THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Torque
Turn a wrench with an angled force
A 40 N force acts at the end of a 0.30 m wrench, making 30° with its handle.
Find the torque magnitude about the bolt.
Organize the givens & assumptions
- r = 0.30 m
- F = 40 N
- θ = 30°
Rigid wrench; pivot at the fastener; force and handle lie in one plane; torque magnitude requested.
Study with a tutor prompt
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Problem: Turn a wrench with an angled force
A 40 N force acts at the end of a 0.30 m wrench, making 30° with its handle.
Question: Find the torque magnitude about the bolt.
Givens:
- r = 0.30 m
- F = 40 N
- θ = 30°
Assumptions: Rigid wrench; pivot at the fastener; force and handle lie in one plane; torque magnitude requested.
Choices (LaTeX):
A. 12\ \mathrm{N\,m}
B. 6\sqrt3\ \mathrm{N\,m}
C. 0\ \mathrm{N\,m}
D. 6\ \mathrm{N\,m}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
Torque can be calculated in two equivalent ways: perpendicular force times handle length, or full force times the perpendicular moment arm.
Choose a physical relation
Only the component perpendicular to the handle produces a turning moment about the fastener.
Resolve the turning component
Resolve the pull perpendicular to the handle. The parallel component acts along a line through the pivot and contributes no moment.
Why is this step valid?
The moment arm for the perpendicular component is the full 0.30 m handle length. Equivalently, the full 40 N force has a shorter perpendicular moment arm.
Substitute and interpret
Torque is 6 N·m; using all 40 N would assume a perpendicular pull.
Using the perpendicular moment arm gives the same turning effect.
TRY THE IDEA AGAIN
A force acts directly along the handle through the pivot. What torque does it produce?
YOUR LEARNING NOTE
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