Mechanical Comprehension Flashcards

A spring-loaded rescue tool requires 80 pounds of force to compress the spring 4 inches. What is the spring constant (k)?

Answer: 20 lb/in

Using Hooke's Law: F = kx, where k = F/x = 80 pounds / 4 inches = 20 lb/in.

A wheel and axle mechanism has a wheel diameter of 24 inches and an axle diameter of 4 inches. What is the mechanical advantage?

Answer: 6:1

The mechanical advantage of a wheel and axle = wheel diameter / axle diameter = 24 / 4 = 6:1 (or equivalently, wheel radius / axle radius = 12/2 = 6:1).

A fire truck's water tank holds 500 gallons. If water weighs approximately 8.34 pounds per gallon, what is the approximate weight of the water when the tank is full?

Answer: 4,170 pounds

Weight = volume × density = 500 gallons × 8.34 lb/gal = 4,170 pounds.

Two workers push a stalled vehicle. Worker A pushes with 150 pounds of force due east, and Worker B pushes with 200 pounds of force due north. What is the approximate magnitude of the resultant force?

Answer: 250 pounds

When forces are perpendicular, the resultant is found using the Pythagorean theorem: √(150² + 200²) = √(22,500 + 40,000) = √62,500 = 250 pounds.

A belt-driven fan system has a motor pulley with a 6-inch diameter driving a fan pulley with an 18-inch diameter. If the motor runs at 1,800 RPM, what is the fan speed?

Answer: 600 RPM

In belt-drive systems, the speed ratio is inversely proportional to pulley diameter: Fan RPM = Motor RPM × (Motor diameter / Fan diameter) = 1,800 × (6/18) = 600 RPM.

A 10-foot ladder is leaning against a wall with its base 6 feet from the wall. How high up the wall does the ladder reach?

Answer: 8 feet

Using the Pythagorean theorem: height = √(ladder² - base²) = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.