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Physics in Everyday Life

The Physics of Motion

Andrew Robinson

What is Physics?

• The study of objects and their interactions

• Observational science – why do things work they way they do

• Predictive science – mathematical models are developed to predict behaviour

• Experimental science – mathematical models are tested to see if they reflect reality

• If they do and are accepted as a generally robust model, then they become a Theory

Physics is Everywhere

• By looking around our surroundings, we can see lots of physics happening

• There is also lots of physics happening which our own senses cannot detect

Course Objectives

• To show you physics at work around us

• To explain why some things we observe happen the way they do

• To show you that physics does not need complicated mathematics to be understandable

• To make you think

Describing Motion

Position

Displacement

Velocity

(and Speed)

Acceleration

Position

• Where are we?

• To describe position, we need a Reference Point, sometimes called the Origin

Equator

Greenwich Meridian

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• René Descartes

• The Cartesian Coordinate System

Describing Motion

Position

Displacement

Velocity

(and Speed)

Acceleration

Velocity and Speed

• These are similar concepts, the rate of change of distance with respect to time

• In Physics there is a distinction between velocity and speed

• Velocity is the speed, but also has a designated direction

– This is an example of a vector quantity

• I drove at 80 km/hour describes a speed

• I drove due North at 80 km/hour describes a velocity

Acceleration

• The rate of change of velocity

• How much faster are we getting?

– Accelerating

• How much slower are we getting?

– Decelerating The concept of separate velocity and

acceleration is a difficult one to

visualise

• A vehicle with a higher acceleration travels further in any given time

• At the end of that time it has a higher speed than the vehicle with the lower acceleration

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The Aristotelians

• The Greek Scholar Aristotle considered what made objects move

• He stated that an object required a Force to keep it moving

• This definition of a “Force being an agent causing motion” lasted until the Renaissance period in western Europe.

Observe

Form

Hypothesis

Perform Experiment

Compare Observation

with Experiments

Reject or Accept

Hypothesis The Great Greek thinkers failed to develop the Scientific Method

• Aristotle did not test his theory of motion with experiments.

• Nevertheless, his ideas on force and motion dominated Western science for thousands of years.

Vincenzo Galilei and the Scientific Method

• Vincenzo Galilei (1520-1591) was an accomplished Lutenist and composer.

• He produced the first description of how the tension in a lute string changed the pitch of the note.

• He did experiments, analysed the results and produced a mathematical formula to describe the relationship

Galileo Galelei

• Vincenzo’s son Galileo applied the scientific method to the study of motion

• His experiments, some rolling marbles down slopes and others, clearly distinguished between velocity (speed) and acceleration

• Some of his results contradicted Aristotle and were very controversial

• Aristotle had hypothesized that the heavier an object, the faster it would fall

• Galileo dropped cannonballs of different weight from the top of the leaning tower of Pisa.

• They hit the ground at the same time!

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Isaac Newton and the Laws of Motion

• In 1686, the English scientist Isaac Newton, took work on motion by Galileo and Descartes, added his own observations and formulated three laws of motion and a law of gravity which describe most observable motion.

The First Law of Motion

• An object continues at constant speed in a straight line (i.e. at constant velocity) unless acted on by an external force.

The natural state of nature is either no motion or motion in a straight line with constant speed

Aristotle was wrong! Aristotle

assumed that objects were

stationary when no force was

exerted

The Second Law of Motion

• The force required to change the velocity of an object is proportional to the mass of the body and the acceleration

• 𝐹𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 × 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛

𝐹𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 × 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛

• If you apply more force to an object, it accelerates more

So What is Mass?

• Sometimes called Inertia or Inertial Mass

• The resistance of a body to a force – a large mass will resist a force more than a small mass, and produce a smaller change in motion (the acceleration)

Dictionary Definition: inertness, especially with regard to effort, motion, action, and the like; inactivity; sluggishness.

Mass and Weight

• Don’t confuse them!

