DOST-SEI Mechanical Reasoning Reviewer: Pulleys & Mechanical Advantage

TEACHER ABI · DOST-SEI MECHANICAL REASONING

Pulleys & Mechanical Advantage

Read pulley diagrams correctly, count the rope segments that actually support the moving load, and connect mechanical advantage to force and distance.

5–10 minute lesson27 original questionsPrecision SVG diagramsSaves progress

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Follow the rope, not just the pulleys

1. Fixed pulley
Its axle stays fixed. Ideally it mainly changes the direction of the pull; IMA = 1.

2. Movable pulley
The pulley travels with the load. More than one rope segment can share the load.

3. Same ideal rope = same tension
In a massless rope over frictionless pulleys, each segment of that continuous rope has the same tension.

4. Count supporting segments
Count tension-carrying rope parts that pull upward on the moving block—not every visible rope segment.

5. Ideal mechanical advantage
IMA equals the number of supporting tension segments in these pulley systems.

6. Force saved means distance paid
If IMA = 4, the ideal effort is one-fourth the load, but the free end moves four times the load distance.

DO IT FAST

MOVES → SUPPORTS → DIVIDE

MOVES: identify the pulley/block that rises with the load. SUPPORTS: count the rope tensions pulling upward on that moving block. DIVIDE: for an ideal system, divide the load by that count to get the required pull.

Fast check: A fixed pulley used only to redirect the free end does not magically add mechanical advantage. Ask whether it adds another upward tension force on the moving block.

WORKED EXAMPLES

Read the rigging before calculating

1. Fixed pulley

The load is supported by one rope tension. For a 100-N load, the ideal pull is 100 N. The useful change is direction.

2. One movable pulley

Two rope segments support the moving pulley. For a 200-N load, 2T = 200, so the pull is 100 N.

3. Four supporting segments

Four equal tensions support the moving block. A 400-N load therefore needs an ideal pull of 100 N.

4. Direction pulley added

The upper fixed pulley makes the free end convenient to pull downward, but the moving block is still supported by two rope segments. IMA remains 2.

5. Force-distance tradeoff

With four supporting segments, raising the load 0.50 m requires pulling 2.0 m of rope in the ideal case.

Common traps

Counting pulleys instead of supporting segments: mechanical advantage comes from supporting tensions. Counting the free end automatically: count it only if it actually pulls upward on the moving block. Giving a fixed pulley IMA 2: a single fixed pulley has IMA 1. Forgetting the distance tradeoff: less force means more rope must move. Using ideal results for real hardware: friction and other losses increase the required effort.

FIVE-FORM SKILL CHECK

Can you read five pulley forms?

This diagnoses your next practice step; it does not verify mastery.

CHOOSE YOUR PRACTICE

Practice at the level you need

FRESH MASTERY CHECK

Verify the competency

Mastery requires 5/5. If you miss an item, your next attempt loads a different five-question set.

FAQ

Quick clarifications

Does every pulley reduce the force?
No. A fixed pulley can simply redirect the force.

Why are the tensions equal?
That is the ideal-rope model used here: a massless rope and frictionless pulleys.

What exactly should I count?
Count the tension forces that directly support the moving block/load. The diagram matters.

What changes in a real pulley?
Friction, pulley mass, rope stiffness, and other losses mean the actual effort is usually greater than the ideal value.

RELATED COMPETENCIES

Continue Mechanical Reasoning

Levers, Torque & Balance · Gears & Gear Trains · Belts, Chains, Racks & Connected Wheels · Wheels & Axles · Forces, Friction & Equilibrium

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DOST-SEI Mechanical Reasoning Reviewer: Levers, Torque & Balance

TEACHER ABI · DOST-SEI MECHANICAL REASONING

Levers, Torque & Balance

Read lever diagrams, predict turning direction, compare moments, and solve balance problems using force × distance.

