Accelerated / Honors Physics Review Packet (for studying for the Midterm and Final Exams)

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1 Motion Graphs: Displacement: Δx = x 2 x Average Speed: s = d t Average Velocity: v = Δx t Average Acceleration: a = Δv t x- t graphs: slopes give velocities v- t graphs: slopes give accelerations while areas give displacements a- t graphs: area gives change in velocity Accelerated / Honors Physics eview Packet (for studying for the Midterm and Final Exams) Equations of Motion (only to be used of acceleration is constant): v 2 = + at v 2 2 = v 2 + 2aΔx Δx = 2 at 2 + t Δx = 2 t(v + v ) 2 x 2 = 2 at 2 + t + x (to be used in chase problems) Vectors: v pg = v pw + v wg (P: Plane, G: ground, W: wind) Projectile Motion: Throw ups / Come downs: ) Draw a picture, choose 2 critical points to work between 2) v top = 0 3) Δt up = Δt down and v throw = v catch (if thrown and caught at same height) Horizontal Projectiles (ex: ball rolls off table): ) Draw a picture, choose 2 critical points to work between, Set up two columns (x & y) 2) y = 0, a y = 9.8 3) Δx = v x t (since a x = 0 ) 4) Only t can cross between X & Y columns Angled Projectiles: ) Draw a picture, choose 2 critical points to work between, Set up two columns (x & y) 2) Break up initial velocity vector ( x = cosθ and y = sinθ ) 3) v top,y = 0, a y = 9.8 4) Δt top = Δt land and = v 2 sin(2θ) g and h = v 2 sin 2 (θ) 2g (on level ground)

2 Newton s Laws: st Law: An object in motion (or at rest) will remain in motion (or at rest) unless acted upon by an unbalanced, external force. 2 nd Law: F = ma 3 rd Law: For every action force there is an equal but opposite reaction force. W = mg F f = µf N g = 9.8 m/s 2 Lawnmowers (pushed downward): F cosθ F f = ma and F N = mg + F sinθ Wagons (pulled upward): F cosθ F f = ma and F N = mg F sinθ Inclines (sliding downward): W F f = ma and F = mgcosθ N and W = mgsinθ Atwood machine (2 masses hanging over a pulley): Mg T = Ma and T mg = ma and Mg mg = (M + m)a Box on table pulled across by a pulley with a mass hanging off the side of the table: T µmg = Ma and mg T = ma and mg µmg = (M + m)a Constant Velocity implies that: ) a = 0 2) FNET = 0 Work & Energy: W = F Δx (+ work is when F & Δx are in the same direction) Wagons (pulled at an angle): W puller = (F cosθ)δx and W friction = F f Δx and W total = ( F cosθ F f )Δx F- x graphs: area under the graph is work (+ area is + work, - area is work) Positive Work means energy was ADDED to the system (- work à energy is removed) KE = 2 mv 2 PE g = mgh Hookian Springs: F = kx (where k is the spring stiffness) and PE spring = 2 kx 2 Conservation of Energy: W = E 2 E = (KE + PE g + PE spring ) 2 (KE + PE g + PE spring ) Power: P = W t and P = Fv Block sliding down hill: (µmgcosθ)d = 2 mv 2 2 ( 2 m 2 + mgdsinθ) oller Coaster: 2 m 2 + mgh = 2 mv mgh 2 Loading the Pendulum: W = mg(l lsinθ) where h = mg(l lsinθ) comes from the pendulum pennant

3 Impulse & Momentum: p = mv FΔt = mδv = mv 2 m = Δp = p 2 p F- t graphs: area under the curve equals impulse O change in momentum Conservation of Momentum: bounce ( m v 2 ) i = ( m v 2 ) f stick ( m v 2 ) i = ( m )v f explosion ( m )v i = ( m v 2 ) f Elastic Collision: energy is conserved Inelastic Collision: energy is lost (objects move separately afterward) Perfectly Inelastic Collision: STICK, and energy is lost Minimum Separation (objects move at same speed momentarily at this moment): ( m v 2 ) i = ( m )v f and m vi2 2 + m v2i2 2 2 = (m + m )v f + kx E permant _ deform Circular Motion: a c = v 2 (inward) F c = mv 2 T = 2π and f = v T INS OUTS = F c = mv 2 car going around a flat turn: F f = F c µmg = mv 2 v = µg car going around a banked turn: frictionless: v = (tanθ)g and F N = mg cosθ g(tanθ + µ) max speed (before slipping upward): v = ( µtanθ) min speed (before slipping downward): swing ride (conical pendulum): v = g(tanθ µ) (+ µtanθ) T sinθ = mv 2 and T cosθ = mg v = (tanθ)g and T = mg cosθ and = lsinθ

