Exam 2

  • Due Oct 27, 2022 at 11:59pm
  • Points 30
  • Questions 31
  • Available Oct 27, 2022 at 7am - Oct 28, 2022 at 3am 20 hours
  • Time Limit 120 Minutes

Instructions

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
vf = v0 + at
d = v0t + 0.5at2
work done = force x (distance moved in the direction of the force)
power = (energy 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 ωave = (θ21)/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
liquid pressure = 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

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

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