A mechanic tightens the same bolt using three different tools
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A mechanic tightens the same bolt using three different tools.
• Situation I: A short wrench produces a constant torque of 25 N·m while the bolt is turned through 0.40 rad.
• Situation II: A medium wrench produces a constant torque of 18 N·m while the bolt is turned through 0.55 rad.
• Situation III: A long wrench produces a constant torque of 12 N·m while the bolt is turned through 1.0 rad.
Assume the bolt is initially at rest and the torque supplied by the mechanic is the only external torque acting on the bolt.
(a) For each situation, indicate whether the mechanical energy of the bolt–wrench system increases, decreases, or remains unchanged. Justify each answer without performing explicit numerical calculations.
(b) Rank the three situations from greatest to least according to the magnitude of the rotational work done on the bolt. Clearly explain the reasoning that leads to your ranking.
(c) The mechanic claims that Situation II is the most efficient because the medium wrench “feels easiest.” Evaluate this claim by discussing the relationship between perceived effort (torque) and the total energy transferred to the bolt in each situation.