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McGill PHYS 131 develops Newtonian mechanics together with oscillations, waves, and wave optics. It forms part of McGill’s calculus-based introductory physics sequence.
Choose a workshop when the topic is included in your instructor’s announced material. These original exercises are not an exam reproduction or a complete course review.
Newtonian mechanicsKinematics and dynamicsEnergy and momentumOscillationsWavesWave optics
Common difficulties
Coordinating a motion graph, vector equation and derivative
Interpreting signs consistently across mechanics and waves
PHYS 131 mechanics: forces, energy or momentum?
Find a scale reading, a speed after a drop and the outcome of a collision. For each problem, choose the system and decide whether to use forces, energy or momentum. Use g=9.8m/s2.
Add rotation, oscillations and waves if they are on your review list.
Before you start: Allow 25 minutes for the three questions, then 10 minutes to check when each conservation law applies.
1. A downward-moving elevator that slows
A 60kg passenger stands on a scale in an elevator moving downward and slowing at 1.2m/s2. Find the scale’s normal-force reading in newtons. Treat the passenger as moving with the elevator.
Show the explained solution
The system is the passenger at that instant. Because downward motion is slowing, the acceleration is upward. Choose upward positive; the forces are the upward normal force and downward weight.
Newton’s second law gives N−mg=ma. Therefore N=60(9.8+1.2)=660N.
The reading exceeds the weight of 588 N. Velocity direction does not set acceleration direction. An energy equation is less direct because the requested quantity is an instantaneous force, not a speed change over a displacement.
A small bead slides from rest down a fixed, frictionless track through a vertical drop of 1.25m. Find its speed at the lower point. The track supports the bead throughout; ignore air resistance and bead rotation.
Show the explained solution
Choose the bead and Earth as the system, from release to the lower point. Gravity changes potential energy; the stationary track’s normal force is perpendicular to the displacement and does no work. No dissipative interaction is included.
Let d=hi−hf=1.25m be the positive vertical drop. Conservation of mechanical energy gives mgd=21mv2. Therefore v=2gd=2(9.8)(1.25)≈4.95m/s.
The mass cancels. The path shape can affect the travel time and support force, but the stated drop determines this speed under these assumptions. Momentum is not conserved for the bead alone because external forces act.
On a level track, a 0.40kg cart moves right at 3.0m/s, and a 0.60kg cart moves left at 1.0m/s. They collide and stick. Neglect external horizontal impulse during impact. Find their common velocity and the change in kinetic energy.
Show the explained solution
Use both carts as the system over the short collision interval. Choose right positive, so the second initial velocity is negative. The negligible external horizontal impulse justifies conservation of total horizontal momentum.
The initial total momentum is pi=(0.40)(3.0)+(0.60)(−1.0) or 0.60kgm/s. The total mass is 1.00kg, so vf=1.00kgpi=+0.60m/s. The carts move rightward.
Using K=21mv2, the carts initially have 1.80J and 0.30J. Hence Ki=2.10J. After impact, Kf=21(1.00)(0.60)2=0.18J.
Thus ΔK=Kf−Ki=−1.92J. Sticking conserves momentum under the stated impulse assumption, but not kinetic energy: energy is transferred into deformation, heating and other internal changes.
Draw one diagram per object. Label velocity and acceleration separately, write signed force components, then compare the result with a zero-acceleration limit.
Unjustified conservation step
Name the boundary of the system and the start and end of the interval. For momentum, inspect external impulse; for mechanical energy, account for nonconservative work and internal changes.
Ready for a mixed set
Use the six questions in the work–energy–momentum lesson linked above. Hide method labels, justify the first equation, and check units and signs. Add your assigned wave and oscillation questions separately.
If choosing a mechanics method is difficult, your tutor can help you draw the forces and compare the conditions for using Newton’s laws, energy or momentum. You can begin with the problem statement; an existing attempt is useful if you have one.
Review vectors, trigonometric components and the relationship between a function and its derivative. Calculus and physical reasoning are used together.
Registration requirements
The guidance above is study preparation, not an eligibility decision. Confirm current prerequisites, restrictions and availability with McGill University.
Let t be time expressed as a number of seconds and x(t)=2t2 position expressed as a number of metres along a straight axis. Find the signed velocity at t=3.
Show the reasoning
Let v(t) denote velocity. Velocity is the time derivative of position, so the power rule gives v(t)=dx/dt=4t metres per second. At t=3, v(3)=12 m/s. Its positive sign indicates motion in the positive direction of the position axis.
For assigned oscillation questions, try this optional spring example when both initial position and velocity are given. Build the motion, check the phase and select the first future equilibrium crossing. Use your section's announced topics to choose your review.
How tutoring can help
If you are unsure how to connect the motion to the mathematics, your tutor can help you draw the situation and relate position, velocity and acceleration using graphs and derivatives. For a conservation or oscillation problem, you can choose the physical principle and identify the assumptions together. Your tutor can then guide you through the equations and a similar example.
Exam preparation for PHYS 131
Practise mixed mechanics and wave problems. Add laboratory uncertainty interpretation when it is assessed in your section, and verify the current calculus corequisite with McGill.
If measurement uncertainty is assessed in your section, practise interpreting ± and comparing a result with a reference in our measurement uncertainty lesson.
Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.
Choose the prerequisite you need
Use a position graph’s slope to find velocity. On a velocity graph, slope gives acceleration and signed area gives displacement. Connect those quantities to the motion before choosing equations.
Two measurements describe the same transverse sinusoidal travelling wave on a string. In a snapshot taken at one instant, adjacent crests are 0.80 m apart. At one fixed position, the displacement repeats every 0.20 s. Find the wavelength λ, period T, frequency f and propagation speed c. Do these two intervals also determine a string particle’s instantaneous transverse velocity?
Before using a formula, identify which measurement holds time fixed and which holds position fixed. Which interval is a length, and which is a time?
Show a hint
A wavelength is one spatial repetition. A period is one temporal repetition. Frequency counts cycles per second, and the wave travels one wavelength during one period.
Show the worked solution
The snapshot holds time fixed, so its crest separation is λ=0.80 m. The fixed-position record holds position fixed, so its repeat time is T=0.20 s.
Frequency is f=1/T=5.0 Hz: five complete cycles per second. The propagation speed is c=λ/T=0.80/0.20=4.0 m/s. The units are length divided by time.
This speed describes a travelling feature such as a crest along the string. A string particle moves transversely. Its instantaneous transverse velocity depends on the local slope of displacement versus time; the two repeat intervals alone do not supply that slope, amplitude or phase. They also do not establish which way the wave travels.
Using the spatial spacing as a period, or treating propagation speed as the transverse velocity of a particle. Label what is held fixed before calculating.
Retry with a changed period
A second transverse sinusoidal travelling wave has wavelength 0.80 m and period 0.40 s. We are not assuming the same unchanged medium or the same propagation speed. Predict how its frequency and speed compare with the first wave, then calculate both.
Check the retry
The period doubles while the wavelength stays the same, so both frequency and speed halve: f=1/0.40=2.5 Hz and c=0.80/0.40=2.0 m/s. Each crest takes twice as long to travel the same wavelength. This still gives no instantaneous transverse velocity for a particular particle.
A tutor can ask you to label the fixed variable on each graph, then distinguish the motion of a crest from the motion of one marked point. Continue with the two-graph lesson for a different numerical example of the same distinction.
Choose work, energy or momentum by system and interval. Solve collisions, read force–position and force–time graphs, and distinguish impulse from work.
Resolve angled forces into components, find the resultant and acceleration, and recover an equilibrant or unknown force. Three worked examples and six questions with hints and solutions.
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