College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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What minimum force must be exerted?
![**Physics Problem: Calculating Torque Requirements**
**Problem Statement:**
If the torque required to loosen a nut on the wheel of a car has a magnitude of 40.0 N·m, what minimum force must be exerted by a mechanic at the end of a 30.0 cm wrench to loosen the nut?
---
**Explanation:**
This problem involves calculating the necessary force to achieve a given torque when using a wrench. Torque (\( \tau \)) is calculated using the equation:
\[ \tau = r \times F \]
where:
- \( \tau \) is the torque (in Newton-meters, N·m),
- \( r \) is the lever arm length (in meters, m),
- \( F \) is the force applied perpendicular to the lever arm (in Newtons, N).
**Given:**
- Torque (\( \tau \)) = 40.0 N·m
- Lever arm length (\( r \)) = 30.0 cm = 0.30 m
**To Find:**
- Minimum Force (\( F \)) required to loosen the nut
**Solution:**
Rearrange the equation to solve for force (\( F \)):
\[ F = \frac{\tau}{r} \]
Substitute the known values:
\[ F = \frac{40.0 \, \text{N·m}}{0.30 \, \text{m}} \]
\[ F = 133.33 \, \text{N} \]
Therefore, the mechanic must exert a minimum force of approximately 133.33 N at the end of the wrench to loosen the nut.](https://content.bartleby.com/qna-images/question/51017fe1-0672-4cad-89e4-c6f0a0bf2651/200aacb4-e17c-473d-89c9-699b5260cca6/ojzy2we_processed.jpeg)
Transcribed Image Text:**Physics Problem: Calculating Torque Requirements**
**Problem Statement:**
If the torque required to loosen a nut on the wheel of a car has a magnitude of 40.0 N·m, what minimum force must be exerted by a mechanic at the end of a 30.0 cm wrench to loosen the nut?
---
**Explanation:**
This problem involves calculating the necessary force to achieve a given torque when using a wrench. Torque (\( \tau \)) is calculated using the equation:
\[ \tau = r \times F \]
where:
- \( \tau \) is the torque (in Newton-meters, N·m),
- \( r \) is the lever arm length (in meters, m),
- \( F \) is the force applied perpendicular to the lever arm (in Newtons, N).
**Given:**
- Torque (\( \tau \)) = 40.0 N·m
- Lever arm length (\( r \)) = 30.0 cm = 0.30 m
**To Find:**
- Minimum Force (\( F \)) required to loosen the nut
**Solution:**
Rearrange the equation to solve for force (\( F \)):
\[ F = \frac{\tau}{r} \]
Substitute the known values:
\[ F = \frac{40.0 \, \text{N·m}}{0.30 \, \text{m}} \]
\[ F = 133.33 \, \text{N} \]
Therefore, the mechanic must exert a minimum force of approximately 133.33 N at the end of the wrench to loosen the nut.
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