Dynamics

Mechanics is the branch of physics that is concerned with the analysis of the action of forces on matter or material systems.

Dynamics is the branch of mechanics that is concerned with the effects of forces on the motion of a body or system of bodies, especially of forces that do not originate within the system itself.

Why are Forces Important?

• Forces help to describe much of what occurs in our Universe. For example, we know that if we push a box with a certain amount of force, it will move.

• In chemistry, intermolecular and intramolecular forces help describe why different elements react with each other and what happens at the subatomic level.

• A force is defined by a push or a pull one object exerts on another and is measured in units of Newtons (N)

• 1 Newton is defined as the magnitude of force required to accelerate a 1.0 kg mass at a rate of 1.0 m/s2.

• Forces are vector quantities (magnitude and direction). They are denoted as Fx (for example the force of gravity is denoted Fg)

Examples of Forces

• Force of Gravity (Fg)- Direction always toward centre of attracting mass

- Earth attracts us we attract earth

Applied Force (Fa)-Contact action force applied by one object to the other

not really in contact, repulsion of nuclei

Fa

Normal Force (FN)-Perpendicular to and provided by a supporting surface

Once again due to repulsion of nuclei, normal forces can be very small or very large

FN

FN

Frictional Force (Ff)- Direction of frictional force generally opposes motion and is caused by particles of both objects being attracted to each other (intermolecular forces)

Ff (Frictional Force)

V

Other forces include the force of tension, FT, and the force of compression, Fc.

The Four Fundamental Forces

1. Strong Interaction: The strong interaction or strong force is the attractive force that holds protons and neutrons together in a nucleus.

Each of the examples of forces mentioned can be divided into the four fundamental forces of our Universe.

2. Electromagnetic force: The force that exists between charged particles (repulsion or attraction). This force is transmitted by electric fields. Magnetic fields are linked to electric fields (as are electricity and magnetism) so it is called the electromagnetic force.

3. Gravitation or gravity is the attractive force that exists between all matter.

4. The weak interaction (often called the weak force or sometimes the weak nuclear force) is an interaction between elementary particles involving neutrinos or antineutrinos that is responsible for certain kinds of radioactive decay.

All About Newton’s Laws

Newton’s First Law of Motion

Every object continues in its state of rest, or uniform motion in a straight line unless acted upon by an unbalanced force.

The car will continue to travel at the same speed at which it is going unless an external force is applied to it. For example, the force on wheels caused by brakes!

Constant velocity of the car

Newton’s first law discusses a property of matter known as inertia.Inertia is the property of matter that causes a body to resist changes in its state of motion. The amount of inertia an object possesses depends directly on its mass.

Think about a hockey puck on ice (which is basically frictionless). It will continue to glide at practically the same speed until it is hit by a stick or hits the boards.

Forces Thinking Exercise

In groups of two or three:

Think of as many examples of uses or dangers of Newton’s first law. If there is a danger then state what counteractive measures are taken.

Newton’s Second Law of Motion

When an unbalanced force acts on an object, the object will accelerate in the direction of the unbalanced force. The acceleration of the object is directly proportional to the size of the force and inversely proportional to the mass of the object.

Demonstrate this with spring loaded cars, with roller bladed students, (can be done as part of third law as well)

From Newton’s Second Law, we can arrive at the conclusion that the acceleration of an object is equivalent to its net force divided by mass.

m

Fa or maF

Mass is the quantity of matter in a body.

Free Body Diagrams

Newton’s Second Law utilizes a quantity called the net force on an object. Forces are vector quantities and if more than one force acts on an object then the forces can be added (summed). The sum of these forces is called the net force or resultant force. This force is symbolized as shown below.

netF

RF

totalF

sumF

FFree Body Diagrams

A free body diagram (FBD) shows all of the forces acting on a object. All forces are shown as a pull on the object.

Draw free body diagrams of the following situations:

pushing against a stationary chair

gF

aF

NF

fF

Newton’s Third Law of Motion

If object A exerts a force on object B, then object B exerts a force equal in magnitude but opposite in direction on object A. These two forces are called action reaction pairs.

“For every action force there is an equal and opposite reaction force.”

Let’s take someone pushing a wall for example. When you (object A) push on a wall (object B) Newton’s Third Law dictates that the wall (object B) should push back on you (object A).

Think about this concept. If there was no force pushing back on you, then essentially you would feel nothing and would be able to go through the wall (as there would no force pushing back on you).

Now what would be the reaction force to that of the force of gravity on a man standing on Earth?

Fg

FM

The reaction force to the force of gravity (Earth pulling down on the man) is the force of the man pulling up on Earth!

Name the reaction pair to the forces below.a) Bill pushes [S] on Mike.b) Jenny pulls westward on the rope.c) Mack pushes a spring down.d) Sue hits a tennis ball up.e) The Sun attracts Earth towards it.f) John experiences friction while sliding [NW] on the hardwood floor. g) Proton A repels proton B left.h) Ana falls and hits the ground.

Fanyan and Atif each pull on a rope so that they slide towards each other, on ice, with a constant velocity (Assume rope is massless)

Fanyan Atif

NF

NF

gF

gF

TF

TF

fF

fF

The ground pushes up on Fanyan and Fanyan pushes down on the ground.

Earth pulls down on Fanyan and Fanyan pulls upwards on Earth.

Fanyan pulls the rope left and the rope pulls Fanyan right.

