Newton s Laws of Motion I. Law of Inertia II. F=ma III. Action-Reaction
While most people know what Newton's laws say, many people do not know what they mean (or simply do not believe what they mean).
Newton s Laws of Motion 1 st Law An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. 2 nd Law Force equals mass times acceleration. 3 rd Law For every action there is an equal and opposite reaction.
1 st Law of Motion (Law of Inertia) An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.
1 st Law Inertia is the tendency of an object to resist changes in its velocity: whether in motion or motionless. These pumpkins will not move unless acted on by an unbalanced force.
Newton s First Law (law of inertia) INERTIA is a property of an object that describes how much it will resist change to the motion of the object. more mass means more inertia
Mass and Inertia Inertia comes from MASS. More Mass = More Inertia The greater the inertia, the greater the force needed to change its motion. Mass is measured in Kilograms. Small objects are measured in grams. 1Kg = 1000g
Once airborne, unless acted on by an unbalanced force (gravity and air fluid friction), it would never stop! 1 st Law
1 st Law Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever.
Why then, do we observe every day objects in motion slowing down and becoming motionless seemingly without an outside force? It s a force we sometimes cannot see friction.
What is this unbalanced force that acts on an object in motion? There are four main types of friction: Sliding friction: ice skating Rolling friction: bowling Fluid friction (air or liquid): air or water resistance Static friction: initial friction when moving an object
Slide a book across a table and watch it slide to a rest position. The book comes to a rest because of the presence of a force - that force being the force of friction - which brings the book to a rest position.
In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever! (Or at least to the end of the table top.)
What is a Force? A push or pull, or ANY action that has the ability to change motion. Ex. A baseball will stay at rest (motionless) until you apply a force to set it in motion.
Forces Forces are created many ways. Muscles, wind, etc. Forces create changes in motion, there can be no change in motion without the presence of a force. Is stopping a rolling ball using force?
Units of Force What do things weigh? In the U.S. we measure in pounds. (Lbs) This is a measure of the force of Gravity acting upon an object. In space????
Units of Force In science, the metric unit for force is the Newton. 1 Newton = The amount of force needed to cause a mass of 1Kg to speed up by 1m/s each second.
Balanced Force Equal forces in opposite directions produce no motion
Unbalanced Forces Unequal opposing forces produce an unbalanced force causing motion
Net Forces Generally, there are multiple forces acting on an object. (Ex: Hitting a golf ball.) Forces act together. The resulting motion of an object is due to the total force acting on the object.
Net Forces Forces may have different directions. Net Force is the total amount of force applied to an object, but it takes into account the direction of the forces.
Net Force Force: any influence that tends to accelerate an object; a push or a pull; measured in NEWTONS (N) Net Force: combination of all the forces acting on an object
Equilibrium An object is said to be in mechanical equilibrium when the net forces acting on it are equal to zero When a suspended object (hanging object) is at rest, the forces acting upward MUST equal the forces acting downward Forces acting down are negative (-) Forces acting up are positive (+)
Support Force/Normal Force-the force pushing back on an object at rest. A book sits on the table: What forces act on it? Force of book on table (due to gravity) Force of table on book (support force, aka normal force) Bathroom scale: What forces act on it? Force of you on scale (due to gravity) Force of scale on you (support force, aka normal force) Gymnast on Rings Rope undergoes stretching force when hanging by it Two vertical ropes share the load (think trapeze, pull ups)
Equilibrium is a State of NO CHANGE Objects at rest: stay at rest when in equilibrium Objects in motion: stay in motion when in equilibrium (*MUST be constant speed in a straight line path) The Moving Earth We move at the same speed as the earth around the sun. (About 30 km/second!) If you are on a plane (or in a car) and toss a coin up, does it fly backwards? Bird flies down from a tree to catch a worm, does the worm move away?
Newtons s 1 st Law and You Don t let this be you. Wear seat belts. Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 m/hour.
