Dynamics

Physics 30S

OutcomesS3P-3-08: Identify the four fundamental forces of nature.S3P-3-09: Perform an experiment to demonstrate Newton’s Second LawS3P-3-10: Define the unit of force as the Newton.S3P-3-11: Define Fnet as the vector sum of all forces acting on a body. Include: force of

friction, normal force, gravitational force, applied forcesS3P-3-12: Construct free-body diagrams to determine the net force for objects in

various situations. Include: balanced and unbalanced forces, inclined planesS3P-3-13: Solve problems, using Newton’s Second Law and the kinematics equations

from S3P-3-07. Include: forces applied along a straight line and perpendicular forces

S3P-4-09: Describe terminal velocity, qualitatively and quantitatively.S3P-4-10: Define the coefficient of friction (μ) as the ratio of the force of friction and

the normal force.S3P-4-11: Distinguish between static and kinetic friction.S3P-4-12: Compare the effects of the normal force, materials involved, surface area,

and speed on the force of friction.S3P-4-13: Solve problems with the coefficient of friction for objects on a horizontal

surface.

What is Dynamics?

• How is it different from Kinematics?– Dynamics is again the study of objects in

motion.– It differentiates itself from Kinematics because

we now begin to include the forces acting on moving objects.

– In this unit, we will be considering Newton’s laws and using them with free-body diagrams to solve problems.

What is a force?• A force is a push or a pull on an object. • Forces can be external to the system or internal.

• This isn’t the type of force that we’re talking about, but what examples of forces can you see in this picture?

Four types of Forces:Strong Nuclear Force

– It is an extremely strong attractive force that holds protons and neutrons together in the nucleus of an atom.

– It is so strong that it overcomes the repulsion that like charges (2 protons), holding the whole nucleus together.

– It only acts at short ranges of about 10-15m

Weak Nuclear Force

– It is a force exerted between all types of subatomic particles.

– It enables the conversion of one type of quark into another

– It is responsible for some types of nuclear decay– (Changes the flavor of quarks (subatomic particles)

Gravitational Force– Attractive force all objects exert on each other and it

is dependant on the masses of the objects involved.– We usually consider gravity only in regards to the

gravity exerted by Earth, but all matter exerts a gravitational pull on other objects.

• For example, I’m exerting a gravitational pull of 2.0 x 10-11 N on a piece of chalk 1 meter away, which is about as much gravitational force as the Earth exerts on a single human cell!

Electromagnetic Force

– The force that two charged objects exert upon each other.

– This is the force that causes opposite charged objects to attract and like charges to repel.

– Electromagnetic force is also responsible for the attraction and repulsion between magnets.

– Most of what we experience can be broken down into this force

Open Topics in Physics

• One of the major aims of physics currently is to unify these forces as different presentations of a single force

• Known as grand unified theory (GUT)• Each of the 4 fundamental forces dominates for a

specific scale– Strong nuclear and weak nuclear – very small; atomic and

subatomic respectively– Electromagnetic – the world we experience– Gravitational – very large; interplanetary

• Currently unsuccessful...

FBD (Free Body Diagrams)• Method of representing the forces acting on a

object• Object is represented as a box (always a box)

or as a single point• Forces (vectors) are represented as arrows• Larger arrows represent larger forces

Example 1

Draw the free body diagram for a human in a slingshot

Girl in human slingshot: http://video.google.com/videoplay?docid=8959221252413764426#

COMMON FORCES

Overview• Gravitational

– Pulls you towards the centre of the Earth– “I’d like to thank gravity - it keeps me grounded...”

• Normal– The force which an object exerts on another object which pushes against it– Keeps a textbook from falling through a desk– Keeps a magnet from zooming into the fridge door

• Applied– A force which we add an object– A person kicking a box

• Tension– Often provided by a rope for hanging objects

• Friction– A force which opposes applied forces– More to come

Applied Force

• Applied– A force which we add to an object– This is the default name given to a force which we are

intentionally creating– A person kicking a box– A man dragging a toboggan– The force of your legs pushing on ice while skating

Gravity• Gravitational

– Pulls you towards the centre of the Earth– Keeps you from floating away– No one really knows what causes gravity

• Why should matter be attracted to other matter?

– Only attractive; it cannot repel you– The more massive the object, the greater the

gravitational attraction– For now, we will only consider the gravitational

attraction of earth (stay tuned for Gr. 11)

Normal Force

• Normal– The force which an object exerts on another object

which pushes against it– Often opposes gravity, but that isn’t always the case– Keeps a textbook from falling through a desk– Keeps a magnet from zooming into the fridge door– Can you come up with an example where it’s not

opposing gravity?

