Ch. 4 Laws of Motion I. First two laws of motion “If I have seen far, it is because I have stood on the shoulders of giants.” - Sir Isaac Newton (referring to Galileo)

Forces Forces can change motion.  Start movement, stop movement, or change the direction of movement  Cause an object in motion to speed up or slow down

Newton’s First Law Experimentation led Galileo to the idea that objects maintain their state of motion or rest. Newton developed the idea further, in what is now known as Newton’s first law of motion:

B. Newton’s First Law Newton’s First Law of Motion  “Law of Inertia” Inertia  tendency of an object to resist any change in its motion  increases as mass increases

Newton’s First Law Which object in each pair has more inertia?  A baseball at rest or a tennis ball at rest Answer: the baseball  A tennis ball moving at 125 mi/h or a baseball at rest Answer: the baseball

What do you think? Imagine the following two situations: –Pushing a puck across an air hockey table –Pushing a book across a lab table What should your finger do in each case to maintain a constant speed for the object as it moves across the table or desk? (Choose from below.) –A quick push or force, then release the object –Maintain a constant force as you push the object –Increase or decrease the force as you push the object Explain your choice for the puck and the book. Imagine the following two situations: –Pushing a puck across an air hockey table –Pushing a book across a lab table What should your finger do in each case to maintain a constant speed for the object as it moves across the table or desk? (Choose from below.) –A quick push or force, then release the object –Maintain a constant force as you push the object –Increase or decrease the force as you push the object Explain your choice for the puck and the book.

A. Newton’s Second Law F = ma F:force (N) m:mass (kg) a:accel (m/s 2 ) 1 N = 1 kg ·m/s 2 F m The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass

Newton’s Second Law  Which produces a greater acceleration on a 3-kg model airplane, a force of 5 N or a force of 7 N? Answer: the 7 N force  A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg and one with a mass of 4 kg. Which has a greater acceleration? Answer: the 3 kg airplane

Classroom Practice Problem Space-shuttle astronauts experience accelerations of about 35 m/s 2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude? Answer: 2625 kgm/s 2 or 2625 N

Practice 1.What is the force of an object with a mass of 12 kg and an acceleration of 4 m/s 2 ? 2.Calculate the acceleration of a 25 kg object that is moved with a force of 300 N 3.What is the mass of an object that is accelerating at 15 m/s 2 when a force of 3000 N is exerted?

Gravity Chapter 4 Section 2

B. Gravity Gravity  force of attraction between any two objects in the universe  increases as... mass increases distance decreases

B. Gravity Who experiences more gravity - the astronaut or the politician? less distance more mass Which exerts more gravity - the Earth or the moon?

B. Gravity Weight  the force of gravity on an object MASS always the same (kg) WEIGHT depends on gravity (N) W = mg W:weight (N) m:mass (kg) g:acceleration due to gravity (m/s 2 )

B. Gravity Would you weigh more on Earth or Jupiter? greater gravity greater weight greater mass  Jupiter because...

B. Gravity Accel. due to gravity (g)  In the absence of air resistance, all falling objects have the same acceleration!  On Earth: g = 9.8 m/s 2 elephant feather Animation from “Multimedia Physics Studios.”Multimedia Physics Studios

B. Gravity What happens when you include air resistance?

Bell Work The attractive force between objects is called? Weight is measured in units called ____ while mass is in____? An object transported from the surface of the Earth to the Moon would have a smaller weight or mass?

A. Projectile Motion Projectile  any object thrown in the air  acted upon only by gravity  follows a parabolic path called a trajectory  has horizontal and vertical velocities PROJECTILE MINI-LAB

A. Projectile Motion Projectile Velocities Horizontal and vertical velocities are independent of each other!

A. Projectile Motion Horizontal Velocity  depends on inertia  remains constant Vertical Velocity  depends on gravity  accelerates downward at 9.8 m/s 2

ConcepTest A moving truck launches a ball vertically (relative to the truck). If the truck maintains a constant horizontal velocity after the launch, where will the ball land (ignore air resistance)? A) In front of the truck B) Behind the truck C) In the truck C) In the truck. The horizontal velocity of the ball remains constant and is unaffected by its vertical motion. Animation from “Multimedia Physics Studios.”Multimedia Physics Studios

B. Circular Motion Centripetal Acceleration  acceleration toward the center of a circular path  caused by centripetal force

B. Circular Motion On the ground...  friction provides centripetal force

B. Circular Motion In orbit...  gravity provides centripetal force ROUND LAB

C. Free-Fall Free-Fall  when an object is influenced only by the force of gravity Weightlessness  sensation produced when an object and its surroundings are in free-fall  object is not weightless! CUP DEMO

C. Free-Fall Weightlessness  surroundings are falling at the same rate so they don’t exert a force on the object

ConcepTest 1 TRUE or FALSE: An astronaut on the Space Shuttle feels weightless because there is no gravity in space. FALSE! There is gravity which is causing the Shuttle to free-fall towards the Earth. She feels weightless because she’s free-falling at the same rate.