Mass vs. Weight Mass and Weight are different but proportional. Mass- Amount of material or matter in something. Measure of Inertia of an object. Measured in Kg Mass is NOT Volume Examples Bag of Marbles vs. Bag of Cotton 16lb. Bowling Ball vs. 10lb. Bowling Ball
Weight- the force of gravity on an object F w or sometimes see as F g Weight is a Force measured in Newtons (N) 1 Newton = force required to accelerate a 1 kg object at 1 m/s 2 Helpful Conversion hints (at surface of Earth) 1 kg = 9.8 N 1 kg = 2.2 lbs Calculate weight F w = mg
Weight on Other Planets Do not copy here is g on different planets Mercury 0.376 Venus 0.903 Earth 1.0 Mars 0.38 Jupiter 2.34 Saturn 1.16 Uranus 1.15 Neptune 1.19 Pluto 0.066 * Moon.166
FORCES AND FREE- BODY DIAGRAMS Newton s Laws Yo!
Recall: Net Forces Force: any influence that tends to accelerate an object; a push or a pull; measured in NEWTONS (N) Net Force: combination of all the forces acting on an object 5 N 5 N Net Force = 10N East Net Force = 0 N 5 N 10 Net N Force = 5N East **FORCE is a VECTOR QUANTITY 5 N 5 N
Support Force/Normal Force-the force pushing back on an object at rest. A book sits on the table: What forces act on it? Force of book on table (due to gravity) Force of table on book (support force, aka normal force) Bathroom scale: What forces act on it? Force of you on scale (due to gravity) Force of scale on you (support force, aka normal force) Gymnast on Rings Rope undergoes stretching force when hanging by it Two vertical ropes share the load (think trapeze, pull ups)
Recall: Friction Friction results from relative motion between objects. Frictional forces are forces that resist or oppose motion. Depends on. 2 surfaces in contact (silk, sand paper ) Normal Force (more weight on top of book Friction
Types of Friction Static friction Sliding (Kinetic) friction Rolling friction
Free-body diagrams Free-body diagrams are used to show the relative magnitude and direction of all forces acting on an object.
This diagram shows four forces acting upon an object. There aren t always four forces.
Problem 1 A book is at rest on a table top. Diagram the forces acting on the book. In this diagram, there are normal and gravitational forces on the book.
Problem 2 An egg is free-falling from a nest in a tree. Neglect air resistance. Draw a free-body diagram showing the forces involved.
Gravity is the only force acting on the egg as it falls.
Problem 3 A flying squirrel is gliding (Straight down, no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. A free body diagram for this situation looks like
Gravity pulls down on the squirrel while air resistance keeps the squirrel in the air for a while. Velocity is constant, but there is no Net Force.
Problem 4 A rightward force is applied to a book in order to move it across a desk. Consider frictional forces. Neglect air resistance. Construct a free-body diagram. Let s see what this one looks like.
Note the larger applied force arrow pointing to the right since the book is accelerating to the right. Friction force opposes the direction of motion. The force due to gravity and normal forces are balanced.
Problem 5 A skydiver is descending with a constant velocity. Consider air resistance. Draw a free-body diagram.
Gravity pulls down on the skydiver, while air resistance pushes up as she falls. Is terminal velocity achieved?
Problem 6 A man drags a sled across loosely packed snow with a rightward acceleration. Draw a free-body diagram.
The applied force arrow points to the right and is larger than the frictional force since the object is accelerating. Since the sled is on the ground, the normal and gravitational force are balanced.
Problem 7 A football is moving upwards toward its peak after having been booted by the punter. Draw a free-body diagram. (Neglect air friction)
The force of gravity is the only force described. (no air resistance).
Problem 8 A car runs out of gas and is coasting down a hill.
The car is coasting down the hill, there is dragging friction of the road (left pointing arrow) as well as gravity and normal forces, but no applied force.
Done.
2 nd Law
2 nd Law The net force of an object is equal to the product of its mass and acceleration, or F=ma.
2 nd Law When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N). One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.