The ground attracts Fanyan to the right and Fanyan attracts the ground to the left.

Draw a sketch of the following systems (underlined items) then draw individual free body diagrams. State action reaction force pairs (some reaction forces may not be present in your system)a) A box sits on the ground, is pushed by Sohaib and remains stationary. b) A ball falls with a constant velocity.c) Greg holds on to Ian who holds on to a rope. d) Alison sits and remains on a rough box that is being pushed west by a spring.

Newton's Third Law at a Traffic IntersectionErnie McFarland University of Guelph Many physics students seem to have the

impression that physics is something found only in textbooks; therefore it is particularly nice to show them physics phenomena in the "real" world. I recently noticed an interesting example of Newton's third law at a traffic intersection on campus, and students are quite intrigued by it.

What happened to the lines? There are traffic lights at this intersection, and each day hundreds of cars stop just to the left of the fines. When the light turns green, the cars accelerate to the right (Fig. 2). To achieve this acceleration, the car tires exert a backward force on the road (to the left in the photograph), and by Newton's third law, the road exerts a forward force on the tires, i.e., on the car. At this particular intersection, the top layer of pavement is poorly bonded to the underlying layers, and the backward force on the road under the tires has actually caused the top layer to slide to the left, as seen from the photo, leading to the unusual bends in the painted fines.

Figure 1 shows part of a road at the intersection, from the curb and gutter in the foreground (bottom of photograph) to the center of the road (top). The white lines painted on the road show a rather unusual pattern ‑indeed, it looks as if the road‑painters went berserk! However, the lines were straight when originally painted, eventually assuming the shape in the photograph.

The Force of GravityEarth is surrounded by a gravitational force field. This means that every mass, no matter how large or small feels a force pulling it directly towards the center of Earth. The force field is measured in N/kg. All objects on Earth have the same ratio of force to mass (demonstrate with spring scale). At Earth’s surface this ratio is 9.81 N/kg [down] The magnitude of this ratio decreases as one moves farther from Earth.

The gravitational field strength at Earth’s surface can be denoted by “g”. 6400 km above Earth’s surface the field strength has decreased to 2.45 N/kg [down] (12800 km above 1.09 N/kg).

Mass is defined as the quantity of matter in an object (kg). The standard kilogram of comparison is a Pt-Ir bar in France.Weight is defined as the force of gravity acting on an object (N).

gmFg

Gravitational field strength (N/kg)

Acceleration due to gravity (m/s2)

g is a variable quantity!

LAW OF UNIVERSAL GRAVITATION

221

r

mGmFG

FG gravitational force (in two directions)

G universal gravitation constant 6.67x10-11 Nm2/kg2

r distance between the objectsm1 mass of the larger objectm2 mass of smaller object

21

221

2

r

Gmg

r

mGmgm

at the Earth’s surface . . .

All objects at the same distance from a large object experience the same acceleration due to gravity.

David (62 kg) stands on a scale in an elevator. Determine the reading on the scale in each of the following situations.a)The elevator is at rest.b)The elevator is moving with a constant velocity upwards.c) The elevator is moving with a constant velocity downwards.d) The elevator is accelerating at 2 m/s2 [up].e) The elevator is accelerating at 7 m/s2 [down].

gF

SF

+ is up

kg

Ng

kgm

FFF gSR

81.9

62

When dealing with forces we will treat acceleration due to gravity as a scalar quantity. “g” is used in many forces which do not have a downward direction. The direction of the force will be

determined by the student by calculation or analysis.

a, b, c) The acceleration is 0 in each of these situations.

upNF

mgF

mgF

FFF

s

s

s

gSR

2.608

0

Since the scale is pushing up on the rider with a force of 608.2 N the scale will read a weight of 608.2 N

d) The acceleration is +2 m/s2.

upNF

F

mgmaF

mgFma

FFF

s

s

s

s

gSR

2.733

)81.92(62

d) The acceleration is -7 m/s2.

upNF

F

mgmaF

mgFma

FFF

s

s

s

s

gSR

2.174

)81.97(62

Normal Forces

When an object rests on a flat surface (parallel to the ground) the normal force of the surface is equal and opposite to the force of gravity on the object. This balance also applies to situations when the object is accelerating parallel to the ground (height remains the same). These situations are encountered often and as a result people often think the force of gravity and the normal force are equal and opposite. Surfaces are, in fact, capable of a wide range of forces. Surfaces are capable of changing an object’s velocity very quickly and thus exert forces much larger than force of gravity on the same object. The following example will illustrate this point.

Alison (55 kg) jumps off a 30 m building and lands inmud! She compresses the mud 20 cm while coming torest.

a)What velocity did she hit the mud with?

b)What was Alison’s acceleration in the mud?

c)What was the mud’s normal force on Alison?

gF

air

gF

NF

mud

+ is up

ga

mgma

FF

airin

gR

a)

0

81.9

30

1

v

kg

Ng

md

s

mv

v

davv

26.24

)30)(81.9(2

2

2

22

21

22

Therefore Alison hits the mud with a velocity of 24.26 m/s [down].

mgFma

FFF

mudin

N

gNR

a)

0

26.24

2.0

2

1

vs

mv

md

Alison’s acceleration must first be calculated.

2

2

21

22

21

22

1471

)2.0(2

)26.24(0

2

2

s

ma

a

d

vva

davv

][81440

)81.91471(55

upNF

F

mgmaF

mgFma

FFF

N

N

N

N

gNR