Unit 3 / SPPU FE Engineering Mechanics

Unit 3: Friction and Trusses — SPPU FE Engineering Mechanics

Topics: Laws of friction, inclined plane, belt friction, ladder friction, method of joints, method of sections, zero force members, and cables.

2019 pattern: friction in in-sem, trusses in end-sem2024 pattern: end-sem Q4Know one friction topic and one truss topic cold

Which exam is this in?

2019 pattern

Friction in in-sem (30 marks); trusses in end-sem Q3 / Q4, 18 marks, attempt 1 of the pair

2024 pattern

End-sem Q4: solve any 2 of 4 sub-questions, 12 marks, with both friction and trusses

Unit-by-unit question frequency and what repeats

Unit III — Friction and Trusses

2024 pattern: Q4 (12 marks). 2019 pattern: friction in in-sem; trusses in Q3 / Q4.

Sub-topic	Frequency	Notes
Block on inclined plane (find force to move or hold)	Every paper
Belt friction over fixed drum	Every paper
Ladder friction	Very common
Method of joints	Every paper
Cable with multiple hanging loads	Every 2019 pattern paper
Zero force members	Very common
Method of sections	Common

Recurring problem families

Problem	Appeared in
100 kg block, cable over fixed drum, μ = 0.3 — find range of P	Apr 2025, Nov/Dec 2025
15 m ladder, 80 N weight, μ at floor = 0.4, smooth wall — find minimum angle	Apr 2025, Nov/Dec 2025
30 kg block on 20° inclined plane, μs = 0.25 — find P to move up the plane	Apr 2025
Truss with all members given — zero force members + remaining member forces	Nov/Dec 2023, Nov/Dec 2025
Cable ABCD with known spans and hanging loads — find support reactions and maximum tension	May/Jun 2022, Nov/Dec 2023, May/Jun 2024, Nov/Dec 2025, May/Jun 2025

Sub-topics and how often they appear

Sub-topic	Priority	Frequency
Block on inclined plane — find force to move or hold	High	Every paper
Belt friction over fixed drum — find range of P	High	Every paper
Method of joints — find all member forces	High	Every paper
Cable with multiple hanging loads — find tensions and max tension	High	Every 2019 pattern paper
Ladder friction — find minimum angle or position before slipping	Medium	Very common
Zero force member identification	Medium	Very common
Method of sections — find forces in specific members	Medium	Common
Cone of friction / angle of repose — theory	Low	Short theory question only

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

🟡 Medium — do this if you have time.

🔴 Low — only asked as a short definition, no full numerical question.

Note for 2019 pattern students: friction is in your in-sem and trusses plus cables are in your end-sem, so they are tested separately. For 2024 pattern students, both appear in end-sem Q4, so know at least one friction topic and one truss topic well enough to choose confidently.

High

Block on Inclined Plane

Formulas that appear

F = μ_sN — limiting static friction

F = μ_kN — kinetic friction

φ = tan^-1(μ)

Perpendicular to plane: N = W cos θ ± P sin α

Parallel to plane: P cos α = W sin θ ± F

Angle of repose: α = φ = tan^-1(μ_s)

Standard problem setup

A block rests on an inclined plane at angle θ. μ is given and a force P acts along the plane or at an angle. Find P either to just move the block up the plane or to just prevent it from sliding down.

1. Draw the FBD with W, N, friction F, and applied force P.

2. Resolve parallel and perpendicular to the plane, not horizontal and vertical.

3. Use N = W cos θ unless P changes the normal reaction.

4. Find friction from F = μN.

5. Write ΣF = 0 along the plane for impending motion.

6. Solve for P.

The most recycled version uses a 20° to 30° plane, μ between 0.2 and 0.35, and asks for P to move the block up.

Common mistakes

Wrong friction direction. Moving up means friction acts down the plane; about to slide down means friction acts up the plane.

Resolving along horizontal and vertical instead of along and perpendicular to the plane, which makes the algebra harder and more error-prone.

Using μs when the problem is already in motion. “Just about to move” means static; “moving” means kinetic.

Ignoring the perpendicular component of P when P is applied at an angle, which changes N and therefore changes friction.

High

Belt Friction over Fixed Drum

Formula that appears

T₂ / T₁ = e^μθ

T₂ = tight-side tension, T₁ = slack-side tension

θ must be in radians

180° = π rad, half-wrap = π rad, full wrap = 2π rad

Standard problem setup

A belt or rope passes over a fixed drum. The wrap angle and μ are given, along with a load on one side. Find the minimum force P to hold it, or the range of P for equilibrium.

1. Identify T₂ as the larger tension and T₁ as the smaller one.

2. Convert θ to radians before substituting.

3. Apply T₂ / T₁ = e^(μθ).

4. For range-of-P questions, compute both Pmin and Pmax.

5. State the final range clearly.

The recurring setup is a 100 kg block connected over a fixed drum with μ = 0.3.

