ASTB-E ASTB-E Math & Mechanical Reasoning 2 — Questions and Answers
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?
- 200 pounds
- 100 pounds (Correct answer)
- 50 pounds
- 25 pounds
Correct answer: 100 pounds
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
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
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?
- 400 gallons
- 500 gallons
- 600 gallons (Correct answer)
- 700 gallons
Correct answer: 600 gallons
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)?
- 20 pounds
- 25 pounds (Correct answer)
- 30 pounds
- 35 pounds
Correct answer: 25 pounds
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?
- 260 mph
- 300 mph
- 345 mph (Correct answer)
- 415 mph
Correct answer: 345 mph
One knot = 1.15 mph; 300 knots × 1.15 = 345 mph.
Question 6: Which of the following represents the greatest mechanical advantage for lifting a heavy load?
- A single fixed pulley
- A ramp with a 30-degree incline
- A ramp with a 10-degree incline (Correct answer)
- A lever with equal arm lengths
Correct answer: A ramp with a 10-degree incline
A shallower incline (10°) provides a longer ramp for the same height, giving a greater mechanical advantage than steeper ramps or fixed pulleys.
ASTB-E ASTB-E Math & Mechanical Reasoning 2
A pulley system has one fixed and one movable pulley.
Ignoring friction, how much force is needed to lift a 200-pound load?