5–10 minute lesson27 original questionsVisual practiceSaves progress

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Levers, Torque & Balance

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What makes a lever turn?

1. Find the fulcrum.
The pivot is the point the lever rotates around.

2. Read the turning direction.
Down on the left tends counterclockwise; down on the right tends clockwise.

3. Distance matters.
The same force has a greater turning effect farther from the fulcrum.

4. Moment = force × distance.
For perpendicular forces, M = Fd, in N·m.

5. Balance means equal opposite moments.
Total clockwise moment = total counterclockwise moment.

6. Same gravity? g cancels.
For masses on a seesaw, m₁d₁ = m₂d₂ because the same g is on both sides.

DO IT FAST

PIVOT → SIDE → PRODUCT

PIVOT: mark the fulcrum. SIDE: decide clockwise or counterclockwise. PRODUCT: compare force × distance only when you need the size of the turning effect.

Fast check: a smaller force can balance a larger one only if it acts farther from the fulcrum.

WORKED EXAMPLES

See the mechanism before the equation

Common traps

Comparing forces only: distance matters too. Using total lever length: measure each arm from the fulcrum. Ignoring direction: opposite moments oppose each other. Multiplying every mass by g: for a balance of masses in the same gravity, g cancels.

FIVE-FORM SKILL CHECK

Can you handle all five forms?

This chooses your next practice step; it does not verify mastery.

CHOOSE YOUR PRACTICE

Practice at the level you need

FRESH MASTERY CHECK

Verify the competency

Mastery requires 5/5. A missed item loads a different five-question set for the next attempt.

FAQ

Quick clarifications

Torque or moment? Here, both describe the turning effect of a force about a pivot. Use force × perpendicular distance.

Do I always need an equation? No. Direction and qualitative force-distance questions are often faster by inspection.

Why can kg be used on both sides of a seesaw? Each weight is mg; the same g cancels.

Several forces on one side? Add their moments, keeping clockwise and counterclockwise effects separate.

RELATED COMPETENCIES

Continue Mechanical Reasoning

Gears & Gear Trains · Pulleys & Mechanical Advantage · Belts, Chains, Racks & Connected Wheels · Wheels & Axles · Forces, Friction & Equilibrium

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DOST-SEI Mechanical Reasoning Reviewer: Gears & Gear Trains

TEACHER ABI · DOST-SEI MECHANICAL REASONING

Gears & Gear Trains

Trace rotation, compare gear speeds, use tooth ratios, and solve multi-gear systems without getting lost in the diagram.

5–10 minute lesson27 original questionsAdaptive practiceSaves progress

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Gears & Gear Trains

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Read the contact before you calculate

Gear questions usually test two separate ideas: direction and speed. Solve those separately. A large gear is not automatically the driver, and a small gear is not automatically faster unless the gears are actually connected in a way that transmits motion.

1. Meshed gears reverse direction

Two external gears touching tooth-to-tooth rotate in opposite directions.

2. Trace one contact at a time

A→B reverses once. B→C reverses again. So A and C rotate in the same direction.

3. Smaller gear = greater angular speed

If a 20-tooth gear meshes with a 40-tooth gear, the 20-tooth gear makes twice as many revolutions in the same time.

4. Tooth count and rpm trade off

teeth₁ × rpm₁ = teeth₂ × rpm₂

For a simple pair of meshed gears, doubling the tooth count halves the rotational speed.

5. An idler does not change the final ratio

The middle gear changes the direction relationship and spacing. The overall speed ratio still depends on the first and last gears.

6. Same shaft means same rpm

If two gears are rigidly attached to the same axle, they rotate together at the same angular speed and in the same direction, even if their sizes differ.

DO IT FAST

Use TRACE → COMPARE → RATIO

TRACE: Mark the direction at every gear contact. Each external-gear mesh reverses direction.

COMPARE: Decide whether the question only asks which gear is faster/slower. Smaller meshed gear → faster rotation.