Common mistakes

Leaving θ in degrees instead of radians before using e^(μθ).

Getting T₁ and T₂ backwards. T₂ is always the larger tension.

Using kinetic friction instead of limiting static friction in range-of-P questions.

Medium

Ladder Friction

Formulas that appear

ΣFₓ = 0, ΣFᵧ = 0, ΣM = 0

Rough surface: normal reaction N and friction force F = μN

Smooth surface: normal reaction only, no friction

Standard problem setup

A ladder of known length and weight leans against a smooth wall while the floor is rough. A person may stand on the ladder. Find the minimum angle to avoid slipping or the reactions and friction force.

1. Draw the FBD of the whole ladder.

2. ΣFₓ = 0 gives floor friction equal to wall reaction.

3. ΣFᵧ = 0 gives the floor normal reaction.

4. Take moments about the base to remove floor forces from the equation.

5. Use limiting friction when the ladder is on the verge of slipping.

Common mistakes

Adding friction at the wall even when the problem says the wall is smooth.

Using the wrong moment arm for the ladder’s own weight. The weight acts at the midpoint of the ladder.

Forgetting that minimum angle means friction is at its limiting value.

High

Method of Joints — Trusses

Key rules before starting

If only two members meet at an unloaded joint and they are not collinear, both are zero-force members.

If three members meet at an unloaded joint and two are collinear, the third is a zero-force member.

At each joint: ΣFₓ = 0 and ΣFᵧ = 0

Assume all members are in tension first; negative means compression.

Standard problem setup

A loaded truss is given. Find all member forces, or the force in named members after support reactions are determined.

1. Find support reactions for the full truss first.

2. Mark all zero-force members before solving anything else.

3. Start at a joint with only two unknowns.

4. Apply ΣFₓ = 0 and ΣFᵧ = 0 at that joint.

5. Move to the next joint with at most two unknowns.

6. State every answer as tension or compression.

Common mistakes

Skipping support reactions, which leaves the first support joint unsolved.

Starting at a joint with more than two unknowns and getting stuck immediately.

Using the wrong angle for diagonal members because the geometry was not sketched carefully.

Writing only the magnitude and not stating tension or compression.

Medium

Zero Force Members

This is already part of method of joints. When it appears as a standalone question, state the two rules, identify which members satisfy them, and explain why each is a zero-force member. In most papers this is a quick 3 to 4 marks if you know the rules.

Medium

Method of Sections

Use method of sections when the paper asks for two or three specific members and you do not want to solve the entire truss. Cut through at most three unknown members, take the easier left or right portion, and use ΣFₓ = 0, ΣFᵧ = 0, and ΣM = 0.

1. Find support reactions first.

2. Pass an imaginary cut through the target members.

3. Choose the side with fewer forces.

4. Take moments about the intersection of two unknown cut-member lines.

5. Solve and state tension or compression.

Common mistakes

Cutting through more than three unknown members in a 2D truss problem.

Taking moments about the wrong point instead of the intersection of two unknown cut-member lines.

Flipping the assumed cut-member directions when switching to the right-hand portion and then losing the sign convention.

High

Cables with Multiple Hanging Loads

Key concept and formulas

At each load point: ΣFₓ = 0 and ΣFᵧ = 0

Horizontal tension component is constant throughout the cable

Tₓ = T cos θ = constant for all segments

T = √(Tₓ² + Tᵧ²)

Standard problem setup

Cable ABCD is supported at A and D with loads hanging at B and C. The spans and loads are known, and one sag or geometric reference is given. Find reactions, segment tensions, and maximum tension.

1. Find support reactions from the full cable free body.

2. Apply ΣFₓ = 0 and ΣFᵧ = 0 at each internal load point.

3. Use the constant horizontal component to connect all segments.

4. Find each segment tension from its horizontal and vertical components.

5. Identify maximum tension from the steepest segment.

This four-point cable family appears five papers in a row from May/Jun 2022 to Nov/Dec 2025.

Common mistakes

Forgetting that the horizontal tension component is constant in every segment.

Confusing sag with absolute y-coordinate when the supports are at different heights.

Picking the wrong segment for maximum tension; it is usually one of the end segments near a support.

Not checking horizontal equilibrium at the two supports.

Low

Cone of Friction / Angle of Repose — Theory

Cone of friction: the cone whose half-angle equals the angle of friction φ = tan^-1(μ). The resultant reaction must lie within this cone for no slipping.

Angle of repose: the maximum angle of an incline at which a block remains stationary under its own weight. It equals the angle of friction, so α = φ = tan^-1(μ).

This only appears as a short definition or diagram question. Learn the wording and move on.

MCQ Sampler

3 free concept checks for Unit 3

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

Friction Direction

In a dry-friction problem, the friction force on a body acts:

Question 2

Limiting Friction

At the point of impending motion, the friction force magnitude is:

Question 3

Belt Friction Ratio

For belt friction on a fixed drum, the tension ratio is given by:

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.

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