#### Transcript Newton`s Laws of Motion

Newton’s Laws of Motion I. Law of Inertia II. F=ma III. Action-Reaction Mass vs. Weight • MASS • How much and what material an object is made of (what types of atoms and how many of them) • Measured in grams or kilograms (kg) • Is constant for an object independent of location • WEIGHT • Force of gravity acting on a mass • Measured in Newtons or Pounds Fg=mag • Force on 1 kg is 9.8 Newtons or 2.2 lbs • 1N = 1kg· m/s2 Newton’s Laws of Motion • 1st 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. • 2nd Law – Force equals mass times acceleration. • 3rd Law – For every action there is an equal and opposite reaction. Forces • A force is a push or a pull • A force can cause – a stationary object to move – a moving object to stop – an object to accelerate (change speed or direction) • Net force – the combination of all the forces acting on an object. – changes an object’s state of motion. • Balanced Force – Net force is 0, object at rest – Or constant velocity • Unbalanced – Net force is not 0, Object moves – Or accelerates 1st 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. INERTIA the tendency of an object to resist any change in its motion Inertia is a property of matter and does not depend on the position or location of the object. But it does depend on: MASS a quantitative measure of inertia FORCE “a push or pull” 1st Law • Once airborne, unless acted on by an unbalanced force (gravity and air – fluid friction), it would never stop! 1st 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? Objects on earth, unlike the frictionless space the moon travels through, are under the influence of 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.) Newtons’s 1st 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. 2nd Law 2nd Law The net force of an object is equal to the product of its mass and acceleration, or F=ma. 2nd 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=mxa • 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 Newton’s 2nd 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 2nd Law we know that they don’t hit the ground with the same force. F = ma F = ma 98 N = 10 kg x 9.8 m/s/s 9.8 N = 1 kg x 9.8 m/s/s Example 2 • How much force must a 30,000kg jet plane develop to achieve an acceleration of 1.5m/s2? (neglecting air friction) • Fnet=ma • Fnet=(30,000 kg) (1.5 m/s2)= 45,000 N • Fapp = Fnet 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/s2. 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? 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/s2. Determine the mass. 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 Example 3 • If a 1400 kg car goes from 0 to 60 mph (27 m/s) in 5 seconds, how much force is applied to achieve this? Example 4 • If I throw a 0.145 kg baseball at 20 m/s baseball and my ‘windup distance’ is 0.6 meters, how much force am I applying? Example 5 • A 2.2 kg book is slid across a table. If Fnet = 2.6 N what is the book’s acceleration? • Fnet=ma • 2.6 N = (2.2kg) a • a = 1.18 m/s2 Example 6 • If you drop a 20 kg object what is its acceleration? What is its weight? • acceleration = 9.8 m/s2 • Weight = force • Fg=ma • Fg= (20 kg) (9.8 m/s2) • Q: If a jet cruises with a constant velocity and the thrust from its engines is constant 80,000 N. What is the acceleration of the jet? • A: Zero acceleration because the velocity does not change. • Q: What is the force of air resistance acting on the jet? • A: 80,000 N in the opposite direction of the jet’s motion 3rd Law •For every action, there is an equal and opposite reaction. 3rd 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. 3rd Law 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. 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). 3rd 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. 3rd 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. Other examples of Newton’s Third Law • The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction). 3rd 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. Types of Forces • Applied Force – Fapp • An applied force is a force that is applied to an object by a person or another object. If a person is pushing a desk across the room, then there is an applied force acting upon the object. The applied force is the force exerted on the desk by the person. • Gravity Force (also known as Weight) = Fgrav • The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation:Fgrav = m * g • where g = 9.8 N/kg (on Earth) and m = mass (in kg) Types of Forces • Normal Force = Fnorm • The normal force is the support force exerted upon an object that is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects that are in contact with each other. For instance, if a person leans against a wall, the wall pushes horizontally on the person. Normal Force and Gravity • Gravity always pulls straight down • Normal force (FN) is perpendicular to surface and equal and opposite to component of gravitational force (Fg) FN Fg • This may lead to an unbalanced ‘sliding’ force that is the component of the gravitational force Types of Forces • Friction Force = Ffrict • The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. • There are four types of friction force – sliding, static friction, rolling, and fluid (through gases or liquids) friction. • Thought it is not always the case, the friction force often opposes the motion of an object. For example, if a book slides across the surface of a desk, then the desk exerts a friction force in the opposite direction of its motion. Friction results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. The maximum amount of friction force that a surface can exert upon an object can be calculated using the formula below: • Ffrict = µ • Fnorm Friction • The force of friction (Ff): 1. Is always opposite to the direction of motion or impending motion 2. Usually has a smaller value if the object moving than if it is stationary (static friction > kinetic friction); 3. Depends on the nature of the pair of surfaces involved (the value of μ); Friction • The force of friction (cont’d): 4. Is proportional to the force pressing the surfaces together (the normal force); ≤μ static friction: Ff kinetic friction: Ff =μk FN s FN 5. Is usually independent of the contact area and speed. Example • If a 1 kg mass sits on a flat surface with a coefficient of static friction of 0.5, what is the force of friction (Ff) if: • A horizontal force of 1 N is applied? • A horizontal force of 10 N is applied? • A horizontal force of 100 N is applied? Types of Forces • Air Resistance Force = Fair • The air resistance is a special type of frictional force that acts upon objects as they travel through the air. The force of air resistance is often observed to oppose the motion of an object. This force will frequently be neglected due to its negligible magnitude (and due to the fact that it is mathematically difficult to predict its value). It is most noticeable for objects that travel at high speeds (e.g., a skydiver or a downhill skier) or for objects with large surface areas. Air resistance • Tension Force = Ftens • The tension force is the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire. Free Body Diagrams • Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams that were discussed. • The size of the arrow in a free-body diagram reflects the magnitude of the force. The direction of the arrow shows the direction that the force is acting. Each force arrow in the diagram is labeled to indicate the exact type of force. It is generally customary in a free-body diagram to represent the object by a box and to draw the force arrow from the center of the box outward in the direction that the force is acting. An example of a free-body diagram is shown at the right. Free Body Diagrams • The only rule for drawing free-body diagrams is to depict all the forces that exist for that object in the given situation. Thus, to construct freebody diagrams, it is extremely important to know the various types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction; label each force arrow according to its type. Free Body Diagram The net force acting on an object is the vector sum of all the forces acting on it. Examples: 9N 8N 8N 8N 3N 4N ? 7N 12 N 6N 5N If an object is remaining at rest, it is incorrect to assume that there are no forces acting on the object. We can only conclude that the net force on the object is zero. 4N 4N 7 N Equations for this unit: • Previous equations we might need: • • • • vf = vi + at (or a = ∆v/t, to rearrange it) ∆x = vi + ½at2 ∆x = ½ (vi + vf)t vf2=vi2+2a∆x • New equations: • • • • F=ma Ff=µFN Ff=µkFN Ff≤µsFN