PHYS 1501Q 1st Edition Exam # 1 Study Guide Lectures: 1-17 Outline of Exam Material I. 1-D KinematicsII. 2-D KinematicsIII. Relative and Circular MotionIV. Newton’s LawsV. Forces and Free Body DiagramsVI. FrictionVII. Work and Kinetic EnergyVIII. Conservative Forces and Potential EnergyIX. Work and Potential EnergyI. 1-D Kinematics- Displacement x(t)- Velocity v(t) ¿dx(t)dtVelocity is the time rate of change of displacemento Average velocity v = Δx/ Δto Instantaneous velocity dx(t)dt- Acceleration a(t) ¿dv(t)dtAcceleration is the time rate of change of velocityEquations for Motion at Constant Acceleration:- Position after a given time:o R = Ro + Vot + ½ at2- Find change in velocity, change in time, or acceleration o Vf = Vo + a(t-to)  or V = Vo +at- Find displacement as a function of timeo X = Xo + Vot + ½ at2- Displacement as a function of velocityo 2a(X- Xo) = V2-Vo2These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.II. 2-D KinematicsAdding Vectors- Must have same units- Place tail of one vector to head of other vector. Draw a line connecting the disconnected head and tail. That line is the sum of the 2 vectors.o Commutative PropertyA + B = B + Ao Associative Property(A + B) + C = A + (B + C)Vector Subtraction Visually- Must have same units- Must reverse direction of vector being subtracted. You can do this by flipping it 180 degrees or by multiplying it *(-1)- It’s the same as adding A + (-B)- A vector minus itself is zero B + (-B) = 0Vector Multiplication Visually (Scalar)- Multiplying a vector by a scalar changes the magnitude (length)- When multiplying you just add the vector to itself- Doesn’t change directionVectors on a Coordinate SystemA = magnitude (length)Θ = angle with respect to x-axisAx = AcosΘ (x-component)Ay = AsinΘ (y-component)Note if Not Visual:1. Break vector into x, y, z components or I, j, k components2. Add/subtract each vector’s same components (a+b)I + (a+b)j +(a+b)k3. Multiply each element in vector by scalar4. Multiplying different unit vectors makes them zero, multiplying the same makes 1a. Ex) i*I = 1 BUT i*j = 0III. Relative and Circular Motion- Relative MotionRelative motion is the calculation of the motion of an object with regard to some other moving object or frame.- Reference Frame- Surroundings which are perceived to be at rest- Motions are universally agreeable in a reference frame- Interpretation of motion depends on reference frameo Inertial Reference FrameNon accelerating reference frameVectors are related by vector additionAssume Frame B moves at constant velocity VBA with respect to A.Position of PRPA in frame ARPB in frame BRBA = Position of B with respect to A Vector AdditionRPA=RPB+RBA(Bs cancel out)Uniform Circular Motion / Centripetal Acceleration- Velocity is constant- Involves acceleration EVEN THOUGH velocity is constanto Why?Velocity is composed of magnitude and direction. The magnitude is constant but the direction is changing as it always points to the center of the circle.AKA CENTRIPETAL ACCELERATIONA=V2RIV. Newton’s LawsNewton’s First Law- An object maintains its velocity if no net force acts on it- This applies to objects at rest (v=0) and objects moving at constant velocity- A force does NOT have to be applied to KEEP an object in motionNewton’s Second Law- Fnet = ma (force and acceleration are vectors)- Fnet is the sum of all external forces acting on a body- If F=0  a=0 V= constant or 0- When a force acts on an object it makes it accelerate in the same direction as the force- MASS – determines the magnitude of the acceleration- FORCE – determines the direction and the cause of accelerationNewton’s Third Law- For every action, there is an equal and opposite reaction-FAB=FBA- Forces are never isolated and always come in pairs- Note FAB means the force exerted on A by BSteps of Applications of Newton’s Laws1. Draw a picture of the system2. Focus on one object at a time3. Draw a free body diagram showing all forces acting on each object4. Choose a coordinate systema. Put one force parallel along an axis5. Apply Newton’s second law to each component in the system. The sum of all forces must equal mass* acceleration6. Include constraints7. Solve component equations for unknowns8. Check limiting casesV. Forces and Free Body Diagrams- Forces: weight (mg), tension (T), push, normal (N), friction (f), spring (Fs)- Free body diagrams: on free body diagrams , arrows represent forceo Arrow at end represents the direction of the forceo Length represents the magnitudeo Acceleration is NOT a force- Spring force F = -k(X-Xo)- Universal gravitation: -G*m1m2/r^2  2 bodies attract each otherVI. FrictionStatic Friction- Occurs when surfaces are not sliding- The coefficient of static friction is μS- f </= μS∗N (friction is the coefficient of static friction times the Normal force)Kinetic Friction- Occurs when surfaces are sliding- Coefficient of static friction is μK- f = μk∗NμS>μk ALWAYSf is parallel to the surface and perpendicular to NI. Example: Friction with Inclined PlaneA mass is on an inclined plane with friction1) At what angles will an object go from being stationary to sliding?2) What is the acceleration?X component: f – mgsinθ = ma = 0 (box is not sliding)Y component: f – mgcosθ =ma = 0 (always zero because box never jumps off ramp)Max friction force before slippage: f = μsNμsN= mgsinθ for max θμs(mgcosθ)= mgsinθ  cancel mg out to becomeTanθ=μsVII.Work and Kinetic Energy- Kinetic Energyo ½ mv2- Worko W=Fdcosθo W=Fd for constant force- Dot producto AxBx +AyBy+AzBz = scalaro OR ABcosθ (where A and B are the length of the vectors A and B and θ is the angle between them)- Work Kinetic Energy Theoremo W=ΔK (work is equal to the change in kinetic energy)- Work Done By Springo Fs= - kx  Ws = ½ kxi2 – ½ kxf2- Work Done By Gravityo W = mgΔyVIII. Conservative Forces and Potential Energy- Conservative Forcei. Work done is independent of path only depends on starting point and ending points- Conservative forces are spring force and gravity - U = potential energy = stored energy- Gravity potential energy: U=mgh (h is height)- Spring = ½ kx2- Conservative forces  w= -ΔU - Conservation of energy:i. Ki + Ui = Kf + UfMeaning energy is not lost, the initial kinetic + potential is equal to the final kinetic + potential energy – although the