FCTC Applying Mechanical Reasoning 4

Question 1

A water pipe narrows from a 4-inch diameter to a 2-inch diameter. How does the water velocity change at the narrow section?

Accepted Answer

Velocity quadruples

Answer

Area decreases by a factor of 4 (since area ∝ radius²), so velocity must increase by 4 to maintain constant flow rate.

Question 2

A spring with a spring constant of 50 lb/in is compressed 3 inches. How much force is required to hold it compressed?

Accepted Answer

150 lb

Answer

Using Hooke's Law: F = k × x = 50 lb/in × 3 in = 150 lb.

Question 3

A bolt is being tightened using a torque wrench set to 60 ft-lb. If the wrench handle is 2 feet long, what perpendicular force must be applied?

Accepted Answer

30 lb

Answer

Force = Torque ÷ Distance = 60 ft-lb ÷ 2 ft = 30 lb.

Question 4

Which material would be BEST for a machine part that must absorb repeated impact without cracking?

Accepted Answer

Ductile low-carbon steel

Answer

Ductile low-carbon steel has high toughness and absorbs impact energy by deforming rather than fracturing.

Question 5

A pneumatic cylinder has a bore diameter of 4 inches and is supplied with air at 100 PSI. Approximately what force can it generate?

Accepted Answer

1,257 lb

Answer

Force = Pressure × Area = 100 PSI × π(2²) ≈ 100 × 12.57 ≈ 1,257 lb.

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