ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Hard
A plumber uses a wrench to tighten a pipe fitting. The wrench has a length of 0.3 meters, and the plumber applies a force of 50 N at an angle of 60 degrees to the wrench handle. What is the magnitude of the torque applied to the fitting?
- A25.0 N·m
- B15.0 N·m
- C7.5 N·m
- D13.0 N·m
Show answer & explanationAnswer & explanation
Correct answer: D. 13.0 N·m
Torque (τ) is calculated as Force (F) × Lever Arm (r) × sin(θ), where θ is the angle between the force vector and the lever arm. Here, F = 50 N, r = 0.3 m, and θ = 60°. So, τ = 50 N × 0.3 m × sin(60°). sin(60°) ≈ 0.866. Therefore, τ = 15 N·m × 0.866 ≈ 12.99 N·m, which is approximately 13.0 N·m.
Why the other options are wrong
- A. Incorrect, miscalculation or incorrect formula application.
- B. Incorrect, this is F × r, ignoring the angle component.
- C. Incorrect, likely calculated without the sine component (50 * 0.3 * 0.5, if sin 30 was used).
Torque with Angle
Torque is the rotational equivalent of force. When force is applied at an angle to the lever arm, only the component of the force perpendicular to the arm contributes to the torque.
- Formula: τ = F × r × sin(θ).
- Units: Newton-meters (N·m).
- Maximum torque occurs when the force is perpendicular (θ = 90°, sin 90° = 1).
Memory trick: Twisting force needs the 'sine' of the angle.