Tension

• Tension– Tension is the name given to a force which is

responsible for providing a stretch– Often provided by a rope for hanging objects– In this example, it’s kind of like the normal force; it’s

opposing gravity

Friction• Friction

– A force which opposes movement and applied forces– We often experience friction as heat– Is not constant

• Friction is the reason it is easier to keep something moving than it is to get it started

– Two types:• Kinetic: the frictional force on a moving object• Static: the frictional force on a stationary object• Kinetic is always less than static

– Friction is dependent on a few factors– The surfaces in contact– The normal force acting on the object– More to come (stayed tuned to Gr. 12)

Example

Draw the FBD for the following items. Identify all of the forces acting on the object and label the diagrams accordingly.A) a coffee mug on a deskB) an student on the swings

ChallengeC) an apple being bitten into

Homework

Draw the FBD for the following items. Identify all of the forces acting on the object and label the diagrams accordingly.A) an apple falling from a treeB) a fallen ice skater sliding across the rink

ChallengeC) a marker writing on the whiteboard

History of study of motion

• Things weren’t always so well defined…• In 330 BC, Aristotle defined two distinct

types of motion: terrestrial & celestial.– To the Ancient Greeks the heavens were perfect,

and thus the Sun, Moon, planets and stars were made from a special perfect material, different from the earth causing different motion.

• In 1513, Copernicus defined the earth as a planet.

• Philosophically though, many of science’s biggest names pondered the question that if the earth was a planet, how could it be made up of a different type of matter?

• Descartes (1644) thus made the logical conclusion that there was no distinction between the heavens & the earth– Descartes theories regarding nature though

could not be proven, and thus were never integrated fully into scientific thought.

Sir Isaac Newton

• In 1666, Sir Isaac Newton at the age of 24 proposed a space without gravity.– Theory of gravitation, that matter attracts

other matter, filled the universe with forces– Invented calculus to solve difficult

mathematical problems, and was able to use the same equations to describe the trajectory of planets and that of a cannon ball (Published in the 1687 Mathematical Principles of Natural Philosophy (Principia).

Newton’s Three Laws

• Newton’s First Law– Law of Inertia– ‘All objects remain in a state of rest or continue

to move with a constant velocity, unless acted upon by an unbalanced force’.

– i.e. A rock that is at rest stays at rest unless a force acts on it.

– i.e. A space probe flies with a constant velocity unless acted upon by another force (Gravity, friction, air resistance, etc…)

• Newton’s Second Law– ‘The acceleration of an object depends inversely

on its mass and directly on the unbalanced force applied to it.’

– i.e. The rate of change in velocity (acceleration) depends on how much force is being applied, and how much mass the object has

–FNET = ma• Fnet is the sum total force acting on the object• A Newton is the k - m - s system unit. It is the force

required to accelerate 1 kg at 1 m/s2

• F is in Newtons, m is in kilograms, a is in m/s2,

• Newton’s Third Law– ‘For every force there is an equal and opposite

reaction force.’– Ex: An asteroid crashes into earth. The earth

applies a force and stops the asteroid, but the asteroid applies an opposite reaction force which causes a crater to be formed.

– Ex: Gravity pushes me into the floor, but the floor pushes back on me with a force that keeps me from falling!

1 Newton, the Base Unit of Force…

• The Newton is the unit of force we are familiar with.

• A one Newton force is defined as the force that gives a 1 kg mass an acceleration of 1 m/s2

The Big Idea!• The equation is:

FNET = ma

This equation will be used in class to analyze forces acting on an object, to calculate

distances and velocities by providing the acceleration, and to solve problems.

The Best Evidence

• Remember slingshot girl?• http://video.google.com/videoplay?docid=895

9221252413764426#

• We didn’t add a force, so what made her move?

PROBLEM SOLVING

Example 1

• A force of 1.20 x 104 N is applied by the brakes of a semi trailer (m=5000. kg). What acceleration does the rig undergo?

a = 2.40 m/s2

Example 2• A dog sled (m=180 kg) carrying a 75 kg man

is being pulled by a team of dogs with a total force of 1000. N. The force of friction against the dog sled is 200. N. What is the acceleration of the dog sled?

• Preview: Assuming the sled began at rest, what displacement does it make in the first 10. seconds?

a = 3.1 m/s2 d = 160 m

Example 3• A dog sled (m=180 kg) carrying a 75 kg man

is being pulled by a team of dogs with a total force of 1000. N. If the sled is travelling at constant velocity, what is the frictional force acting on the sled?

Ff = 1000.N

This is known as equilibrium (Fnet =0).

Homework

• FBD Equilibrium and Non Equilibrium• Equilibrium #1-5• Non-Equilibrium #10, 11

Putting it All Together

• We will use F = ma with some things we are familiar with.– Free Body Diagrams– BIG 4– Vector Algebra

Example 1

• A baseball (m = .250 kg) is thrown by a pitcher with a velocity of 40. m/s. The batter makes contact with the ball for .15 s, which causes a change in velocity to 28 m/s in the opposite direction. – What acceleration does the ball undergo?– What force does the batter apply on the ball?

