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PHYS 2001 (1)

physics 2001 notes

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PHYS 2001
Kenneth Nollett

8/27/2013 1. Standards and Units a. Use S. I. system i. Second ii. Meter iii. Kilogram b. Use scientific notation i. 3e8 = speed of light ii. 1e-10 = x-ray length iii. E for computer, superscript for anything else c. Can’t add/subtract different units d. Can always multiply by one i. Use it to cancel unitsstoichiometry e. Look at given conversions!!! f. Watch positive vs. negative exponents i. Watch ALL exponents ii. Negative exponents mean inverseput in denominator iii. 1 m/s = 1mse-1 g. Dimensional analysis i. Dimension means type of quantity 1. Length 2. Mass 3. Time ii. Can be built from simpler dimensions 1. Velocity = length/time iii. Things being added/subtracted must be in same dimension iv. Use multiplication/division to change dimensions v. Sig figs- preciseness of measurement determined by preciseness of instrument 8/29/13 2. Formulas a. a=f/m acceleration is inversely proportional to mass b. A=pi(r^2) c. Trig formulas i. A^2+b^2=c^2 ii. S=o/h iii. C=a/h iv. T=o/a v. S-1A = angle means the angle that gives a=sin(angle) 3. Scalars and Vectors (size = magnitude) a. Scalars i. Magnitude only: time, mass, $ ii. Use basic math, abs. value so no neg. values iii. For 2 scalars to be equal, they must have equal magnitude b. Vectors i. Have magnitude and direction: force, displacement, velocity ii. If it makes sense to put a direction, it’s a vector iii. When doing math, must include directions (use trig!) 1. Vector + or - vector=vector, A+ or -B=R 2. Scalar x vector = vector 3. -1 (vector) = vector in opposite direction 4. Can add any # of vectors by placing tail-to-head 5. Easiest if parallel/antiparallel 6. Semi-easy if perpendicular 7. If not any of the above, break into x and y components iv. 2 vectors are equal if same magnitude and direction 9/3/2013 v. Adding vectors by components 1. Break all vectors being added into components 2. Add all x components 3. Add all y components 4. Find magnitude & direction using trig 4. Kinematics a. Mathematical description (NOT explanation) of motion i. Dynamics (considering forces) includes description of what causes motion b. 3 quantities (all vectors) describe all motion: displacement, velocity, acceleration i. Displacement: change of position 1. NOT the same as distance traveled (path doesn’t matter here0 2. Avg. speed = distance traveled/elapsed time a. No direction scalar ii. Velocity: how fast displacement is changing 1. Avg. velocity = displacement/elapsed time 2. Speed is absolute value (scalar) of velocity iii. Acceleration: how fast velocity is changing 1. Acceleration goes the same direction as CHANGE in velocity a. Can be in different direction than velocity itself 2. Always related to a force c. 4 kinematics equations i. V final = v initial +at ii. X = ½(v initial +v final)(t) iii. X = v initial (t) + ½ a(t^2) iv. V final ^2 =v initial ^2 +2ax 5. Slope of a function on a graph a. ALWAYS CHECK AXIS LABELS!!! b. Slope is how fast the height changes as you move right i. Rise/run ii. How steep? c. Up to rightpositive slope d. Down to rightnegative slope e. Straight line has same slope everywhere, curved line=changing slope i. Slope at 1 point is slope of tangent line f. When finding slope, use longest possible part of line g. Position vs. time graph i. Shows displacement ii. Slope is velocity h. Velocity vs. time graph i. Shows velocity ii. Slope is acceleration iii. Area under is displacement 6. Average vs. Instantaneous values a. Average, interval from beginning to end “events” i. Any given event has a time, location, velocity, and acceleration ii. Use 0 for initial time and distance b. Instantaneous-at a given instant i. Smallest possible t 9/5/13 7. Constant acceleration a. Constant net forceconstant acceleration b. Change in x = v(change in t) c. Change in v=a(change in t) d. If a is constant, average acceleration equals instantaneous acceleration e. Deceleration = a going opposite to v 8. Problem solving a. Read the problem & figure out the story b. Draw out a diagram i. Lay out coordinate system ii. Always convert units c. What is known/unknown i. What are you looking for d. What are the relevant equations/rules e. Solve problem 9. Free fall a. An object is in free fall when the only force acting on it is gravity i. An object going upward CAN be in free fall b. Near earth’s surface, gravity causes all objects in free fall to accelerate at 9.8 m/s^2 c. The magnitude of the gravitational acceleration (g) can be either direction i. Decide which way (up/down) is positive/negative d. G depends mainly on distance from center and mass of earth i. Difference on space station (greater