4 Vertical Circles (ball on string): T mg = mv 2 T = mv 2 + mg (bottom, max Tension) mg + T = mv 2 T = mv 2 mg (top, min Tension) T = mv 2 (side) v = g (min velocity needed at top to complete circle) Loop- de- Loops: For cars/bikes, replace T in above equations with FN. For planes, replace T in above equation with either FN or FL. Woop- de- Doos: Bottom of Dip: F N mg = mv 2 Top of Hump: mg F N = mv 2 F N = mg + mv 2 F N = mg mv 2 # of g's = F N W = F N mg v = g (critical velocity before leaving ground Planetary Mechanics: a c = v 2, F = mv 2 c, T = 2π v, f = T F g = GMm 2 ( F g m, F g M, F g mm, F g ) 2 g = GM 2 ( g M, g ) 2 G = N m 2 Kepler s Laws: kg 2 st : Planets orbit in elliptical paths with sun at Focus 2 nd : planets sweep out equal areas in equal amounts of time (sling shot effect) 3 rd : K = 3 T 2 altitude = h = rplanet satellite equation(s): v = GM and a c = g

5 Static Electricity: m e = 9.E 3kg q = ±ne F e = kqq d 2 E = F e q E = kq d 2 PE E = qed PE E = kqq d (e =.602E -9C) (k = 8.99E9 m p =.67E 27kg N m2 C 2 ) (for a uniform electric field) (for the non - uniform electric field around a point charge) (energy stored in a UNIFOM electric field) (energy stored in a non - uniform electric field around point charges) ΔV = ΔPE E q ΔV = Ed (Voltage Difference O Electric Potential Difference) (Electric Potential Difference, or Voltage difference, in a UNIFOM electric field) Electric Circuits: Q = ne e = C I = Q t = V I or V = I = ρ L (where ρ is resistivity) A = o ( + αδt) (temp dependence of ) P = E t or P = IV or P = I 2 or P = V 2 SEIES CICUITS: current is the same through all resistors eq = and I = I = I 2 =... and V = V +V PAALLEL CICUITS: voltage is the same across each resistor Kirchoff s ules: eq = and I = I + I and V = V = V 2 =... ) The sum of the voltages around a closed loop is zero. 2) The current into a node equals the current out of a node.

6 Magnetism: F = qvb (charged particle moving through a B- field) F = B Il (force felt by a current- carrying wire) ΔV = Blv (voltage induced in a loop of wire where one end of the loop is moved through a B- field) ight- Hand- ules: o H Thumb (v), Fingers (B), Palm (Force felt by + charge) o H2 Thumb (I), Fingers curl in direction of B- field (around straight wire) o H3 Fingers (curl around coil in current direction), Thumb (point in direction of th field lines passing thorough the loop) Transformers o N s N p = V s V p = I p I s o Ideal T- former: P p = P s or I p V p = I s V s o Non- Ideal T- former: e = I s V s I p V p 00% Mirrors/Lenses: v = fλ f = + h and i = d i = M d o d i h o d o n = c v and n n sinθ = n 2 sinθ 2 and θ critical = sin 2 n Waves: v = fλ Young s Double Slit Experiment: o λ = xd or λ = dsinθ nl because x L = sinθ n λ = wavelength of light used (m) x = distance from central fringe (m) d = distance between the slits (m) n = the order of the fringe L= length from the screen with slits to the viewing screen (m) θ = angle between central fringe and the fridge being measured o n = 0 (Central Fringe), n = ( st order fringe), etc, etc, etc