2.1

Aristotle on Motion:

• Divided motion into two categories:

  • Natural motion

  • Violent motion

• Natural motion occurs due to the nature of the object and depends on the elements it contains (fire, air, water, earth).

  • A lump of clay is of the earth. When it isn’t supported, it falls to the ground.

  • A puff of smoke is made of air and will rise to the air.

  • A feather is a mixture of earth and air and will fall to the ground when unsupported, but not as fast as the lump of clay.

• Heavier objects fall faster, lighter objects fall slower, i.e., objects fall at speeds proportional to their weight.

• The heavier the object, the faster it falls.

• Natural motion is either straight up or straight down for objects on earth, and circular for celestial bodies.

• Circular motion has no start or end; it keeps repeating.

• He believed that different rules thus applied to celestial bodies. He stated that they were perfect spheres made of perfect, unchanging substances. He called this quintessence.

• Violent motion is a result of pushing or pulling forces.

• It is an imposed motion. It is externally caused. Objects do not move by themselves.

  • Someone pushing a cart.

  • Someone lifting a heavy weight.

  • Wind motion imposed on ships.

• Difficulties in the concept of violent motion: forces causing the pushes and pulls weren’t always obvious.

  • Arrow moving due to a bowstring at first, but seeming to move on its own after that.

[Aristotle’s reasoning behind the arrow continuing to move: Parting of air by the moving arrow resulted in a squeezing effect at the end of the air, causing the air to rush back and prevent a vacuum from forming. Arrow then gets propelled through the air.]

Quick Summary: Motions of objects are due to either:

1. the nature of the object (comes from within)

2. external forces acting on the object (pushing/pulling)

• An object in its proper place doesn’t move unless subjected to an external force.

• Except for celestial objects, the normal state for an object is a state of rest.

Copernicus and the Moving Earth:

• For his theory of the moving Earth, he assumed that Earth and other planets circled the Sun.

• Worked privately for years because:

  • he was afraid of being persecuted, because his theory was entirely different from public opinion.

  • he wasn’t entirely sure of it himself. (The concept of a moving Earth didn’t make sense with the then existing theories on motion.)

• His exposition was called De Revolutionibus. He sent it to the printer in his final years of life.

• His theory and Aristotle’s views on motion challenged the beliefs of the Church. They threatened their authority and faith. Eventually, however, the Church accepted them.

2.2

Galileo’s Experiments:

He was a scientist of the early 17th century.

He proved Copernicus’ notion.

He did this by discrediting Aristotle’s views.

Leaning Tower:

• Galileo dropped objects of different weights from the top of the Leaning Tower of Pisa and compared their falls.

• When the objects were released together, they hit the ground at the same time. Their weight had nothing to do with the speed of their fall. This disproved Aristotle’s theory.

• There was the minimal effect of air resistance.

• Despite proving this publicly, some people still stuck to Aristotle’s word.

Inclined Planes:

• Galileo was more concerned with how things moved than why they moved.

• Aristotle based his theories on what he observed in nature around him, and thus came to the conclusion that motion always required a medium to resist it, like air or water. He believed that vacuums couldn’t exist because there was no medium.

• Galileo rejected this principle. He tested his own hypothesis by judging the motions of objects on plane surfaces tilted at different angles.

• Balls rolling downwards went faster. Balls rolling upwards went slower. Balls rolling on a horizontal plane stayed the same speed.

  

• He stated that the balls finally came to rest because of friction, not because of their internal nature.

• He backed this theory up by observing motion on smoother surfaces. The smoother the surface, the lesser the friction, the longer the object moved at the same speed.

• Galileo thus realized that an object moving on a horizontal frictionless surface would keep moving at that speed infinitely.

• Another experiment Galileo used to prove his theory:

  • Placed two inclined planes facing each other.

  • If a ball was released from rest from the top of a downward sloping plane, it would rise to almost the same height again on the opposite upward sloping plane.

  • He stated that the only reason the ball didn’t rise to the exact same height was because of friction.

  • The smoother he made the planes, the higher the ball rose.

  • When he reduced the angle of the upward sloping plane, the ball had to travel a longer distance to reach the same height.

  • The steeper the slope, the more rapidly the ball loses its speed.

  • When there is no slope and no resistive force, the speed of the ball doesn’t change at all.

• The property of an object to resist changes in motion is called inertia**.**

• Aristotle couldn’t pin down the concept of inertia because he never imagined motion without friction.

Quick Summary:

→ Aristotle said moving objects are propelled by a steady force.

→ Galileo said moving objects are propelled by the absence of a force acting on them.

→ Inertia: The tendency of objects to resist changes in motion.

2.3

Newton’s First Law of Motion:

• It’s called the Law of Inertia.

• Statement:

  Every object continues to remain in a state of rest or of uniform speed in a straight line, until it is acted upon by a nonzero net force.

• keyword: continue.

• Object continues doing what it’s doing until a force acts on it.

• Eg:

  • state of rest: whipping a tablecloth out from under the dishes on the tabletop, without actually disturbing the dishes.

  • state of motion: space probes moving constantly in outer space.

2.4

Net Force and Vectors:

• Changes in motion happen due to forces or combinations of forces.

• Force → a push or pull.

• Forces can be gravitational, electrical, magnetic, or muscular effort.