distance) ii. Different on moon (different mass) 9/10/2013 10. Implied conditions a. Max height-figure out implications for velocity b. Use “just after” and “just before” to avoid complications c. Up, down, east, west, etc. determine coordinates and signs d. Look for connections between parts of a problem to help find variables 11. Kinematics in 2 directions a. A 2-d problem can simplify into 2 1-d problems i. Break the motion into x and y components ii. Time will be the same for both b. Velocity is tangent to trajectory i. Points in direction of instantaneous motion c. Same equations as 1-d motion, but twice i. Once with x once with y ii. Emphasize that the quantities are VECTORS since now in 2-d d. Make sure to pick which way is +/- 12. Projectile motion:2-d free fall a. In free fall, gravity is only forcey acceleration is 9.8 m/s^2 down b. If y axis is chosen as vertical (usually is), then ax=0 m/s^2 ay=9.8 m/s^2 down c. The motion of a projectile can be broken into x and y components i. Vertical and horizontal are separate ii. Dif. horizontal components don’t matter for vertical motion 9/12/2013 13. Intro to forces a. Equilibrium i. Forces balanced  a =0 ii. AKA if a= 0, the forces are balanced b. Weight means force due to gravity Fg=mg c. Force is a vector if forces are balanced, x and y are balanced in their own rights 14. Projectile motion is symmetric a. Same y = same absolute vy b. w/out air resistance, v has the same magnitude up and down i. but with opposite sign c. speed=magnitude of velocity 9/17/13 15. Free body diagrams a. Used to keep track of forces acting on an object b. Forces the object is inflicting on other objects are not included c. Gives visual, helps keep track of directions d. Procedure: i. Draw the object as a dot or small square ii. Draw and label an arrow for each force acting on the object, approx. to scale 16. Newton’s laws a. 1 law of motion: An object maintains constant velocity (can be zero) unless there is a change in net force i. Net force= sum of all forces on an object ii. 0 net force can mean all forces cancel, rather than no force period iii. “an object in motion will stay in motion, an object an rest will stay at rest unless acted upon by an outside force” nd b. 2 law of motion: When a net external force acts on an object with mass m, the acceleration that results is directly proportional to the net force on the object and has a magnitude inversely proportional to the mass i. F=ma, a = Fnet/m ii. Inertia = object’s tendency to resist change in motion iii. Mass measures inertia, S.I. units are kg c. 3 law of motion: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body i. Occur simultaneouslynot a reaction ii. All forces come in pairs iii. The two forces act on different objects, not the same one d. Law of universal gravitation: every object in the universe attracts every other object i. Gravitational force between objects is along a straight line between them ii. Magnitude depends on mass and proximity iii. F=G(m1m2/r^2) 1. G is newton’s constant 2. R is the distance between the objects’ centers iv. g at earth’s surface = 9.8Fg=mg v. weight means force applied by gravityperson weighs less on mount Everest that at dead sea b/c more distance between centers 17. Fundamental forces a. Electroweak force i. Electricity ii. Magnetism iii. Weak nuclear (nuclear decay) b. Strong nuclear force-holds atomic nuclei together c. Gravitational force i. Projectile motion ii. Orbits d. Ultimately, all are “action-at-a-distance” forces, no matter how small the distance, but most can be treated as contact forces 9/19/2013 18. Forces review a. The net force is proportional to acceleration, i. as stated by Newton’s 2 law b. Gravitational force AKA weight is proportional to mass 19. Forces cause by surfaces a. Force perpendicular to surface: normal i. The equal and opposite force of Newton’s 2 law ii. Keeps things from passing through each other iii. What is perceived as weight is really the normal force of the floor 1. This is what is read on a scale iv. Fn=mg+may b. Force parallel to surface: friction i. Tries to stop things from slipping against each other ii. Always acts in direction to stop/prevent motion iii. Strength determined by normal force and acceleration 1. Depends on if surfaces are already slipping or not a. If they are: Kinetic friction, Fkf=msFn b. If not: Static friction, Fsf is less than/equal to msFn c. Fs > fk d. M’s are muse 2. Ms and mk are determined by the materials 3. Ms is only enough to balance the other forces, not overcome them 20. Tension force a. Acts on hanging objects b. No normal force because no surface contact c. Tension restricts motion instead i. T-mg=may ii. Fn>weight, acceleration is upFn-Fg=may>0 iii. Fn
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