Solving Problems Always use these units when using force in Newtons: Mass in Kg Distance in meters Time in seconds Speed in m/sec Acceleration in m/s²
2 nd Law (F = m x a) How much force is needed to accelerate a 1400 kilogram car 2 meters per second/per second? Write the formula F = m x a Fill in given numbers and units F = 1400 kg x 2 meters per second/second Solve for the unknown 2800 kg-meters/second/second or 2800 N
Force and Mass If mass remains constant, doubling the acceleration, doubles the force. If force remains constant, doubling the mass, halves the acceleration.
Newton s 2 nd Law proves that different masses accelerate to the earth at the same rate, but with different forces. We know that objects with different masses accelerate to the ground at the same rate. However, because of the 2 nd Law we know that they don t hit the ground with the same force. F = ma 98 N = 10 kg x 9.8 m/s/s F = ma 9.8 N = 1 kg x 9.8 m/s/s
Check Your Understanding 1. What acceleration will result when a 12 N net force applied to a 3 kg object? A 6 kg object? 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s 2. Determine the mass. 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec? 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?
Check Your Understanding 1. What acceleration will result when a 12 N net force applied to a 3 kg object? 4 m/s/s, 12 N = 3 kg x 4 m/s/s 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s 2. Determine the mass. 3.2 kg, 16 N = 3.2 kg x 5 m/s/s 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec? 66 kg-m/sec/sec or 66 N 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec? 9800 kg-m/sec/sec or 9800 N
3 rd Law For every action, there is an equal and opposite reaction.
3 rd Law According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.
There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces. 3 rd Law
Newton s 3rd Law in Nature Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. In turn, the water reacts by pushing the fish forwards, propelling the fish through the water. The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards).
3 rd Law Flying gracefully through the air, birds depend on Newton s third law of motion. As the birds push down on the air with their wings, the air pushes their wings up and gives them lift.
Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards). Action-reaction force pairs make it possible for birds to fly.
Other examples of Newton s The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction). Third Law
Consider the motion of a car on the way to school. A car is equipped with wheels which spin backwards. As the wheels spin backwards, they grip the road and push the road backwards. 3 rd Law
3 rd Law The reaction of a rocket is an application of the third law of motion. Various fuels are burned in the engine, producing hot gases. The hot gases push against the inside tube of the rocket and escape out the bottom of the tube. As the gases move downward, the rocket moves in the opposite direction.
FRICTION MATH
What is Friction again? Force that acts oppose the relative motion of two surfaces High for dry and rough surfaces Low for smooth and wet surfaces
Free Body Diagram Applied Force F Normal Force F N Friction Force f f Gravity Force F g F g = mg F N = F g f f = F
Static Friction The Force of Static Friction keeps a stationary object at rest! F F N f s f s s F N coefficien t s of static F g friction
Kinetic Friction Once the Force of Static Friction is overcome, the Force of Kinetic Friction is what slows down a moving object! f k F N Motion F F g f k k F N k coefficien t of kinetic friction
Types of Friction To initiate motion of the box the man must overcome the Force of Static Friction Upon sliding, the baseball player will come to a complete stop due to the Force of Kinetic Friction
Representative values for the coefficient of friction Surfaces μstatic μsliding rubber on concrete 0.80 0.65 wood on wood 0.50 0.20 ice on ice 0.10 0.03 glass on glass 0.94 0.40 steel on steel 0.74 0.57
Problem 1: How much force is needed to keep a 78Kg block moving at a constant speed across the floor if the coefficient of friction b/n the block and the floor is 0.21?
First, find the weight (measure of Fg on an object.) and then find Ff. Fw=mg Fw = (78kg)(9.8m/s/s) Fw = 764.4N Ff =μfn Ff = (.21)(764.4) Ff = 160.5N Fw=mg Ff =μfn
Problem 2: What is the coefficient of friction b/n a box with a weight of 637N and the floor if it is pulled at a constant speed with a force of 75N?
Simply solve for μ. Ff =μfn To solve for μ you need only the friction force and the normal force. Since the box is pulled at a constant velocity, meaning a net force of 0N, the Fapp will equal the Ff. Thus: Ff=μFn 75N=μ(637N) μ = 0.117 or 0.12