Aristotle & Newton's Laws of Motion

• The learning objectives include comparing Aristotelian, Galilean, and Newtonian conceptions of motion.
• Being able to explain Newton's three laws of motion and how they relate to real-world situations.
• You should understand key terms like force, acceleration, and inertia.

Aristotle's Views of Motion

• Aristotle was the most influential philosopher and scientist of his time, shaping scientific thought for nearly 2000 years.
• An object's motion was determined by its composition of earth, water, air, and fire.
• Aristotle believed substances on Earth were different from those in the heavens.
• Aristotle classified motion into two types: natural and violent.
• Natural motion occurs based on the object's inherent nature.
• Violent motion is caused by external forces.
• Every object has a "proper place" in the universe based on its nature.
• Clay falls to the ground (earth) and smoke rises (air).
• Earth objects experience natural motion, either vertically upward or downward.
• Celestial objects (Sun, Moon, planets) are perfect spheres and move in circular motion.
• Violent motion happens when external forces push or pull objects.
• For example, a cart moves when pushed.
• Natural objects on Earth are stationary, but celestial bodies are in natural motion.
• Objects need a force to move and will come to rest once the force is removed, according to Aristotle.
• Celestial bodies are always in motion because of continuous force from the "Prime Mover."
• Heavier objects fall faster than lighter ones due to more "earth" element content, returning them to their "proper place" faster, making the rate of fall proportional to weight.

Galileo's Views of Motion

• Galileo challenged and disproved Aristotle's ideas through observations and experiments.
• Galileo dropped objects of different weights from the Leaning Tower of Pisa, finding they fell at the same rate regardless of weight.
• Galileo experimented with balls rolling on inclined planes: balls rolling downhill gained speed, while balls rolling uphill slowed down.
• Galileo predicted that balls on level surfaces would move at a constant speed but eventually stop due to friction.
• Friction is the action of one surface or object rubbing against another.
• Objects moving horizontally continue moving in the absence of friction.
• Galileo's development of the concept of inertia came from these observations.
• Galileo experimented with a ball rolling on a level surface from an inclined plane and noticed the ball rolled farther as the surface became smoother.
• Galileo reasoned that if the surface were perfectly smooth, the ball would continue rolling indefinitely unless something stopped it.
• He concluded that some objects could naturally remain in motion.
• Isaac Newton recognized this phenomenon and included Galileo's conclusion in his first law of motion.
• Newton's first law of motion is also known as the Law of Inertia.

Newton's Law of Motion

• Newton's first law: Law of Inertia.
• Newton's second law: Law of Acceleration.
• Newton's third law: Law of Action-Reaction.

Law of Inertia

• An object at rest tends to stay at rest.
• An object in motion tends to stay in motion unless acted upon by an unbalanced force.
• An object "will keep doing what it was doing" unless acted on by an unbalanced force.
• If an object is sitting still, it will remain stationary and if it is moving at a constant velocity, it will keep moving.
• It takes force to change the motion of an object.
• When there are an equal and opposite forces, they are said to be balanced, and the object experiences no change in motion.
• If they are not equal and opposite, then the forces are unbalanced, and the motion of the object changes.
• A soccer ball sits at rest and takes an unbalanced force from a kick to move.
• Two teams in a tug-of-war with equal force result in no change of motion.
• Inertia is the tendency of an object to resist changes in its state of motion.
• Newton's first law is also called the Law of Inertia.
• All objects have inertia, with more massive objects having more inertia and being harder to change their motion.
• Newton's First Law says because of inertia, objects resist changes in their motion.
• If a car traveling at 80km/hour is stopped, the occupants will continue moving at that speed.
• A powerful locomotive needs a large force to change the motion of massive boxcars that have a great deal of inertia.
• A bug has very little inertia and exerts a very small force when it flies into a windshield.
• Objects in motion need an unbalanced force to prevent them from moving forever.
• A book stops sliding across the table due to the force of friction.
• A ball thrown upwards eventually slows down and falls because of gravity.
• In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed and direction would keep going indefinitely.

Example Problem for the Law of Inertia

• A car is traveling at a constant speed of 20 m/s on a flat road when the driver applies the brakes, stopping the car after 10 seconds.
• The car’s initial state of motion is traveling at a constant speed of 20 m/s.
• According to the law of inertia, the car would continue moving at this constant speed unless an external force, like the brakes, acts on it.
• Inertia is the tendency to resist any change in its state of motion.
• To calculate the car’s acceleration: (Vfinal - Vinitial) / (tfinal - tinitial) = (-2 m/s²).
• To find the distance, use the kinematic equation d = vt + ½ at² = 100 meters.

Law of Acceleration

• Law of Acceleration can be summarized by the equation: Force = mass x acceleration, or F = ma.
• Acceleration is a measurement of how quickly an object is changing motion.
• Force is directly proportional to mass and acceleration.
• Imagine a ball of a certain mass and moving at a certain acceleration exhibiting a certain force.
• If that ball is made twice as big (double the mass), F = ma says this new ball has twice the force of the old ball.
• If the original ball is moving at twice the original acceleration, F=ma says the ball will again have twice the force of the ball at the original speed.
• F= ma basically means that the force of an object comes from its mass and its acceleration.
• Doubling the mass and the acceleration quadruples the force: (2m)(2a) = 4F
• The example scenario on a massive but slow glacier still has force.
• On the other hand, Something very small (low mass) moving quickly (high acceleration), like a bullet, can still have great force.
• Something very small changing speed very slowly will have a low force.

Example Problem for the Law of Acceleration

• A 10 kg box is pushed across a frictionless surface with a force of 50 N.
• Apply Newton's Second Law of Motion, F = ma, to find the acceleration of the box, which is 5 m/s².
• If the force applied to the box is increased to 100 N, the new acceleration will be 10 m/s², using F = ma again.
• If the box is initially at rest, it will travel 62.5 meters in 5 seconds under the influence of the 50 N force using the kinematic equation d=1/2 at².

Law of Action-Reaction

• For every action there is an equal and opposite reaction.
• For every force acting on an object, there is an equal force acting in the opposite direction.
• For example, gravity is pulling you down in your seat, but your seat is pushing up against you with an equal force, which is why you are not moving.
• Therefore, there is a balanced force acting on you with gravity pulling you down and your seat pushing you up.
• If you are standing on a skateboard or a slippery floor and push against a wall, you will slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back.
• When you stub your toe, your toe exerts a force on the rock, and the rock exerts an equal force back on your toe.
• The harder you hit your toe against the rock, the more force the rock exerts back on your toe, which is why it hurts.

Example problem for the Law of Action-Reaction

• A 500 kg boat is initially at rest in a calm lake and then exerts a force of 2000 N.
• The action force in this scenario is the force exerted by the boat's engine on the water, where the engine pushes backward on the water with a force of 2000 N

Quiz Activity

• A sled with a mass of 15 kg is being pushed across a flat surface with a force of 45 N, with a frictional force of 5 N acting opposite to the direction of motion.
• A'rocket with a mass of 5000 kg is launched into space, with the engines providing a thrust of 150,000 N and a gravitational force of 50,000 N in the opposite direction.