight Facts

Mass is an exception to the rule for base units, the base unit for mass is kilograms (kg) not grams (g)

In this course weight will always be measured in Newton’s

Weight is always directed radially downwards towards the center of the earth

Weight has both magnitude and direction therefor it is a vector

Weight is always present even during free-fall

Weight will change slightly with altitude

Weight is different on each planet

DO

Pg 137 #’s 1 – 4 (pdf 23)

Friction

Friction is the force that opposes the motion between two surfaces that are in contact.

(Makes things hard to move)

On the microscopic scale all surfaces are rough.

When two surfaces are in contact with each other the high points on one surface temporarily bond or lock with the high points of the other surface.

There are two types of friction.

Static friction is when there is no relative motion between the two objects.

“Such as a square pig sitting motionless on the floor.”

Kinetic (sliding) friction is when there is relative motion between the two objects.

“Such as when you manage to start to push that same square pig across the floor.”

**Kinetic friction is “always” a lesser value then static friction.**

Friction depends on two things

1. The nature of the surfaces in contact, every different pair of surfaces will act differently with respect to friction.

Every surface has a different amount of “grippeness”. This grippeness can be measured, and then for every pair of surfaces an associated value is given.

This grippeness value is called the coefficient of friction.

The symbol for the coefficient of friction is Mu (μ), which can only be determined experimentally.

“DO NOT COPY TABLE”

(Table can be found on pg 140 of text)

Note how the grippy surfaces have higher coefficients of friction that the slippery surfaces.

The second thing that the force of friction depends on is:

2. The magnitude of the force pushing the two surfaces together. This force is called the normal force (fn) and for simple cases where an object lying on a level surface, it is equal to the weight of that object.

Normal Force

Many people seem to struggle with the concept of “normal force” perhaps it is because the normal force is not an obvious force, take for example the following

A 2 kg book is sitting on a shelf.

If the only force acting on the book is that of weight, then the book should fall down because there is no other force present to counter act that of gravity.

If there is only weight present then an object will always fall

If the object is not falling then there must be a second force balancing the weight.

This second force is known as the “normal force”, and in the case of an object sitting on a surface it is always directly opposite the weight..

The normal force is always perpendicular to the surfaces in contact. This is the origin of its name “normal force” it is normal to the surface.

The normal force is not always equal to the weight of an object; it is the force pressing the surfaces together.

In this case the normal force is equal to the applied force from the hand, which is pushing the surfaces together.

The force of friction depends on both the coefficient of friction and the normal force. It can be found using the following formula

Using Normal Force to Calculate Friction

Find the force of friction in between Calvin’s toboggan and the snow if the coefficient of friction between wood and snow is 0.30, and the normal force for the toboggan is 400 N.

ff = 120 N in the opposite direction

Example:

In the winter, people will often place square pigs in the back of their trucks to increase the amount of friction between the tires and the road. Find the increase in the frictional force that would result by placing a 200 kg square pig in the back of a truck.

1400 N

Example:

A horizontal force of 85 N is required to pull Mr. Harper on a sled at constant speed over dry snow to overcome the force of friction. If Mr. Harper and the sled have a combined mass of 52 kg. Calculate the coefficient of kinetic friction between the sled and the snow.

μ = 0.17

Example

A smooth wood block is placed on a smooth wooden tabletop. You find that you must exert a force of 14.0 N to keep the 40.0 N block moving at a constant velocity.

- a) what is the coefficient of sliding friction for the block and table?

μ = 0.350

b) if a 20.0 N brick is placed on the block, what force would be required to keep the block and brick moving at a constant velocity?

fa = 21.0 N

Free Body Diagrams

FBD’s are often used to summarize all the forces acting on an object

Net Force

We often have questions dealing with more than one force at the same time. To deal with this we need to define what is meant by net force.

The net force (F) is simply all of the forces added together, keeping in mind at forces are vectors and they have associated directions.

For example, if a force was applied in the negative direction it would have a negative (-) sign.

Upper case (F) is used to denote Net force from all other forces which are always lower case (f).

