Exam 3 (Final)

This is a CLOSED-book exam. Using any book, notes, or other form of outside assistance is NOT ALLOWED. You may use (1) scratch paper that is entirely blank at the start of the exam, (2) writing implements, and (3) the on-screen scientific calculator that can be accessed from the 24/7 Proctoring Support toolbar. You are NOT PERMITTED to use any other type of calculator or any electronic device (cell phone, smart watch, headphones, ...) except the computer on which you are taking the test. You must remain in front of your computer for the duration of the exam. NO BATHROOM BREAKS. Failure to follow these instructions could result in a violation.

You can refer to the following formulae at any time. Read to the end of this question to get an easy point.

Newton’s First Law (“Law of Inertia”): If F = 0, then v is constant
Newton’s Second Law: F = ma
Newton’s Third Law: “action = reaction”, “forces come in pairs”

Linear (translational) motion:
distance traveled = d = (average speed) x time
total displacement = d = (average velocity) x time
v_f = v₀ + at
d = v₀t + 0.5at²          
work done = force x (distance moved in the direction of the force)
power = (energy change or work) / time
translational kinetic energy = 0.5 mv²
gravitational potential energy = mgh
conservation of momentum: (mv)_{total initial} = (mv)_{total final}
impulse = change in momentum = force x time
elastic collisions conserve kinetic energy

Rotational motion:
avg. angular velocity ω_ave = (θ₂-θ₁)/t
angular acceleration α = (ω₂ - ω₁)/t
motion in a circle: arc length d = rθ,  tangential velocity v=rω,  centripetal acceleration a = v²/r
torque τ = force x (perpendicular distance) = Iα
rotational kinetic energy = 0.5 Iω²
for point mass, I = mr²
conservation of angular momentum: I₁ω₁ = I₂ω₂

Gravity and fluids:
Newton's law of gravity: F = Gm₁m₂/r²
Archimedes' principle: buoyant force equals weight of fluid displaced
density ρ = M/V
pressure p = force / area
liquid pressure p = ρgh
density of water ρ = 1000 kg/m³
Take the acceleration due to gravity near the Earth's surface to be g = 10m/s²
Take atmospheric pressure = 10⁵ Pa

Thermal physics:
universal gas law: pV/T is a constant
heat in Q = m C Δ T for change of temperature, Q = m L for change of phase
specific heat capacity of water: C = 4.2 kJ/(kg.K) = 1 cal/(g.⁰C) = 1 kcal/(kg.K)
temperature conversions: ^oF = (1.8 ^oC) + 32,  ^oC = (^oF - 32) / 1.8,   K = ^oC + 273

Electricity and magnetism:
Coulomb’s law: F = kq₁q₂/d²
voltage V = (energy change or work) / charge
electric field E = force / charge = voltage / distance
circuits: V = IR, power P = IV
resistors in series: R_T = R₁+R₂, resistors in parallel: 1/R_T = 1/R₁+1/R₂
force on a current-carrying wire = I L B sinθ

Waves, vibration, and light:
wave speed v = λf
springs: F = -kx , potential energy = 0.5kx²
Snells’s law of refraction: n₁sinθ₁  = n₂sinθ₂

Trigonometry:
sin 45⁰ = cos 45⁰ = 1/√2 = 0.71
sin 30⁰ = cos 60⁰ = 0.5,  cos 30⁰ = sin 60⁰ = (√3)/2 = 0.866
sin 37⁰ = 0.6,  cos 37⁰ = 0.8