• Net force → the force that’s a result of multiple forces acting on the same object.

  • e.g: two people pulling an object in the same direction with the same amount of force each doubles the force acting on the object.

  • if the two people pull with the same amount of force but in opposite directions, the sum of the forces (net force) becomes equal to zero.

• Vector → an arrow drawn to represent a force, the length and direction of these arrows are drawn to scale.

• Vector quantity → a quantity that’s defined by both magnitude and direction.

  • e.g: force, velocity, acceleration.

• Scalar quantity → a quantity defined only by its magnitude.

  • e.g: mass, volume, speed

• When two vectors are parallel to each other:

  • they’re added if they act in the same direction.

  • they’re subtracted if they act in opposite directions.

• Resultant → Sum of two or more vectors.

• The Parallelogram Rule is used to find the resultant of two vectors that aren’t exactly in the same or opposite direction.

  (How to implement it: )

  • construct a parallelogram with the vectors as adjacent sides.

  • the diagonal of the parallelogram is the resultant.

• The parallelogram turns into a square for vectors equal in magnitude and perpendicular to each other. For any square, the length of the diagonal is root 2. So, the resultant is root 2 times one of the vectors.

Force Vectors:

• The figure shows force vectors acting on a box:

  

• The next figure shows a doll hanging from a clothesline:

  

• This figure shows three forces acting on the doll.

  1. Her weight.

  2. A tension in the left hand side of the rope.

  3. A tension in the right hand side of the rope.

• Due to the different angles, the rope tensions are different on either side.

• The parallelogram rule shows us that the tension is greater in the right hand side.

• Both the rope tensions combine to balance the weight of the doll.

2.5

The Equilibrium Rule:

• If you tie a string around a 2-pound bag of flour and hang it on a weighing scale, a spring in the scale stretches until the scale reads 2 pounds.

• Tension → the stretching force causing the string to stretch.

• A scale in the science lab would read 9 newtons.

• Pounds and newtons are units of weight, which are units of force.

• 2 pounds is equivalent to 9 newtons.

• There are two forces acting on the bag of flour:

  1. tension force acting upwards

  2. weight acting downwards

• These two forces are equal and opposite; they add up to zero. So, the bag stays in a state of rest. No net force acts on the bag.

• The bag is in mechanical equilibrium.

• ΣF = 0 → Equilibrium equation

  • Symbol stands for “vector sum of”, F stands for “forces”.

• For a suspended object, if the sum of the forces acting upwards and the forces acting downwards is zero, it stays at rest.

2.6

Support Force:

• A book lying at rest on a table is in equilibrium. Forces acting on the book:

  1. gravity, exerted downwards, due to weight of the book.

  2. support force, exerted upwards, to counter the force of gravity.

• The support force is sometimes called the normal force.

• It keeps the book in a state of equilibrium so it doesn’t move.

• It’s equal to the weight of the book.

• The book pressing down on the table is similar to pressing down on a spring. The table exerts a force back onto the book to keep it in place, just like how a spring pushes back onto your hand.

When you are in equilibrium, your weight is equal to the force of gravity acting on you.

2.7

Equilibrium of Moving Things:

• Rest is one form of equilibrium.

• An object moving at a constant speed in a straight line is another form of equilibrium.

• Equilibrium is a state of no change.

  • Static Equilibrium → when the object is at rest.

  • Dynamic Equilibrium → when the object is moving at a constant speed in a straight line path.

• By Newton’s first law, an object under the influence of only one force can’t be in equilibrium, because the net force can’t be zero.

• To test whether something is in equilibrium or not, check for changes in its state of motion.

  • A crate being pushed across a factory floor is in dynamic equilibrium. (which means that more than one force acts on it.)

  • The force of friction acting between the crate and the floor is equal and opposite to the pushing force acting on the crate.

• For any object in static or dynamic equilibrium, the sum of forces acting on it is always zero.

2.8

The Moving Earth:

• Copernicus put forth the concept of a moving earth in the 16th century, but it sparked a lot of argument, as:

  1. Inertia wasn’t understood then.

  2. The amount of force required to keep the Earth moving was unfathomably large.

  3. For a bird dropping vertically downwards from a tree to catch a worm, it wouldn’t have been able to catch it if the Earth moved.

• The Earth would have to move at a speed of 107,000 km/h to circle the Sun in a year. That’s 30 km/s. Even if the bird managed to get to the worm in one second, the worm would’ve been moved 30 km away.

• Without inertia, the concept of a moving Earth would never have been understood.

  • The Earth moves at 30 km/s. So does the tree, the bird, and the worm.

  • When things are in motion, they stay that way until unbalanced forces act on them.

• If you stood next to a wall and jumped (so your feet aren’t in contact with the floor anymore), the wall wouldn’t slam into you.

• It was hard to understand concepts like these 400 years ago, especially when people didn’t have fast moving vehicles to prove it to them.

  • If you flipped a coin vertically in a high speed vehicle, you’d be able to catch it. This is due to inertia.

• Aristotle didn’t recognize the idea of inertia because, to him, all moving objects didn’t follow the same rules.

  • He saw vertical movement as natural, horizontal movement as unnatural and requiring a sustaining force.

• Galileo and Newton acknowledged that all moving objects followed the same rules.

Moving objects continue to move until there’s an opposing force (like friction) stopping them.