Chapter Boss: Machine Shop

Why it matters

The contract: lift 600 N, rope rated 250 N, and every pulley you add comes off your profit. Physics is about to make you money — or lose it.

The idea in plain words

Engineering = physics + a budget. Tap the terms.

tension = load ÷ n ≤ rope rating

Load 900 N, rope rating 250 N. Minimum segments?

n = 4 (tension 225 N)

• newton: tension — each supporting segment carries load/n — the number that snaps ropes
• newton: rating — the rope's safe working limit — cross it once and the load is on the floor
• ₹: cost — every sheave adds friction AND price — real design is the cheapest safe answer
• n ≥ 900 ÷ 250 = 3.6
• segments are whole numbers

Predict first

With rope that snaps above 250 N, the minimum rope segments to hold 600 N is…

600 ÷ 3 = 200 N ≤ 250 N ✓, while 600 ÷ 2 = 300 N snaps. Three segments: safe AND cheapest.

• 3 — tension becomes 200 N per segment — correct
• 2 — 300 N each is close enough
• 6 — always double for safety

What you do

Add ropes until the tension is safe — then remove any you don't strictly need. The contract pays for minimalism.

Check yourself

A machine is 75% efficient with VR = 8. Its MA is…

MA = ηVR = 0.75 × 8 = 6.

Oiling a machine raises its…

Less friction → more of your effort reaches the load → MA and η rise. VR never moves without a redesign.

Why do cranes use block & tackle instead of one giant motor pulling directly?

Trading speed for force means modest motors lift enormous loads — the whole chapter in one crane.

• 6 — correct
• 8
• 10.7
• MA and efficiency (VR is unchanged geometry) — correct
• VR
• load capacity of the rope
• n segments let a small, cheap motor exert n× the force (slower is fine) — correct
• ropes look professional
• motors can't pull straight up