Unit 5 / SPPU FE Engineering Mechanics

Unit 5: Kinetics — SPPU FE Engineering Mechanics

Topics: Newton's second law, work-energy theorem, impulse-momentum, impact and coefficient of restitution, and curvilinear kinetics.

2019 pattern: end-sem Q7 / Q82024 pattern: end-sem Q6Highest density of recurring exam families in the course

Which exam is this in?

2019 pattern

End-sem Q7 / Q8, 18 marks, attempt 1 of the pair

2024 pattern

End-sem Q6: solve any 2 of 4 sub-questions, 12 marks

Unit-by-unit question frequency and what repeats

Unit V — Kinetics

2024 pattern: Q6 (12 marks). 2019 pattern: Q7 / Q8.

Sub-topic	Frequency	Notes
Newton's 2nd law: block on inclined plane	Every paper	μk is given and you solve for acceleration or time
Work-energy: block or crate with friction	Every paper
Impulse-momentum: ball thrown vertically	Very common	30 kg ball at 15 m/s is recycled exactly
Impact: coefficient of restitution + momentum	Every paper	Ball rebound or two-body collision
Curvilinear kinetics: circular motion	Common
Man on rotating platform	Common
Spring combined with impact	Occasional	Hardest multi-step family

Recurring problem families

Problem	Appeared in
Ball 30 kg thrown vertically at 15 m/s — find time to reach max height using impulse-momentum	Nov/Dec 2023, Nov/Dec 2025 (identical)
Block 80 kg on 30° inclined plane, μk = 0.2 — find acceleration using Newton's 2nd law	Nov/Dec 2023, Nov/Dec 2025 (identical)
Railroad car 20 Mg at 0.5 m/s collides with stationary 35 Mg car, e = 0.65 — find velocities after impact	Nov/Dec 2023, May/Jun 2024 (identical)
Man 80 kg, 3 m from centre of rotating platform, aₜ = 0.4 m/s², μs = 0.3 — find time before slipping	Nov/Dec 2023, May/Jun 2024 (identical)
Ball 1 kg dropped from 5 m, rebounds to 3 m — find e and rebound height if dropped from 3 m	May/Jun 2023, Nov/Dec 2023 (identical)
Racing car on circular track radius 100 m, aₜ = 7 m/s² — find time when total acceleration = 8 m/s²	May/Jun 2023, Nov/Dec 2023 (identical)
Cylinder A 0.5 kg dropped 2.4 m onto pan B 2.5 kg, spring k = 3 kN/m, plastic impact — find compression	May/Jun 2023, May/Jun 2025 (identical)
Ball A 5 kg at 10 m/s strikes stationary Ball B 1 kg, B moves at 10 m/s — find velocity of A and e	May/Jun 2023, May/Jun 2025 (identical)

Sub-topics and how often they appear

Sub-topic	Priority	Frequency
Newton's second law — block on inclined plane, find acceleration	High	Every paper
Work-energy theorem — block or crate with friction, find velocity or distance	High	Every paper
Impulse-momentum — ball thrown vertically, find time	High	Very common
Impact — coefficient of restitution, find velocities after collision	High	Every paper
Curvilinear kinetics — circular motion, tension in cord or normal force	Medium	Common
Man on rotating platform — find time before slipping	Medium	Common
Spring combined with impact — find spring compression after plastic collision	Low	Occasional, hardest sub-topic

🟢 High — do this first, appears in every paper.

🟡 Medium — do this if you have time.

🔴 Low — hard multi-step problem, skip if time is short.

Unit 5 has the highest density of recurring exam families in the course. The 30 kg ball, the 80 kg block on 30°, the railroad car collision, and the man on the rotating platform all returned in very similar forms across multiple papers. If you solve the 2022 to 2024 Unit 5 papers, you are directly preparing for the next exam.

High

Newton's Second Law — Inclined Plane

Formulas that appear

ΣF = ma

Perpendicular to plane: N = mg cos θ

Sliding down the plane: mg sin θ − μ_kN = ma

Pushed up the plane: F − mg sin θ − μ_kN = ma

Friction during motion: F_friction = μ_kN

Standard problem setup

A block is on an inclined plane with a given kinetic friction coefficient. The paper asks for acceleration after release or after applying a force along the plane.

1. Draw the FBD with mg, N, and friction.

2. Resolve perpendicular to the plane to get N.

3. Compute friction using μkN.

4. Write ΣF = ma along the plane.

5. Solve for acceleration.

The 80 kg block on a 30° plane with μk = 0.2 is one of the most recycled problems in the subject.

Common mistakes

Using μs instead of μk even though the block is moving or has been released.

Putting friction in the wrong direction. It must oppose the motion.

Using mg directly in the along-plane equation instead of resolving it into mg sin θ and mg cos θ.

Confusing mass in kilograms with weight in Newtons.

High

Work-Energy Theorem

Formulas that appear

W_net = ΔKE = ½mv₂² − ½mv₁²

Applied force over distance d at angle α: W = Fd cos α

Gravity moving down by height h: W = +mgh

Gravity moving up by height h: W = −mgh

Friction: W = −μ_kNd

Normal reaction: W = 0

Standard problem setup

A crate or block moves over a distance with friction, sometimes under an inclined applied force, and the paper asks for final velocity or distance traveled.