ConcepTest 2 Describe the path of a marble as it leaves the spiral tube shown below. It will travel in a straight line since the tube is no longer exerting a net force on it.

The 3 rd Law of Motion Chapter 4 Section 3

C. Newton’s Third Law Newton’s Third Law of Motion  When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.

A. Newton’s Third Law Newton’s Third Law of Motion  When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.

A. Newton’s Third Law Problem:  How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? NO!!!  Aren’t these “balanced forces” resulting in no acceleration?

A. Newton’s Third Law  forces are equal and opposite but act on different objects  they are not “balanced forces”  the movement of the horse depends on the forces acting on the horse Explanation:

A. Newton’s Third Law Action-Reaction Pairs The hammer exerts a force on the nail to the right. The nail exerts an equal but opposite force on the hammer to the left.

A. Newton’s Third Law Action-Reaction Pairs The rocket exerts a downward force on the exhaust gases. The gases exert an equal but opposite upward force on the rocket. FGFG FRFR

A. Newton’s Third Law Action-Reaction Pairs Both objects accelerate. The amount of acceleration depends on the mass of the object. F m Small mass  more acceleration Large mass  less acceleration

JET CAR CHALLENGE CHALLENGE: Construct a car that will travel as far as possible (at least 3 meters) using only the following materials. scissors tape 4 plastic lids 2 skewers 2 straws 1 balloon 1 tray How do each of Newton’s Laws apply?

B. Momentum Momentum  quantity of motion p = mv p:momentum (kg ·m/s) m:mass (kg) v:velocity (m/s) m p v

B. Momentum Find the momentum of a bumper car if it has a total mass of 280 kg and a velocity of 3.2 m/s. GIVEN: p = ? m = 280 kg v = 3.2 m/s WORK : p = mv p = (280 kg)(3.2 m/s) p = 896 kg·m/s m p v

B. Momentum The momentum of a second bumper car is 675 kg·m/s. What is its velocity if its total mass is 300 kg? GIVEN: p = 675 kg·m/s m = 300 kg v = ? WORK : v = p ÷ m v = (675 kg·m/s)÷(300 kg) v = 2.25 m/s m p v

C. Conservation of Momentum Law of Conservation of Momentum  The total momentum in a group of objects doesn’t change unless outside forces act on the objects. p before = p after

C. Conservation of Momentum Elastic Collision  KE is conserved Inelastic Collision  KE is not conserved

C. Conservation of Momentum A 5-kg cart traveling at 1.2 m/s strikes a stationary 2-kg cart and they connect. Find their speed after the collision. BEFORE Cart 1: m = 5 kg v = 4.2 m/s Cart 2 : m = 2 kg v = 0 m/s AFTER Cart 1 + 2: m = 7 kg v = ? p = 21 kg·m/s p = 0 p before = 21 kg·m/sp after = 21 kg·m/s m p v v = p ÷ m v = (21 kg·m/s) ÷ (7 kg) v = 3 m/s

C. Conservation of Momentum A 50-kg clown is shot out of a 250-kg cannon at a speed of 20 m/s. What is the recoil speed of the cannon? BEFORE Clown: m = 50 kg v = 0 m/s Cannon: m = 250 kg v = 0 m/s AFTER Clown: m = 50 kg v = 20 m/s Cannon: m = 250 kg v = ? m/s p = 0 p before = 0 p = 1000 kg·m/s p after = 0 p = kg·m/s

C. Conservation of Momentum So…now we can solve for velocity. GIVEN: p = kg·m/s m = 250 kg v = ? WORK : v = p ÷ m v = (-1000 kg·m/s)÷(250 kg) v = - 4 m/s (4 m/s backwards) m p v

Do Now TRUE or FALSE? The object shown in the diagram must be at rest since there is no net force acting on it. FALSE! A net force does not cause motion. A net force causes a change in motion, or acceleration. Taken from “The Physics Classroom” © Tom Henderson, The Physics Classroom

ConcepTest 2 You are a passenger in a car and not wearing your seat belt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation?...

ConcepTest 2 1. Before and after the collision, there is a rightward force pushing you into the door. 2. Starting at the time of collision, the door exerts a leftward force on you. 3. both of the above 4. neither of the above 2. Starting at the time of collision, the door exerts a leftward force on you.