NATS From the Cosmos to Earth Projectile Motion The vertical and horizontal components of the motion of a projectile are independent of each other. Three projectiles fired with initial horizontal velocities of 0, v 1, and v 2 will all hit the ground at the same time. V h = 0V h = v 1 V h = v 2

NATS From the Cosmos to Earth A monkey is on a branch in the air. A hunter is on the ground some distance from the monkey. He fires a gun at the instant the monkey drops from the tree. Should he aim above or below the monkey? Shoot the Monkey (or The Monkey and the Coconut )

NATS From the Cosmos to Earth

A New View of Nature Sir Isaac Newton ( ) - followed Galileo’s lead - developed fundamental laws of motion - revolutionized mathematics and science - experienced moment of inspiration at 24 years old - saw apple fall from tree and suddenly understood gravity - published most famous book in science in Philosophiae Naturalis Principia Mathematica - Principia for short - built first reflecting telescope - invented calculus

NATS From the Cosmos to Earth First law: A body remains at rest or moves along a straight line with constant velocity so long as no external force acts upon it. Second law: A body (m) acted upon by a force (f) will accelerate (a) in the direction of the applied force. The greater the force or the smaller the mass, the greater will be the acceleration. F =ma Third law: A body subjected to a force reacts with an equal counter force to the applied force: That is, action and reaction are equal and oppositely directed, but never act on the same body. Newton's Three Laws of Motion

NATS From the Cosmos to Earth 1st Law A body moves along a straight line with constant velocity so long as no external force acts upon it. 2nd Law Force equals mass times acceleration 3rd Law For every force, there is an equal and opposite force

NATS From the Cosmos to Earth Examples: Pulling a table cloth out from under a table setting The reaction of coffee in a cup when accelerating or decelerating in a car Tightening of a hammerhead by banging hammer on the ground Getting ketchup out of a bottle Not wearing a seatbelt during a head- on car crash Headrests in a car to prevent whiplash during a read-end collision

NATS From the Cosmos to Earth Pushing Cart Animation Newton’s 2nd Law F=ma or a=F/m

NATS From the Cosmos to Earth Velocity and Acceleration Newton showed that acceleration (a) is the change of a body’s velocity (v) with time (t): 1.Acceleration in the conventional sense (i.e. increasing speed) a = Dv/Dt Differential calculus! Different cases of acceleration: Velocity and acceleration are vectors. 3.Change of the direction of motion (e.g., in circular motion) 2.Deceleration (i.e. decreasing speed) a v

NATS From the Cosmos to Earth Newton’s 2nd Law Explains the Feather and the Ball 1 kg on the Earth weighs 9.8 N or 2.2 lbs F = W = mg W = 1kg X 9.8 m/s = 9.8 kg m/s = 9.8 N Take a 1 kg rock and a 10 kg rock and drop them from the same height a 1 = F 1 /m 1 = W 1 /m 1 = 9.8 N/1 kg = 9.8 m/s = g a 2 = F 2 /m 2 = W 2 /m 2 = 98 N/10 kg = 9.8 m/s = g

NATS From the Cosmos to Earth A body subjected to a force reacts with an equal counter force to the applied force: That is, action and reaction are equal and oppositely directed, but never act on the same body. Newton’s Third Law For every action (force), there is an equal and opposite reaction (force)

NATS From the Cosmos to Earth Examples of Action/Reaction Swimming - your hands and the water Walking - your feet and the ground Driving - a car’s tires and the road A bug and a car’s windshield A falling object - the object and the earth A person pulling a spring A deflating balloon - the air rushing out and the balloon Pushing on the wall - your hand and the wall Rocket ship - expelled fuel and rocket

NATS From the Cosmos to Earth apparent weight - weight force that we actually sense not the downward force of gravity, but the normal (upward) force exerted by the surface we stand on - opposes gravity and prevents us falling to the center of the Earth - what is measured by a weighing scale. For a body supported in a stationary position, normal force exactly balances earth's gravitational force - apparent weight has the same magnitude as actual weight. If no contact with any surface to provide such an opposing force - no sensation of weight (no apparent weight). - free-fall - experienced by sky-divers and astronauts in orbit who feel "weightless" even though their bodies are still subject to the force of gravity - also known as microgravity. A degree of reduction of apparent weight occurs, for example, in elevators. In an elevator, a spring scale will register a decrease in a person's (apparent) weight as the elevator starts to accelerate downwards. This is because the opposing force of the elevator's floor decreases as it accelerates away underneath one's feet. Apparent Weight

NATS From the Cosmos to Earth Apparent Weight Animation

NATS From the Cosmos to Earth The Earth is round - its surface drops about 5 m for every 8 km of distance. If you were standing at sea level, you would only see the top of a 5-meter mast on a ship 8000 m away - remember the story of Columbus and the orange. Given h=1/2gt 2, if t=1 s then h = 5 m. So if a projectile is fired horizontally at ~8 km/s, it will fall fast enough to keep “falling around” the Earth - becomes a satellite. So a spacecraft is in free fall around the Earth - free fall is not an absence of gravity. If a satellite is given a velocity greater than 8 km/s, it will overshoot a circular orbit and trace an elliptical path. Escape velocity - velocity at which gravity can not stop outward motion - 40,000 km/hr for Earth Cannonball Animation Orbital Velocity

NATS From the Cosmos to Earth Momentum is mass times velocity, a vector quantity: Mom=mv Law of Conservation of Momentum The total momentum of an isolated system is conserved, I.e., it remains constant. An outside or external force is required to change the momentum of an isolated system. The Law of Conservation of Momentum is an alternate way of stating Newton’s laws: 1. An object’s momentum will not change if left alone 2. A force can change an object’s momentum, but… 3. Another equal and opposite force simultaneously changes some other object’s momentum by same amout Momentum

NATS From the Cosmos to Earth Billiard Balls

NATS From the Cosmos to Earth A Rifle and a Bullet When a bullet is fired from a rifle, the rifle recoils due to the interaction between the bullet and the rifle. The force the rifle exerts on the bullet is equal and opposite to the force the bullet exerts on the rifle. But the acceleration of the bullet is much larger that the acceleration of the rifle - due to Newton’s 2nd law: a = F/m The acceleration due to a force is inversely proportional to the mass. The force on the rifle and the bullet is the same but the mass of the rifle is much larger than the the mass of the bullet so the acceleration of the rifle is much less than the acceleration of the bullet.

NATS From the Cosmos to Earth Angular Momentum Momentum associated with rotational or orbital motion angular momentum = mass x velocity x radius

NATS From the Cosmos to Earth Torque and Conservation of Angular Momentum Conservation of angular momentum - like conservation of momentum - in the absence of a net torque (twisting force), the total angular momentum of a system remains constant Torque - twisting force

NATS From the Cosmos to Earth A spinning skater speeds up as she brings her arms in and slows down as she spreads her arms because of conservation of angular momentum