⋆ there is a net force: 4 Conservation of momentum
⋆ p⃗ = p⃗ ′ : momentum is conserved (in an isolated system ⇒ no external net force on the object i.e. no/negligible friction)
5 Conservation of energy
⋆ ⋆ ⋆ ⋆ ⋆
Elastic: Eki = Ekf only for quantum collisions Inelastic: Eki ̸= Ekf for “large-scale” collisions (deformation/friction ⇒ thermal energy loss) Energy is a scalar so ignore direction and angles Units are Joules := J = kg·m/s2 1 1 1 1 ′2 ′2 2 2 2 m1 v1 + 2 m2 v2 = 2 m1 v1 + 2 m2 v2
Conservation of momenum (p ⃗ ) in 2 dimensions
{ } horizontal vectors px = p′x • Divide the question into then use vertical vectors py = p′y Conservation of momentumt (p ⃗ ) in 1 dimension
m1 v1′
• Masses rebound:
m1 v1 + m2 v2 =
• Stick together:
m1 v1 + m2 v2 =
+ m2 v2′ (m1 + m2 )v ′
p py
θ px
The “=” sign is the event; the number of objects determines the number of “mv ” terms. 0 = m1 v1 + m2 v2
• Explosion:
Impulse—change in momentum (∆p)
⇒
• F⃗ ∆t = m∆⃗v
N·s ≡ kg·m/s2
⋆ used to calculate forces in a collision ⋆ time of collision affects forces; increase interaction time to decrease force + − ⋆ impulse is a vector quantity so direction matters: ⋆ F
Area under an F -t graph is impulse F ∆t ; use A = l · w and/or A = 12 bh t
Two masses in a collision
• Both experience… ⋆ same F⃗ ⋆ same impulse ∆⃗ p ⋆ different ∆⃗v (if masses are different)
Physics 30—Unit 2 Review: Electric & Magnetic Forces & Fields ....................................................................................................... Electrostatics
• • • •
only e- move within insulators charges accumulate on the outside of conductors as well as on irregular surfaces Law of Charges: like repel, opposite attract charging occurs through friction, contact (conduction), and induction (with grounding)
Electric energy
• E = V q and E = 12 mv 2 ⋆ V := potential difference in volts with units J/C ⋆ ∆V = Vf − Vi Electric force
• Coulomb’s law Fe =
kq1 q2 and Cavendish’s torsion experiment r2
⋆ use vector diagram’s to find direction:
,
, or
Electric field
• direction defined by direction a small positive (+) test charge travels when placed in the field • magnitude given by: kq ⃗ = ⋆ |E| for a charged object r2 ⃗ |E| ⃗ = Fe for a charged object ⋆ |E| q r } ⃗ = V for electric plates constant between plates ⋆ |E| d Trajectory questions e-
−
−
−
−
−
−
•
horizontal: d v= t
vertical:
d = vi t + 21 at2 F = ma
+
+
+
+
+
+
⃗ = |E|
Fe q
Milikan’s oil drop experiment
• electric force overcomes gravitational force
⋆
Fe = Fg ⃗ = mg |E|q
or
Fe = Fg ± Fa ⃗ = m(g ± a) |E|q
⃗ |E|
slope = qe- = 1.6 × 10−19 C
mg
Magnetic field
⃗ and units of teslas (T) • symbol B ⋆ direction defined as the direction the north end of a compass needle points (N seeks S) Magnetic force
• symbol F⃗m ⋆ for a charged particle: Fm = qvB⊥ ⋆ in a wire: Fm = IℓB⊥ Direction of force/field/current (Hand Rules)
⋆ frequency is constant; colour linked to frequency Dispersion
• Different colours experience different amounts of refraction, so white light disperses into ROYGBV. ⋆ Red refracts through the smallest angle, violet refracts through the largest angle Speed of EMR
d and v = λf t d • Michelson’s Rotating Mirror: v = t • v=
2d (there and back) f −1 ÷ # of sides on mirror
⃗ → ∆B ⃗ → ∆E ⃗ → ∆B ⃗ → · · · at c and everything is mutually ⊥ • ∆E Mirrors & lenses
•
1 1 1 = + f di do 1 1 1 ⋆ For graphing: =− + ⇔ y = mx + b di d f { } {o } + real + upright ⋆ di hi − virtual − upside-down hi di ⋆ M= =− ho do
• Concave mirror • Convex mirror
Converging Lens Diverging Lens
: Converging, f + : Diverging, f −
real, enlarged, upside-down
no image
virtual, enlarged, erect
f always virtual, diminished, and erect
Wave model
• Every point on a wave may be considered a secondary source of spherical wavelets which spread out as the wave travels (Huygens) ⋆ Newton’s Rings and Poisson’s Bright-spot ⋆ Polarization – horizontal and vertical slits (plane-polarization of light) ⋆ Diffraction – the bending and spreading out of EMR around edges or openings – the effect is greater if the opening is close to the wavelength of EMR ⋆ Interference – constructive/bright lines/antinodes – destructive/dark bands/nodes Quantum model
• EMR has mass like (particle) properties ⋆ Energy (Einstein & Planck) hc – E = hf = λ ⋆ Momentum (Compton) h – p = and E = pc λ e-
–
∆λ = θ
h (1 − cos θ) mc mass of escattered X-ray has larger λ
◦ can also do a 2-D momentum analysis ◦ can also use energy as quantum collisions are elastic ⋆ Photoelectric Effect EEMR = Ee- + W –
• Thomson—rasin bun model ⋆ calculated the charge-to-mass ratio ⋆
Fm = Fc mv 2 qvB = r
• Millikan—oil drop experiment ⋆ calculated the e- charge
⋆
Fe = Fg
mg
slope = q
|E|q = mg |E|
• Rutherford—planetary model ⋆ scattering experiments showed the nucleus is small and positive Fe = Fc ⋆ kqq mv 2 = 2 r r • Maxwell—problem with planetary model ⋆ e- within atoms are accelerating (centripetal motion) and thus should give off EMR and collapse into the nucleus. • Bohr—electrons can orbit certain energy levels without emitting EMR e-
⋆ e- only release or absorb energy when changing orbitals
e-
• Compton Effect—EMR has momentum h h ⋆ p = , E = pc , ∆λ = (1 − cos θ) λ mc • de Broglie λ—electrons travel with a whole number of λ around the nucleus h h ⋆ p = p ⇒ mv = ⇒ λ= λ mv • Standard Model ⋆ Fermions [matter] Leptons
e- and ν
⋆ Bosons (mediating particles) [forces] Hadrons
Mesons quark with antiquark
Baryons 3 quarks: p+ (uud) n0 (udd)
Force
Particle
Strong Nuclear
gluon
Weak Nuclear
W + , W − , Z0
Electromagnetic
photon
Gravity
graviton
Duality Particles
EMR
• has mass
• no mass
• can have a charge
• no charge
• has momentum p = mv
• has momentum p = h/λ or E = pc
• has energy E = 12 mv 2 or E = V q
• has energy E = hf = hc/λ
• follows a circular or parabolic path in electric and magnetic fields
• not effected by |E| or B
Mass spectrometer
• velocity selector—particles pass undeflected through ⊥ |E| and B ⋆