BHS Freshman Physics Review Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science. Galileo (1564-1642): 1 st true scientist and 1 st person to use an efficient and rational method of research Kinematics: study of motion Motion is always relative to something else. Rate: something quantity divided by time. Example, my rate of pay is $5.00 per hour. Speed: how fast something is moving; a scalar. Units: m/s (meters / second) Examples, 5 meters/second or 25 miles/hour. Instantaneous Speed: the speed at a given moment. (Like the speedometer in your car.) Average Speed = total distance covered / total time Velocity: how fast something is moving in a given direction; a vector. Example: 15 mph west. If either, the speed (15 mph) or the direction (west) changes, then the velocity changes. = change in; is the Greek letter delta Example, v = change in velocity. Acceleration: change in velocity per unit time; a = v/ time Units: m /s 2 (meters / second 2 ) Example, my acceleration is 10 m/s 2 Deceleration or negative acceleration is slowing down. Free fall: object falling due to gravity with no air resistance g = acceleration due to Earth s gravity g = 10 m/s 2 In free fall, the acceleration is always g. v = a t d = ½ a t 2 Distance Time Graph: Three objects Graphs comparing distance, velocity and acceleration.
Chapter 3 "Projectile Motion" Vector: a quantity with both a magnitude (size) and a direction. Usually depicted as an arrow in the direction indicated and the length of the arrow is proportional to the magnitude. Example: 20 mph (magnitude) north (direction) Scalar: only a magnitude; a number. Example: 20 miles/hour. Components: the vertical (y) part of a vector and the horizontal (x) part of a vector vertical component original vector horizontal component To solve for the original vector or components, use the Pythagorean Theorem: a 2 + b 2 = c 2 Special right triangles: 53 0 45 0 5 2 3 1 37 0 45 0 4 1 Resolution: breaking a vector into its vertical (y) and horizontal (x) components Vector Addition: adding together vectors to get a resultant (the answer in vector form) 1) Hook all the vectors together; head to tail 2)Draw the resultant (the answer) by starting from the tail of the first vector and ending at the head of the last vector + = resultant Projectile motion: the path of something shot into the air that is only acted on by gravity and air resistance. There is acceleration only in the y direction, which is 'g' due to gravity. The flight path for all projectiles is a parabola, time up = time down initial v y = final v y v x is constant throughout the flight v y at top of parabola = 0. For projectiles: With no gravity, objects would follow a straight-line path. With gravity, all objects - no matter what angle - fall below the straight-line path just For instance, objects fall beneath the straight-line path by 5 m after 1after 2 seconds, and so on. 45 = longest horizontal distance (range) 90 = highest vertical distance (height) Equations for projectile motion: In the horizontal (x) direction: no acceleration; v x = constant; d x = v x t In the vertical (y) direction: acceleration is always g = 10 m/s 2 ; v y = gt; d y = ½ g t 2
Chapter 4 "Newton's First Law of Motion - Inertia" Aristotle: believed that objects naturally wanted to move in a certain direction natural motion: the way an object will move on its own violent motion: forcing an object to move in the opposite direction to its natural motion earth & water: natural motion is down air (wind) & fire: natural motion is up Galileo: came up with idea of inertia in his inclined plane experiments forever Ignoring friction, a ball will keep rolling until it reaches its original height. A ball that rolls onto a flat surface will roll forever, trying to get back to its original height. Newton's First Law of Motion - Inertia: every object will stay in motion in a straight line at a constant speed or will stay at rest unless acted upon by a force. An object in motion stays in motion and an object at rest stays at rest, unless acted upon by an outside force. Mass is a measure of inertia: the more mass something has, the harder it is to change its speed (even in space!). Force: any pull or push on an object; forces can create acceleration (units are Newtons (N)) Net force: sum of all the forces acting on an object Examples of Forces: Friction: force due to contact/rubbing that always slows down an object Tension: a force usually applied through a rope or wire Support force (normal force): force that holds up a plate or book on a table Equilibrium: when all of the forces are balanced net force = 0 either at rest or moving at a constant speed (no acceleration) Weight vs. Mass: Weight: how heavy something feels (changes on different planets) units = N (Newtons) Mass: How much stuff is in something (amount of matter in an object: always stays the same) units = kg (kilograms) Weight = mass x gravity or w = mg (in units on earth: 10 N = 1kg x 10 m/s 2 ) Holding something with your arm straight out vs. your arm straight down It is harder to hold something out to the side, as opposed to straight down, because only the vertical component of the force holds the object up. When you hold something out to the side, you have to exert much more force because most of force in your arm is wasted in the horizontal direction.