Example:

Three people are pushing on a square pig. The first pushes to the right with force of 40 N, the second pushes to the left with a force of 75 N, the third also pushes to the left with a force of 15 N. If the pig has a mass of 25 kg, find the net force acting on the pig.

Example:

Mr. Harper is trying to lift is pet pig Peter in to the back of his truck in an attempt to increase the amount of friction between the truck tires and the road. He very quickly realizes that he is to much of a wimp to be able to do it by him self so he recruits some of his physics students to give him a lift. If Mr. Harper is able to lift 529 N and Mark can lift 641 N and Sally can lift 734 N:

a) Draw a FBD of the forces involved.

b) What is Peter’s mass?

194 kg

DO

Dynamics Extra Pr Work Sheet

Friction lab

**Extra problems if students want to do.**

End of chapter Review Pg 149 -151

#’s 1 - 35

Omit #’s 3, 7, 10, 13, 18, 20, 21, 25, 29,

Newton’s three laws of motion

Newton’s first law of motion: an object at rest or in uniform motion will remain at rest or in uniform motion unless acted on by an external force.

(AKA) an object at rest stays at rest

Remember the table cloth demo?

Here Newton is simply restating the definition of inertia from Chapter 4.

Newton’s second law of motion:

The acceleration of the body is directly proportional to the net force on it and inversely proportional to its mass.

(AKA) F = ma

Newton’s third law of motion:

When one object exerts a force on second object, the second exerts a force on the first that is equal in magnitude but opposite in direction.

(AKA) action/reaction forces

Example:

A 2.0 x102 g spherical Chicken is accelerated upwards at 2.3 m/s2. What is the value of the applied force?

2.4 N

DO

Practice Problems Pg 163 #’s 1-3

Example:

An artillery shell has a mass of 55 kg. The shell is fired from a gun, leaving the barrel with a velocity of 770 m/s. The gun barrel is 1.5 m long. Assume that the force, and thus the acceleration, of the shell is constant while the shell is in the gun barrel. What is the force on the shell while it is in the gun barrel?

f = 1.1 x 107 N

Example:

A TV produces light when fast-moving electrons collide with phosphor molecules on the surface of the screen. Electrons of mass 9.1 x 10-31 kg are accelerated from rest in the electron “gun” at the back of the vacuum tube. Find the velocity of the electron when it exits the gun after experiencing an electric force of 5.8 x 10-15 N over a distance of 3.5 mm.

6.7 x 106 m/s

Example:

A curler exerts an average force of 9.50 N on 20.0 kg stone. ( Assume that the ice is frictionless.) The stone started from rest and was in contact with the girl’s hand for 1.86 seconds.

a) Determine the average acceleration of the stone.

0.475 m/s2

b) Determine the velocity of the stone when the curler released it.

0.884 m/s

DO

Practice Problems, Pg 168 #’s 4-8

Practice Problems, Pg 170 #’s 9,10

Section Review, Pg 176 #’s 1-7 omit # 5

Example:

A 55 kg person is standing on a scale in an elevator. If the scale is calibrating newtons, what is the reading on the scale when the elevator is not moving? If the elevator begins to accelerate upwards at 0.75m/s2, what will be the reading on the scale?

540 N & 580 N

Example:

A spherical pig in a square chicken are riding in a vacuum sealed elevator. The combined mass of the elevator and its occupants is 700 kg. Calculate the magnitude and direction of the elevators acceleration if the tension in the supporting cable is 7500 N.

0.904 m/s2

Example:

A spring scale hangs from the ceiling of an elevator. It supports a package that weighs 25 N.

a) what upward force does the scale exert when the elevator is not moving ?

25 N up

b) what force most the scale exert when the elevator and object accelerate upward at 1.5 m/s2?

29 N up

DO

Practice Problems Pg 186 #’s 21 - 23

Section Review Pg 194 #’s 1-7 omit # 4

**Extra problems if students want to do.**

End of Chapter Review

Pg 206 #’s 1, 2, 3, 5, 6, 10, 16, 23, 28, 29, 30, 32

(note: No Momentum Questions)

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