Physics for Engineers: practice problems and exam questions

First-year physics for engineering students: mechanics, fluids and thermodynamics. Exams mix short calculations from each area, so speed on the standard methods pays off.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Kinematicsspeeding up · braking · vertical throwcalculations
  2. Newton’s lawspush with friction · inclined plane · table and pulleycalculations
  3. Projectile motionhorizontal launch · launch from ground · launch from heightcalculations
  4. Work & energyfree fall · slope with friction · ramp, friction and springcalculations
  5. Momentum & collisionsperfectly inelastic · elastic · impulse and forcecalculations
  6. Hydrostatic forcevertical wall · submerged gate · centre of pressurecalculations
  7. Continuity & Bernoullicontinuity · horizontal reducer · rising pipecalculations
  8. Ideal gas lawP from n, V, T · from mass · state change or densitycalculations
  9. Heat engines & refrigeratorsfirst law of a cycle · Carnot limit · refrigerators and heat pumpscalculations
  10. Waves, sound & opticswave speed, sound level and refraction · standing waves, lenses and Doppler · interference, gratings, mirrors and fibrescalculations

Exam tips for Physics for Engineers

  • Write down the known quantities with their units before you choose a formula.
  • Check the order of magnitude of every answer: a car does not drive at 3000 m/s.
  • Absolute temperature and absolute pressure belong in the gas laws.

Worked examples

KinematicsEasy
t (s)v (m/s)20 s10

A train slows down uniformly from 15 m/s to 10 m/s in 20 s. How far does it travel in that time? Find s.

v₀ = 15 m/sv = 10 m/st = 20 s

Find s (m)

Show hints
  1. With constant acceleration the average speed is the mean of the initial and final speeds.
  2. s = (v₀ + v)/2 · t. It is the area under the v–t graph.
  3. average speed = 12.5 m/s.
Show the answer and the step-by-step solution

Motion with constant acceleration: v = v₀ + a·t, s = v₀·t + ½·a·t² and v² = v₀² + 2·a·s. Pick the equation that contains the three things you know and the one you want, and keep the signs consistent with one positive direction.

Average speed

(v₀ + v)/2 = (15 + 10)/2 = 12.5 m/s

Distance

s = 12.5·20 = 250 m

Answer

s = 250 m
Newton’s lawsMedium
25 kg35°F = 140 Nμ = 0.25

A 25 kg sled is pulled across level snow by a rope at 35° above the horizontal with a force of 140 N. The coefficient of kinetic friction is 0.25. Use g = 9.81 m/s². Find the acceleration a of the sled.

m = 25 kgF = 140 Nθ = 35°μ = 0.25g = 9.81 m/s²

Find a (m/s²)

Show hints
  1. Split the pull into F·cos θ (forward) and F·sin θ (up).
  2. Vertically: N + F·sin θ = m·g. Friction is μ·N.
  3. N = 164.9 N.
Show the answer and the step-by-step solution

Newton’s second law: the net force on a body equals its mass times its acceleration, ΣF = m·a. Draw a free-body diagram, choose a positive direction along the motion, and add every force in that direction: applied forces, friction μ·N against the motion, and the components of gravity.

Normal force

N = m·g − F·sin θ = 245.3 − 140·sin 35° = 164.9 N

Horizontal forces

m·a = F·cos θ − μ·N = 114.7 − 41.24
a = 73.44/25 = 2.938 m/s²

Answer

a = 2.938 m/s²

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Projectile motion calculatorBernoulli equation calculatorCarnot efficiency and COP calculatorIdeal gas law calculatorKinematics calculator (SUVAT)Collision and momentum calculatorDensity calculator (mass, volume and density)Kinetic energy calculator (and potential energy, work and power)Free fall calculator (time, height and impact speed)Engineering unit converterCombined gas law calculator (Boyle, Charles and Gay-Lussac)Acceleration calculator (and average velocity)

Related courses

Physics 1: MechanicsDynamicsAP Physics 1 practice problemsFE Mechanical exam practiceThermodynamics 1Fluid MechanicsHydraulic EngineeringMaterial and Energy Balances
Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.