Chapter 5 "Newton's Second Law of Motion - Force and Acceleration" Directly proportional: As one quantity increases, the other quantity increases. Example: The amount of force acting on a certain object from the gravity of the Earth at sea level is proportional to the object's mass, with the gravitational constant being the constant of proportionality. In simpler terms, the greater the mass, the greater the force of gravity. Inversely proportional: As one quantity increases, the other quantity decreases. Example: time at mall and money in pocket Example: the time taken for a journey is inversely proportional to the speed of travel; Newton's 2nd Law of Motion: F = ma or a = F/m Acceleration measured in m/s 2 Force measured in Newtons (N) Mass measured in kilograms (kg) Example: as mass on car increased, the acceleration decreased (inversely proportional) as force on car increased, the acceleration increased (directly proportional) Net force: sum of all forces Forces in opposite directions are subtracted Examples: 1. weight and air resistance 2. pulling force and friction Friction: The force that acts to oppose the motion between two materials moving past each other. Static friction: The resistance force that must be overcome to start an object in motion. Kinetic or sliding friction: The resistance force between two surfaces already in motion. Rolling friction: The resistance force between a surface and a rolling object. Fluid friction: The resistance force of a gas or a liquid as an object passes through. One example of fluid friction is air resistance. The force of sliding friction between two surfaces depends on the normal force pressing the surfaces together, and on the types of surfaces that are in contact with each other. The magnitude of this force is written as force of sliding friction = (Coefficient of sliding friction)(normal force) F f = F N Air Resistance: friction on object as it moves through air Pressure = Force /Area As area increases, the pressure goes down. As force increases, the pressure goes up. Units of pressure are Pascal (Pa): 1 Pa = 1 N /1m 2 Example of pressure: sharpness of knife blade and how well it slices Terminal velocity: the maximum velocity for a falling object. At terminal velocity: weight = air resistance, Net force = 0, Acceleration = 0, Constant velocity As speed increases, the air resistance increases. As surface area increases, the air resistance increases. As mass increases, the weight increases.
Chapter 6 "Newton's Third Law of Motion - Action and Reaction" Newton's 3 rd Law of Motion: For every action, there is an equal and opposite reaction. Essentially, Newton's 3rd law is the conservation of momentum. Example: Pushing off a skateboard. Example: Leaning against your locker. When you lean against your locker (action), your locker pushes back (reaction). If the locker did not push back with the same force, then the locker would buckle and break. Example: A Rocket. When a rocket fires out fuel at a high rate (action) the rocket moves forward (reaction). The forces are the same. Because the rocket has a much larger mass, it moves more slowly than the fuel. Chapter 7 "Momentum" Momentum = mass x velocity (p = mv) If a car is coasting and it loses its trailer, the car will speed up. Why? Less mass means greater velocity. If a person is rollerblading and they pick up their backpack as they coast by it, they will slow down. Why? Greater mass means less velocity. Impulse = force x time (J =F t Impulse causes a change in velocity. If the length of time in increased, then the force is smaller. Ex., air bags, cushions If the length of time is decreased, then the force is greater. Ex., moving into a punch, hitting a wall Bouncing: twice the impulse/force because the momentum changes twice The first change is to stop the object, the second change is to push it back. Law of Conservation of Momentum: the sum of the initial momenta = the sum of the final momenta Unless, there is an outside force acting on an object, momentum is conserved. Singular: momentum Plural: momenta Elastic collision: objects bounce off each other (m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f ) Ex: marbles, tennis balls Inelastic Collision Inelastic collision: objects stick to each other (m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f Ex: clay, football tackle