1. Compute the normal reaction first if the applied force is inclined.

2. Find the work done by the applied force.

3. Find friction work and include it with the correct negative sign.

4. Include gravity work if there is a height change.

5. Set total work equal to change in kinetic energy.

Common mistakes

Ignoring friction work, which makes the final velocity too large.

Assuming N = mg when the applied force has a vertical component.

Using the wrong sign for gravity on an incline.

Forgetting the kinetic energy expression uses v², not v.

High

Impulse-Momentum

Formulas that appear

F × t = m(v₂ − v₁)

In vector form: ΣF × t = mv₂ − mv₁

At maximum height of a vertical throw, v₂ = 0

Taking upward as positive: −mg × t = m(0 − u)

Therefore t = u / g

Standard problem setup

A ball is thrown vertically upward and the paper specifically asks for the impulse-momentum method to find the time to maximum height.

1. Set the final velocity to zero at maximum height.

2. Use weight as the only external force.

3. Apply the impulse-momentum equation with a clear sign convention.

4. Solve directly for time.

The 30 kg ball at 15 m/s appeared unchanged in Nov/Dec 2023 and Nov/Dec 2025.

Common mistakes

Using Newton's kinematics method when the question explicitly asks for impulse-momentum.

Giving weight the wrong sign when upward is taken as positive.

Using g = 10 instead of 9.81 when the expected answer uses 9.81.

High

Impact and Coefficient of Restitution

Formulas that appear

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

e = (v₂ − v₁) / (u₁ − u₂)

Perfectly plastic: e = 0 and both bodies move together after impact

Perfectly elastic: e = 1

For bounce height: e = √(h₂ / h₁)

Standard problem setup

The paper either gives a two-body collision with masses and initial speeds, or a rebound-from-height question asking for e and a new rebound height.

1. Write conservation of momentum first.

2. Write the restitution equation second.

3. Solve the two equations together for post-impact velocities.

4. For rebound-height questions, use e²h₁ = h₂.

Common mistakes

Writing the restitution equation backwards and getting e > 1.

Losing track of sign convention after choosing a positive direction.

Using h₂ = eh₁ instead of h₂ = e²h₁ for rebounds.

Assuming the bodies stick together even when e is not zero.

Medium

Curvilinear Kinetics — Circular Motion

Normal direction: ΣFₙ = maₙ = mv²/r

Tangential direction: ΣFₜ = maₜ = m(dv/dt)

For a string or pendulum problem: T − mg cos θ = mv²/r along the cord direction.

The common setup is a racing car on a circular track with given tangential acceleration. Use total acceleration a = √(aₙ² + aₜ²), then solve for time.

Medium

Man on Rotating Platform

Use aₙ = v²/r and aₜ as given, then combine them with a = √(aₙ² + aₜ²).

Slipping begins when the required friction force equals μ_smg, so √(aₙ² + aₜ²) = μ_sg.

Starting from rest, v = aₜt, so aₙ changes with time. Substitute that into the slipping condition and solve for t.

This exact 80 kg, 3 m, aₜ = 0.4, μs = 0.3 question repeated in Nov/Dec 2023 and May/Jun 2024.

Common mistakes

Adding normal and tangential acceleration directly instead of using Pythagoras.

Using diameter instead of radius in v²/r.

Using μk instead of μs before slipping has started.

Treating normal acceleration as constant even though v grows with time on the rotating-platform problem.

Low

Spring Combined with Impact

Attempt this only after the four high-priority topics are solid. It is a two-phase problem: momentum across the impact first, then energy during spring compression.

Formulas that appear

Phase 1, plastic impact: m₁u₁ + m₂(0) = (m₁ + m₂)v_common

Phase 2, spring compression: ½(m₁ + m₂)v_common² + (m₁ + m₂)gx = ½kx²

Standard problem setup

A falling mass collides plastically with a pan or block connected to a spring. The paper asks for maximum spring compression.

1. Find the falling body's speed just before impact from √(2gh).

2. Use momentum only to find the common speed just after impact.

3. Use work-energy from just after impact to maximum compression.

4. Be consistent about whether compression is measured from natural length or static equilibrium.

Common mistake

Using conservation of energy across the impact itself. Plastic impact is momentum first, energy second.

MCQ Sampler

3 free concept checks for Unit 5

These starter questions cover the highest-frequency ideas first. The full bank has 50 questions, and all 50 are temporarily open through June 30, 2026, including the harder hint layer.

Open full MCQ bank

Question 1

Newton's Second Law

For translational particle motion, the net force relation is:

Question 2

Work-Energy Theorem

The net work done on a particle between two positions equals:

Question 3

Impulse-Momentum

Impulse delivered to a particle is equal to:

The remaining 47 questions are open right now. Use the beta window to work the harder concept checks before the paid boundary returns.

Sub-topics, formulas, setups, and mistakes on this page are drawn from 32 SPPU FE Engineering Mechanics papers from 2013 to 2026. See paper trends for the full frequency analysis.

Open practice drills