Physics Final

• powers of ten
• mult- add exponents
• div- subtract exponents
• powers- multiply exponents

• MKS
• length- meters
• mass- kilograms
• time- seconds

• w/ decimal- atlantic
• w/o decimal- pacific
• adding/subtracting- smallest decimal place
• multiply/dividing- smalles # of sig figs

• x - independent variable
• y - dependent variable

• Δy/Δx
• slope=mx+b
• y-intercept- b=y₂-mx₂

• magnitude
• direction

• a # can be - or +
• ex) time, age, temp

• dots closer = slower
• dots farther apart = faster

• V_avg= Δx / Δt
• displacement over time

• d=V_it+1/2at²
• V_f=V_i+at

V_f²=V_i²+2aΔx

• d=V_it+1/2at²
• V_f=V_i+at
• V_f²=V_i²+2aΔy

forces that cause motion

• "Law of inertia"
• an object at rest stays at rest
• an object in motion stays in motion

act sto change an objects velocity

F_net=ma [N]

• F_g
• attracts
• between masses

• F_N
• perpendicular force between surface and objects resting or moving along it

• F_f
• parallel force btwn two objects that oppose relative motions

• if object on surface moving
• f_k=µ_kF_N
• µk=coefficient of kinetic friction

• if object on surface @ rest
• f_s=µ_sF_N

• F_t
• pulls by massless "string"

• F_e
• attractive or repulsive
• btwn charges

• "law of action and reaction"
• a=F_net/m

• kinetic (motion)
• potential (spring)
• energy is neither created nor destroyed
• E=KE+PE
• KE_i + PE_i = KE_f + PE_f

• KE = 1/2mv²
• KE is scalar
• measured in joules [J]

• ΔKE=KE_final - KE_initial [J]
• W_g=-ΔPE_g
• work done against gravity = mgΔh

• F_s=kx
• PE_s=1/2kx²

PE_g=mgΔh

• mgh_i + 1/2mv_i² = mgh_f + 1/2mv_f²--->
• V_f² = V_i² - 2g(h_f -h_i)
• use in roller coaster examples

• P = work / time [J/s]
• P_avg = F * V_avg

• P = mv [kg * m/s]
• P_f = P_i
• collision of two objects:
• P_1i + P_2i = P_1f + P_2f
• P_T = m₁v₁ = m₂v₂

• change in linear momentum
• =ΔP = Δ(mv)
• F_net = ma = m(Δv/t)
• ΔI = F_net * Δt

• momentum and KE is conserved
• P_f = P_i
• KE_f = KE_i
• for 2 body system:
• 1/2mv_i1² + 1/2mv_i2² = 1/2m_iv_f1² + 1/2m₂v_f2²

• see distorting and heating
• completely inelastic = stick together:
• V_1f = V_2f = V_sysf
• V_f = m₁v_1i + m₂v_2i / m₁ + m₂

• F = (Gm₁m₂) / r²
• G = 6.67 X10^-11
• near the earth- F = (GM_E) / r_E²

• field is strong when lines are closer together
• trajectories of a test charge
• field describes the property of space around one object

• nucleus = protons and neutrons
• electrons orbit nucleus
• fundamental unit of charge - e = 1.6 X10^-19
• neutron = 0

• lFel = (k lq₁l lq₂l) / r²
• k = 8.99 X10⁹ [N * m²/c²]

neg. rod close to top = pos. atoms and the negatively charged particles repel

neg. rod touches ball, share electrons, bring it back and they repel

• E = F / q [N/C]
• positive - go out
• negative - go in
• E = (k lql) / r²

• field lines are perpendicular to PE lines
• PE_e = kq₁q₂ / r
• V = kq / 2 [volts]

• parallel plate capacitor: uniform electric field inside
• F = -= ΔPE/Δx = qΔV/Δx = qE ->E =-ΔV/Δx

I = Δq / Δt

the direction in which the positive charges flow

W = ΔPE = qΔV = ΔqE -> P = IV

• R = ρ (L/A)
• ρ - resistivity of material
• L - length of wire
• A - cross sectional area = ∏r²

V = IR

• P = W/Δt =ΔqE/Δt = IE
• P = IV = I²R = V²/R

• I = I₁ = I₂ = I₃
• V = V₁ + V₂ + V₃
• R_eq = R₁ + R₂ + R₃

• I = I₁ + I₂ + I₃
• V = V₁ = V₂ = V₃
• 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

• P₁ = I₁V₁
• P₂ = I₂V₂
• P_T = P₁ + P₂
• P_T = I_TV_T

• P_T = I_TV_T
• P₁ = I₁V₁
• P₂ = I₂V₂
• P_T = P₁ + P₂
• power = E/t

• two charges
• flow from a postive charge to a negative charge

• N = out
• S = in

• F = qVB
• q = charge
• V = velocity
• B = magnetic field
• right hand rule:
• palm = B
• fingers = V
• thumb = force
• ( x= in, ∙ = out )

• force on a current carrying wire- F = ILB sinƟ
• magnetic field created- B=µ_iI/2∏d
• right hanf rule:
• thumb- direction of current
• fingers- wrap in direction of field (B)

• thumb- direction of field
• fingers- current
• B = µ_iIN/L
• mag B = Nµ_iI/2R

changing current and B_field in the primary induces a changing B_field and current in the secondary

• power is the same in both circuits
• V_p/V_s = I_s/I_p
• V_p/V_s = N_p/N_s
• I_s/I_p = N_p/N_s

oscillates perpendicular to direction intensity of the light ray/wave

• for light- c =λf
• speed of any wave - V = λf

• source moving towards observer:
• f_obs > f_source , λ_obs < λ_source = blue shift
• source moving away from observer:
• f_obs < f_source , λ_obs > λ_source = red shift

angle of reflection is = to the angle of incidence

• image is upright
• image is same size
• image is virtual
• h_i = mh_o
• m = -d_i/d_o

• d_o>c>f
• form a real image
• inverted
• smaller
• c>d_o>f
• real image
• inverted
• larger
• c>f>d_o
• virtual
• upright
• larger

• virtual image
• upright
• smaller

• V = c/n
• less dense to more dense->closer to normal

• n₁sinƟ₁ = n₂sinƟ₂

• n₁>n₂, if Ɵ "too big" ->total internal reflection
• critical angle = sin^-1(n₂/n₁ * sin 90)

• either a real or a virtual image
• double convex or plano convex

• only virtual images
• double concave
• plano concave

• d_o > f
• real
• inverted image
• f>d_o
• virtual
• upright image

• d_o > f
• upright
• virtual image
• f>d_o
• upright
• virtual image

• 1/f = 1/d_o + 1/d_i
• m = -d_i/d_o

• = 1/f
• two lenses:
• d_effective = d₁ + d₂
• f_eff = 1/d_eff