ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Hard
A construction crane lifts a 1000 kg beam vertically upward at a constant speed of 0.5 m/s. What is the power exerted by the crane in lifting the beam?
- A4900 W
- B9800 W
- C2450 W
- D500 W
Show answer & explanationAnswer & explanation
Correct answer: A. 4900 W
Power (P) is the rate at which work is done, or P = Work / time. Alternatively, for an object moving at a constant velocity against a constant force, Power = Force × Velocity. Here, the force required to lift the beam at a constant speed is equal to its weight (Force = mass × gravity). So, Force = 1000 kg × 9.8 m/s² = 9800 N. Then, Power = 9800 N × 0.5 m/s = 4900 W.
Why the other options are wrong
- B. Incorrect, this is the force (weight) of the beam, not the power.
- C. Incorrect, miscalculation or used g=4.9.
- D. Incorrect, likely calculated mass × velocity.
Power in Lifting
The rate at which work is done against gravity when lifting an object. It is calculated by multiplying the force required to lift the object (its weight) by the constant vertical velocity.
- Formula: P = F × v (where F is the lifting force and v is the constant velocity).
- Force (F) = mass × gravity (mg).
- Units: Watts (W), where 1 W = 1 J/s (Joule per second).
Memory trick: Power is Force times Velocity, or Work over Time.