• In physics, a weight is a force due to gravity acting on a mass

• The mass is constant

• The weight depends where you are in the universe

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Walking On The Moon

• On the Moon, the gravitational force is a sixth that on Earth

• The astronauts from Apollo 17 (Gene Cernan and Harrison Schmitt) weigh less than they do on Earth

• Their inertia (mass) is still the same

http://www.youtube.com/watch?v=wo3-fuYKWB4

Video: NASA

The Third Law of Motion

• When a force is exerted on an object, the object exerts an equal and opposite force back.

• Known as the Reaction Force

• This law is sometimes quoted as

• “Action and reaction are equal and opposite”

How Do We See It In Action?

• The Third Law was Newton’s major contribution to development of the laws of motion.

• If you push on an object, the object pushes back on you with an equal force which is in the opposite direction

“Child pushing Grandmother on tricycle”

Boy pushes grandmother

Grandmother’s back pushes on boy’s hands

Gravity pulls down on

grandmother, pushing her

towards the floor

Floor pushes back on grandmother, stopping her from sinking into the ground

Forces Can Cancel Out

• Force is a vector quantity (with magnitude and direction).

• Vector quantities can be added together, so that they cancel each other out, and the net effect is zero

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Vase with Irises (Van Gogh, 1890)

We know gravity is pulling the vase down: things fall towards the Earth

Why doesn’t the vase fall through the table?

The table pushes back on the vase, with a force equal to the force of gravity. There is no force, no acceleration, and a stationary object remains stationary

• In a tug of war contest, the teams are pulling on the rope in opposite directions

• If both teams are evenly matched, then the two forces exerted on the rope are equal and opposite. They cancel out.

• There is no net force on the rope, so the rope does not change its motion

• If the rope was stationary, it remains stationary

• If one team is slightly stronger than the other, the forces do not cancel out, and there is a small force acting on the rope in the direction that the stronger team are pulling

• Newton’s Second Law says that if there is a force, then there must be acceleration.

• The stationary rope must start to move in the direction of the acceleration

• Adding force vectors and cancelling them out works with any number of vectors

If each of these three force vectors are equal, the net force is zero

Engine Thrust

Air resistance (drag)

Lift

Aircraft Climbing

Gravity

• This is a free body diagram, it shows the main forces acting on the aircraft

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Gravity

• In the Principia Newton also formulated a Law Of Gravity to describe the easily observable fact that things fall down towards the surface of the Earth

Apple tree at Woolsthorpe Manor, Grantham, where Newton formulated the Law of Gravitation

Newton’s Law of Gravity

• The gravitational force is exerted between any two masses and depends on the value of each of the masses.

• It also gets weaker with distance

With distance squared to be exact

Kepler’s Laws

• Newton’s Law of Gravitation was able to explain the earlier observations of planetary motion made by Johannes Kepler (1571-1630)

Earth Blue Mars Red

• Earth and Moon seen from the Galileo Probe

• Earth attracts the Moon

• Moon attracts the Earth

• The forces are equal and opposite

Lunar Tides

• The gravitational pull of the moon is one of the two contributing factors to explaining tides in the seas and oceans

• The gravitational pull of the sun is the other influencing factor

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Circular Motion

• If the Earth and Moon are pulling on each other, why don’t they collide?

Direction of Velocity for a Rotating Object

• The velocity vector is always at a tangent to the spinning object

• The velocity vector is always at a tangent to the spinning object

• So the vector points in a different direction

• This counts as a change in velocity over time

This is a definition of acceleration

• A rotating object is always subjected to a force, because its velocity is always changing

• The force always acts to push the object into a circular path – it is always towards the centre

Centripetal Force

• From Latin centrum "centre" and petere "to seek“

• The Centripetal force is any force which always acts to make an object move in a circular path

Where Does the Centripetal Force Come From?

• It is not a new force of nature, it has to come from a force which is already acting on the object

Bolas: South American Lasso

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• For a ball on a string, it’s the tension force in the taut string that pulls the ball around in a circle

Tension Force

• For the moon going round the sun, it’s gravity that provides the centripetal force

Gravitational Force

Turning a Corner in Your Car

Canadian Grand Prix 2006, Montreal

You turn in a circular path, so where does the centripetal force come from?