RATIO: Only calculate when numbers are needed. Use N₁n₁ = N₂n₂, where N is tooth count and n is rpm.

Two fast checks

Direction check: an even number of external-gear contacts gives the same final direction; an odd number gives the opposite direction.

Magnitude check: if the driven gear has more teeth than the driver, your calculated driven rpm should be smaller.

WORKED EXAMPLES

Five forms you should recognize

1. Direct direction

Problem: A turns clockwise and meshes directly with B.

Reasoning: One contact = one reversal.

Answer: B turns counterclockwise.

2. Multi-gear train

Problem: A–B–C–D–E form a line. A turns clockwise.

Trace: A ↻ → B ↺ → C ↻ → D ↺ → E ↻.

Answer: B and D are the counterclockwise gears.

3. Relative speed

Problem: A 15-tooth gear meshes with a 45-tooth gear.

Reasoning: The smaller gear has one-third as many teeth, so it turns three times as fast.

Answer: The 15-tooth gear has three times the rpm of the 45-tooth gear.

4. Numerical ratio

Problem: A 24-tooth driver turns at 150 rpm and drives a 60-tooth gear.

24(150) = 60n → n = 60 rpm

Check: The driven gear is larger, so 60 rpm being less than 150 rpm makes sense.

5. Idler transfer

Problem: A 20-tooth gear drives a 30-tooth idler, which drives a 50-tooth output. A turns clockwise at 200 rpm.

Direction: Two contacts → output turns clockwise.

20(200) = 50n → n = 80 rpm

The idler's 30 teeth do not appear in the final speed ratio.

COMMON TRAPS

Check before you commit

• Assuming all gears in a train alternate speed by the same amount
• Using gear size to decide direction
• Forgetting that every external-gear contact reverses direction
• Multiplying rpm by tooth count in the wrong direction and making a larger driven gear faster
• Including a simple idler in the final driver-to-output ratio
• Assuming two gears on the same shaft have different rpm because they have different sizes
• Using the simple idler shortcut on a compound train where two gears share a shaft
• Answering a direction-only question with unnecessary calculations

FIVE-FORM SKILL CHECK

Do you need the lesson—or just practice?

One original question in each form checks direction, gear trains, relative speed, ratios, and transfer. It recommends your next step but does not yet verify mastery.

CHOOSE YOUR PRACTICE

Work at the level you need.

Foundations

Build direction, reversal counting, size-speed intuition, and idler basics.

Core Practice

Mix direction with tooth counts, rpm, and longer gear trains.

DOST-Style Transfer

Apply the rules to racks, shared shafts, compound trains, and unfamiliar setups.

FRESH MASTERY CHECK

Ready to verify this competency?

A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-question bank.

QUICK ANSWERS

Gears & Gear Trains FAQ

Do bigger gears always turn more slowly?

Only compare speeds after identifying how the gears are connected. Two gears rigidly fixed to the same shaft have the same rpm. Two gears meshing at their teeth have speeds inversely related to tooth count.

Does an idler gear change the gear ratio?

In a simple train, no. It changes direction transmission and allows spacing between the driver and output. The overall speed ratio depends on the first driver and final driven gear.

How can I tell the final direction quickly?

Count external-gear contacts from the starting gear to the target. Even number of contacts → same direction. Odd number → opposite direction.

What if two gears are on the same shaft?

Treat them as one rotating unit for rpm and direction. Their different tooth counts matter only when each meshes with another gear.

Do I need to memorize many formulas?

No. For the gear questions in this reviewer, the main numerical relationship is N₁n₁ = N₂n₂. Most errors come from direction tracing or from misunderstanding the connection, not from algebra.

RELATED COMPETENCIES

Continue your Mechanical Reasoning review.

Belts, Chains, Racks & Connected WheelsLevers, Torque & BalancePulleys & Mechanical AdvantageWheels, Axles & Rotational Systems

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