Module 15Canvas Practice Exam 3

Instructions

You can refer to the following formulae at any time.

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 ΔT 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

Be careful to give all answers in the correct units.

Guidelines and Grading

This is an ungraded, practice exam.