• Sideways friction forces from the tires (tyres) provides the centripetal force

• If the friction force is not sufficient to hold you in the circle, then you slide off the road

Ice

Slide off, if there is not enough centripetal force

• Whether friction can generate sufficient force to hold you on the road depends on

1. The speed you are going – there is a maximum safe speed

2. The radius of the turn (tighter turns – must go slower)

3. How good your tires are (tread and rubber compound)

4. The nature of the road surface – slippery surfaces generate much less friction force (ice, puddles of water)

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Banked Turns

• In many cases of turning, the object turns more easily if it is banked

• Why?

– If the turn is banked, then part of another force can provide an extra contribution to the centripetal force

– More force: easier to turn more quickly and in a tighter turn

Friction

Weight

Force of road pushing on car

• Centripetal force has contributions from friction and normal force

• It is larger than it would be for a flat turn

• The car can take the banked turn faster than it can take a flat turn

Centripetal force

• There is a similar effect for aircraft, where banking uses part of the lifting force generated by the wings to provide centripetal force

• The part of the lift force which is parallel to the ground provides the centripetal force.

• The vertical part of the list force has to counterbalance gravity, otherwise the plane loses height!

grav

ity

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Modes of Transport

• Moving ourselves around is mostly about providing a force to push against something in order to change our state of motion

The exception to this statement is the rocket motor, which depends upon a

different physical principle, the Conservation of Momentum. We will discuss this principle in another class.

Sail Power

• We use the wind to provide a force

• The sails change the direction of the wind velocity (which means the wind is accelerating around the sail)

• The wind exerts a force on the sail

• The Sail exerts a force on the air. This force is the one which moves the boat

http://www.phys.unsw.edu.au/~jw/sailing.html

• Wind changes direction

Force of sail on air. The sail pushes on the air and this is the force which can move the boat

Force on air making it change direction

• The force of the sail on the wind is applied to the hull of the boat through the mast.

• The hull has a force on it, which changes its motion

Propulsive force, moves the boat forward through the water

Unwanted sideways force

• The sideways force (which is not wanted) is counteracted by a drag force from the keel under the hull

Sideways force

Propulsive force Drag force from keel

Drag force from water

Flettner Rotor Ship

• In the 1920’s the German engineer Anton Flettner, used the Magnus effect to power ships, by using wind power coupled to rotating cylinders to generate a propulsive force more efficiently than sails

Flettner Rotors

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• The Flettner rotors were powered by low power electric motors

Wind velocity

Force generated on rotor

Oar Power

• Use the oar to push on the water

• Newton’s Third Law, means that the water pushes back on the oar.

• The oar is held by the crew, who sit in the boat. The push of the water on the oar propels the boat

Gondolas in Venice

• The oar pushes on the water

• The water pushes back on the oar

• This force is transmitted through the oar and gondolier to the gondola

It actually depends on the grip of the gondolier’s shoes to the deck!

Propellers or Paddlewheels

• The paddlewheel or propeller in a ship turns and exerts a force on the water

• The water pushes back on the propulsion system, moving the boat

Walking, Jogging or Running

• Our muscles move our skeletal system so that we exert a force on the road.

• The road pushes back on our feet

• We move along

• Force is efficiently transferred to the ground if there is plenty of grip

– A large friction force is applied between the ground and the foot

– We wear shoes which are optimized to give good grip in various conditions

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• Wheelchair basketball (Canada vs Australia, Sept 2012, Paralympics)

• Athlete pushes on the wheel

Wheel pushes on the floor Floor pushes on the wheel, wheelchair moves forward

• To propel a car forward is similar, except that the force to turn the wheel comes from the engine

• Forward progress depends on there being efficient transmission of force from wheel to ground.

• This requires a large friction force.

– In slippery conditions, the wheel turns, but slips on the road, and so no forward progress is made

Conclusions

• By studying motion, we can deduce many things about the physical universe.

• We can see Newton’s Laws of Motion operating all around us, even on objects which do not appear to be moving.