FCTC Applying Mechanical Reasoning 4 β Questions and Answers
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?
- Velocity stays the same
- Velocity doubles
- Velocity quadruples (Correct answer)
- Velocity is halved
Correct answer: Velocity quadruples
Area decreases by a factor of 4 (since area β radiusΒ²), 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?
- 17 lb
- 53 lb
- 150 lb (Correct answer)
- 450 lb
Correct answer: 150 lb
Using Hooke's Law: F = k Γ x = 50 lb/in Γ 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?
- 15 lb
- 30 lb (Correct answer)
- 60 lb
- 120 lb
Correct answer: 30 lb
Force = Torque Γ· Distance = 60 ft-lb Γ· 2 ft = 30 lb.
Question 4: Which material would be BEST for a machine part that must absorb repeated impact without cracking?
- Cast iron
- High-carbon steel
- Ductile low-carbon steel (Correct answer)
- Hardened aluminum
Correct answer: Ductile low-carbon steel
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?
- 400 lb
- 800 lb
- 1,257 lb (Correct answer)
- 1,600 lb
Correct answer: 1,257 lb
Force = Pressure Γ Area = 100 PSI Γ Ο(2Β²) β 100 Γ 12.57 β 1,257 lb.
Question 6: When a metal shaft is rotated by a belt drive, the belt on the slack side has 50 lb of tension and the tight side has 200 lb. What net force drives the pulley?
- 50 lb
- 150 lb (Correct answer)
- 200 lb
- 250 lb
Correct answer: 150 lb
Net driving force = tight side tension β slack side tension = 200 β 50 = 150 lb.
Question 7: Two objects are connected by a rope over a frictionless pulley. Object A weighs 80 lb and Object B weighs 50 lb. What is the acceleration direction of the system?
- Object A accelerates downward (Correct answer)
- Object B accelerates downward
- The system remains in equilibrium
- Both objects accelerate downward
Correct answer: Object A accelerates downward
The heavier object (A at 80 lb) accelerates downward because the net unbalanced force acts in that direction.
FCTC Applying Mechanical Reasoning 4
A water pipe narrows from a 4-inch diameter to a 2-inch diameter.
How does the water velocity change at the narrow section?