Chapter 8 "Energy" Work: work = force x distance (W = Fd) Units for work: Joule (J) You can only do work by moving an object in the opposite direction from where it wants to go. For instance, lifting something against gravity. Power: Power = work / time (P = W/t) Units for power: Watt (W) Energy: mechanical energy generally comes in two forms: kinetic and potential Kinetic Energy: KE = ½ mv 2 Kinetic energy comes from motion. Potential Energy: PE = mgh Potential energy is stored energy. Potential energy usually comes from lifting something against gravity. The relationship between work and energy is: If you do work on an object, then you add potential energy. Units for energy (same as work): Joule (J) Conservation of Energy: Energy can neither be created nor destroyed; it only changes form. The total energy is always conserved. Simple Machines There are 3 basic types of simple machines: inclined plane, pulley, and lever Work input = Work output With simple machines, there is always a trade-off. You apply a small force through a large distance to move a heavy object a small distance. Examples: car jack, pulley system, ramp for loading dock. Mechanical Advantage = F F output input = d d input output Useful work Effeciency = Total work output input = Ideal Mechanical Advantage Actual Mechanical Advantage
Chapter 9 Circular Motion Rotation vs. Revolution The point or line that is the center of the circle is the axis of rotation. If the axis of rotation is inside the object, the object is rotating (spinning). If the axis of rotation is outside the object, the object is revolving. Linear (tangential) speed vs. rotational (angular) Speed Objects moving in a circle still have a linear velocity = distance/time. This is often called tangential velocity, since the direction of the linear velocity is tangent to the circle. v Linear velocity of a point depends on: The rotational velocity of the point. More rotational velocity means more linear velocity. The distance from the point to the axis of rotation. More distance from the axis means more linear velocity Objects moving in a circle also have a rotational or angular velocity, which is the rate angular position changes. Rotational velocity is measured in degrees/second, rotations/minute (rpm), etc. Common symbol, (Greek letter omega) Centripetal Acceleration The acceleration of an object moving in a circle points toward the center of the circle. This is called a centripetal (center pointing) acceleration. The centripetal acceleration depends on: The speed of the object The radius of the circle a cent = v 2 /r Centripetal Force: Newton s Second Law says that if an object is accelerating, there must be a net force on it. IMPORTANT! There is no such thing as a "centripetal force"!!! When an object undergoes uniform circular motion there is a net force directed toward the center of the circle, but this force has a physical origin, such as gravity, the normal force, tension, or friction. For an object moving in a circle, this is called the centripetal force. The centripetal force points toward the center of the circle. Centripetal force on an object depends on: The object s mass - more mass means more force. The object s speed - more speed means more force The object s distance from the axis (radius) If linear velocity is held constant, more distance requires less force. If rotational velocity is held constant, more distance requires more force. Centrifugal Force - centrifugal force is a fictitious force - it is not an interaction between 2 objects, and therefore not a real force. Nothing pulls an object away from the center of the circle.
Chapter 12 "Universal Gravitation" m1m 2 Newton's Law of Universal Gravitation F grav = G (G = 6.67x10-11 Nm 2 /kg 2 ) 2 r m 1 and m 2 are the masses of the two objects r is the distance between the two objects (DO NOT CUT THIS DISTANCE IN HALF!) (This is a special form of the inverse square law a common math function.) An object has a gravitational attraction to every other object in the universe depending on its mass. The Earth pulls on the Moon and the Moon pulls on the Earth. The planets stay in a circular orbit because gravity provides the centripetal force. If there were no gravity, the planets would fly off in straight lines (along the tangent). Newton discovered that the same force that pulls an apple to the Earth keeps the Moon in orbit around the Earth. The Moon falls around the Earth because 1) it is pulled towards the Earth by gravity and 2) it is moving too quickly to hit the Earth. Because G is so small, the force of gravity is very weak.