ASTB-E ASTB-E Math & Mechanical Reasoning 2

Question 1

A pulley system has one fixed and one movable pulley. Ignoring friction, how much force is needed to lift a 200-pound load?

Accepted Answer

100 pounds

Answer

A single movable pulley doubles the mechanical advantage, so only half the load force is needed: 200 ÷ 2 = 100 pounds.

Question 2

Solve for x: 3x + 9 = 30

Accepted Answer

7

Answer

Subtract 9 from both sides: 3x = 21, then divide by 3: x = 7.

Question 3

Water flows through a pipe at 4 gallons per minute. How many gallons flow through in 2.5 hours?

Accepted Answer

600 gallons

Answer

2.5 hours = 150 minutes; 150 minutes × 4 gal/min = 600 gallons.

Question 4

A spring compressed by 3 inches requires 15 pounds of force. How much force is needed to compress it 5 inches (assuming linear spring)?

Accepted Answer

25 pounds

Answer

Spring rate = 15 ÷ 3 = 5 lb/inch; force for 5 inches = 5 × 5 = 25 pounds.

Question 5

An aircraft travels at 300 knots. Approximately how many miles per hour is this?

Accepted Answer

345 mph

Answer

One knot = 1.15 mph; 300 knots × 1.15 = 345 mph.

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