Study guide PHYS201012
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This 7 page Study Guide was uploaded by Udbluehen03 on Sunday September 25, 2016. The Study Guide belongs to PHYS201012 at University of Delaware taught by Gogoladze,Ilia in Summer 2016. Since its upload, it has received 11 views. For similar materials see Introductory Physics I in PHYSICS (PHY) at University of Delaware.
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Date Created: 09/25/16
Significant figures - Multiplication or division o The number of significance is equal to the number of significant figure in the least accurately known quantity - Addition and subtraction o The number of decimal places after addition or subtraction is equal to the smallest number of decimal places in any of the individual terms. Problem Solving in Physics; here are some guidelines: 1. Read the problem carefully 2. Sketch the system 3. Visualize the physical process 4. Strategize 5. Identify appropriate equations 6. Solve the equations 7. Check your answer 8. Explore limits and special cases Mechanics - The study of how objects move, how they respond to external forces, and how other factors, such as size, mass and mass distribution, affect their motion - This time we treat all physical objects as point like particles Position - Coordinate System o Defines an origin, a positive direction (orientation) and a unit of length o Uses one or more numbers to uniquely determine the position of a point Earth is three dimensional (length, width, and height) Space-time is four dimensional o A Cartesian Coordinate System Specifies a location on a point relative to a fixed reference point - Initial position =x i - Final position = x f Distance - The total length of travel - SI unit: meter, m - Always positive - Scalar, because it has no direction Displacement - The change in position = final product – initial position - Δx = x - x f i - SI unit: meter, m - Can be positive, negative or zero - A vector Speed - Is described as the distance covered per amount of travel/time - Speed = distance covered/travel time - (m/s) - Always positive - When we know both speed and direction of an object we know its velocity Average Speed and Velocity - The average speed is defined as the distance traveled divided by the time the trip took o Average speed = distance/elapsed time - Average velocity o Displacement/elapsed time Δx x −x = f i o Vav = Δt tf−ti o SI unit: meter per second, m/s - If you return to your starting point, your average velocity is zero.Instantaneous Velocity lim Δx - V = Δt→ 0t - SI unit: meter per second, m/s - Tangent of the curve Acceleration - Acceleration Is the rate at which velocity changes with time. The change in velocity may be in magnitude, in direction, or in both - Acceleration = change in velocity/time interval Δv vf−vi - aav= = Δt tf−ti - SI unit: meter per second per second= m/s 2 - When the velocity and acceleration of an object have the same sign, the speed of the object increases o The velocity and acceleration point in the same direction - When the velocity and acceleration of an object have opposite signs, the speed of the object decreases o The velocity and acceleration point in the opposite directions. o Deceleration Instantaneous Acceleration ΔV - a = lim Δt Δt→ 0 2 - SI unit: m/s Constant Acceleration Equations of Motions Variables Related Equations Velocity, time, acceleration V=V +0at Initial, final, avg velocity Vav = ½(V +0) Position, time, velocity X = X 01/2(V +V)0 Position, time, acceleration X =X 0 V t 0(1/2)at 2 Velocity, position, acceleration V = V +02a(X-X0) = V 0 + 2aΔx Scalar - A scalar quantity is completely specified by a single value with an appropriate unit and has no direction o Can be positive (speed), negative, and a direction (temperature) o Length, area, volume, speed, mass, density, temperature, energy, work, power Vector - A mathematical quantity with both a magnitude and a direction - Cannot have more than three components - Displacement, direction, velocity, acceleration, momentum force, lift, drag, weight Equality of two Vectors - Two vectors are equal if they have the same magnitude and the same direction. - If |A| = |B| and they point along parallel lines Adding Vectors - Vector addition is very different from adding scalar quantities. - When adding vectors, their directions must be taken into account. - Units must be the same - Two ways to add vectors o Graphically Tip to tail or head to tail The resultant is drawn from the origin of the first vector to the end of the last vector When you have many vectors, just keep repeating the process until all are included o Algebraic More convenient - When two vectors are added, the sum is independent of the order of the addition. This is the Commutative Law of Addition. o A+B=B+A - When adding three or more vectors, their sum is independent of the way in which the individual vectors are grouped. This is called the Associative Property of Addition. ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ o A+(B+C)+(A+B)+C Components of a Vector - A component is a projection of a vector along an axis. o Any vector can be completely described by its components Ax+Ay A - are the component vectors of o They are vectors and follow all the rules for vectors. Ax+Ay A - are scalars, and will be referred to as the components of A x+A y2 - A = √ Ay - θ = tan ( ) Ax - Ax = A cosθ - Ay = A sinθ - The components can be positive or negative and will have the same units as the original vector - The signs of the components will depend on the angle Multiplying Vector - Multiplying vectors by scalars o the multiplier changes the length, and the sign indicates the direction Adding Vectors Using Components - Find the components of each vector to be added. - Add the x- and y-components separately. - Find the resultant vector Subtracting Vectors - The negative of a vector is a vector of the same magnitude pointing in the opposite direction. - D=A−B ⃗ Unit Vectors - A unit vector is a dimensionless vector with a magnitude of exactly 1 - Unit vectors are used to specify a direction and have no other physical significance - Provide a convenient way of expressing an arbitrary vector in terms of its components - Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown near the surface, and it moves along a curved path under the action of gravity only . Projectile Motion – Problem Solving Hints - Conceptualize o Establish the mental representation of the projectile moving along its trajectory. - Categorize o Confirm air resistance is neglected. o Select a coordinate system with x in the horizontal and y in the vertical direction. - Analyze o If the initial velocity is given, resolve it into x and y components. o Treat the horizontal and vertical motions independently. - Analysis o Analyze the horizontal motion with the particle-under-constant- velocity model. o Analyze the vertical motion with the particle-under-constant- acceleration model. o Remember that both directions share the same time. - Finalize o Check to see if your answers are consistent with the mental and pictorial representations. o Check to see if your results are realistic
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