Physics 30 Unit 1 Review: Conservation of Momentum & Impulse

Physics 30—Unit 1 Review: Conservation of Momentum & Impulse ............................................................................................
Author: Mark Gaines
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Physics 30—Unit 1 Review: Conservation of Momentum & Impulse ....................................................................................................... Physics principles 0 Uniform motion (F⃗net = 0)

⋆ no acceleration = constant speed v =

d t

= zero net force:

1 Accelerated motion (F⃗net ̸= 0)

⋆ 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)

⃗ around wire (Oersted) • B current in wire

⃗ B

magnetic north

current

• Solenoid

• Force

⃗ B ⃗m F

current in wire

Circular Path



Fm = Fc mv 2 qvB = r

Lenz’s Law

• Fm opposes direction of motion

                                            

⋆ For negative charges/current (electrons), use your LEFT HAND; ⋆ For positive (conventional) current, use your RIGHT HAND.

Physics 30—Unit 3 Review: EMR as Wave & Particle ....................................................................................................... Reflection



θi

θr

θi = θr

θ1

v1 λ1 n2 sin θ1 = = = sin θ2 v2 λ2 n1

Refraction



θ2

⋆ 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 –

eW

hf or

hc λ

1 2 2 mv

or V q

hf0 or

hc λmax

Physics 30—Unit 4 Review: Atomic Physics ....................................................................................................... Atomic models

• 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 ⋆

Fm = Fe qvB = |E|q

• particles bend through a second B ⋆

Half-life



Fm = Fc mv 2 qvB = r N0

( )n 1 N = N0 2 time n= T1

N1

2

T1 2

Radioactive decay

• • • •

0 β + ν or; Beta Negative −1 Beta Positive 01 β + ν Alpha α2+ Gamma (EMR) 00 λ

Increasing danger and more shielding required

Fission & fusion



AX Z

with A = mass # (nucleons: p + n ) and Z = atomic # (protons)

• E = mc2 ⋆ m: mass defect – elements: predicted mass minus actual mass – reactions: mass of reactants minus mass of products