Fnet = -110 N a = -450 m/s2

Example 2

• A kid’s remote control car can be accelerated at constant rate from rest to 15.0 km/h in 12.0 m. What is the magnitude of the required force (assume it is constant) if the car has a mass of 675 g?

• Fnet = 0.488N

Example 3

• A box (m = 11 kg) accelerates from 2.0 m/s to cover 25 m in 3.3 s. What is the applied force acting on the box if it also experiences a frictional force of 50.0N?

• The applied force on the box is 87 N.

Homework

• Finish FBD Equilibrium and Non Equilibrium

More about Friction

• What changes to cause a difference between kinetic friction and static friction?

• It’s the same object, same surfaces in contact, only difference is what is moving...

• So, what is friction? What is it caused by?• Ever thought about why it takes more force to

get an object moving...• Demo: Spring Scale

Friction vs. Time

• If we were to plot the applied force on the object as a function of time, we would see something like this

• Two distinct phases

Static Friction

• Static friction applies when an object is not moving

• Will increase with applied force until it reaches the limit set by the coefficient of static friction

• The split second the object begins to move is when the applied force reaches the limit:

Kinetic Friction

• Kinetic friction applies once an object is moving

• Stays at a constant amount

Why?• Think at the molecular level• When an object is in contact with

a surface, bonds are made between the object and surface– At rest, more bonds have time to

form– It takes additional force to break

these bonds• When an object is moving, it is

more difficult to form these bonds, – fewer bonds are created – it takes less force to keep the object

moving

Coefficient of Friction

• The coefficients are dimensionless measures of the “slipperiness” of a surface

• Ranges between 0 and 1 for most applications– 1: very sticky– 0: very slippery

• A coefficient greater than 1 implies that less force would be required to lift the object than to slide it

• http://www.engineershandbook.com/Tables/frictioncoefficients.htm

The New Twist

• When solving a question, you need to decide if the object is moving first, and then pick the correct coefficient of friction

• If there is no way of knowing whether the object is moving from the question, solve for static friction and compare it to the applied force

• If static > applied force, friction = applied force• If static< applied force, friction = kinetic friction

Question 1

A box (2.0 kg) is being pulled across the floor with a horizontal force of 15 N. If the coefficient of static friction is 0.35, will the box slide?

The box slides since the maximum static friction is less than the applied force (8.14N vs. 15N respectively).

Question 2

A box (3.0 kg) is being pulled across the floor with a force of 12.99 on the horizontal. If the coefficient of kinetic friction is 0.30 and the coefficient of static friction is 0.35, find:a) if the box moves, and if so, b) the acceleration of the box.

The box will move with an acceleration of 1.4 m/s2.

Apply What You Know

• Push the eraser out from out beneath my hand.

Question 3

A box (m = 5.5 kg) is pushed with a force constantly increasing in magnitude until it just begins to slide. At this point, the force stays constant. If the box accelerates at 1.3 m/s2 and the coefficient of kinetic friction is 0.25, what is the coefficient of static friction?

μs = 0.38

Homework

• Why do you need to push harder to remove dirty spots on the pan when scrubbing dishes?

• Glencoe Physics Pg.133 - check– #14, 15

Air Resistance

• Up until now, we have been ignoring air resistance

• Whenever an object falls, it experiences a force from the particles in the air which oppose the fall – this is air resistance or drag

where k is a constant (drag coefficient) that is proportional to the filters' cross-sectional area, and v is the object’s velocity

The Twist

• Because k is dependent on the cross sectional area of the object, an object which can change shape or rotate during a fall will complicate our calculations.

• Because the magnitude of the force is dependent on velocity, this force is not constant!

• As v increases, so does Fa until eventually...

Fa = Fg (Terminal Velocity)

• Terminal velocity is the final maximum velocity achieved by an object in free fall.

• Derivation

Example 1

• Suppose a 60.0 kg person achieves a terminal velocity of 200.0 km an hour. Find the drag coefficient for the person.

Example 2

• Suppose two similar (different only in their masses) objects were released from the same height at the same time. How would their terminal velocities compare?

• See terminal velocity notes

Homework

• Suppose a 55 kg person achieves a terminal velocity of 180.0 km an hour. Find the drag coefficient for the person.

• and• Read through the coffee filters lab for

tomorrow.

The Plan

Max Classes: 91. What is a force, 4 Fundamental forces and free body diagrams2. Common forces (normal force, gravitational force, applied forces,

friction)3. Newton’s laws4. Problem solving5. Problem solving plus kinematics6. Coefficient of friction7. Air resistance and terminal velocity8. Lab – falling coffee filters9. Review10. Test