A pair of forces with equal magnitudes, opposite directions, and different lines of action is called a “couple.” When a couple acts on a rigid object, the couple produces a torque that does not depend on the location of the axis. The figure shows a couple acting on a tire wrench, each force being perpendicular to the wrench. Let L = 0.389 m and F = 24.4 N. Determine the torque produced by the couple when the axis is perpendicular to the tire and passes through (a) point A, (b) point B, and (c) point C.
A pair of forces with equal magnitudes, opposite directions, and different lines of action is called a “couple.” When a couple acts on a rigid object, the couple produces a torque that does not depend on the location of the axis. The figure shows a couple acting on a tire wrench, each force being perpendicular to the wrench. Let L = 0.389 m and F = 24.4 N. Determine the torque produced by the couple when the axis is perpendicular to the tire and passes through (a) point A, (b) point B, and (c) point C.
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A pair of forces with equal magnitudes, opposite directions, and different lines of action is called a “couple.” When a couple acts on a rigid object, the couple produces a torque that does not depend on the location of the axis. The figure shows a couple acting on a tire wrench, each force being perpendicular to the wrench. Let L = 0.389 m and F = 24.4 N. Determine the torque produced by the couple when the axis is perpendicular to the tire and passes through (a) point A, (b) point B, and (c) point C.
![The image illustrates the use of a wrench to apply torque on a bolt in a wheel.
**Components of the Image:**
1. **Hands and Wrench:**
- There are two hands holding a wrench that is positioned to unscrew a bolt on a wheel.
- Hand 'A' applies a force labeled as \(-F\).
- Hand 'C' is bracing at another point along the wrench.
2. **Wrench Positions:**
- The wrench is depicted as a straight line connecting points A, B, and C.
- The wrench is shown at an angle with respect to the wheel, extending from point B to the bolt at point C.
3. **Forces and Directions:**
- Arrow \(-F\) represents the force applied by hand 'A'.
- Arrow \(F\) represents the reaction force at the bolt in the opposite direction.
- These forces create a couple, a pair of equal and opposite forces whose lines of action do not coincide, resulting in a rotation.
4. **Distance Labels:**
- The distance between point A and point B is labeled \(L/2\).
- The distance between point B and point C is also labeled \(L/2\).
- Combined, the total length of the wrench \(A \rightarrow C\) is represented as \(L\).
**Explanation:**
This diagram illustrates the principle of torque, which is calculated as the product of force and the lever arm distance from the pivot point. Torque (\(\tau\)) is given by:
\[
\tau = F \times L
\]
In this case, the forces \(-F\) and \(F\) create a rotational effect on the wheel's bolt, with the total lever arm length being \(L\). This setup is commonly used for changing wheels or tightening bolts and demonstrates how leverage can be used to apply a significant amount of rotational force with relatively small input force.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cc909b9-6e66-4544-951b-fbea744c0578%2F31c3e325-733e-4efe-84ba-097684e27d80%2Fkpim0pj_processed.gif&w=3840&q=75)
Transcribed Image Text:The image illustrates the use of a wrench to apply torque on a bolt in a wheel.
**Components of the Image:**
1. **Hands and Wrench:**
- There are two hands holding a wrench that is positioned to unscrew a bolt on a wheel.
- Hand 'A' applies a force labeled as \(-F\).
- Hand 'C' is bracing at another point along the wrench.
2. **Wrench Positions:**
- The wrench is depicted as a straight line connecting points A, B, and C.
- The wrench is shown at an angle with respect to the wheel, extending from point B to the bolt at point C.
3. **Forces and Directions:**
- Arrow \(-F\) represents the force applied by hand 'A'.
- Arrow \(F\) represents the reaction force at the bolt in the opposite direction.
- These forces create a couple, a pair of equal and opposite forces whose lines of action do not coincide, resulting in a rotation.
4. **Distance Labels:**
- The distance between point A and point B is labeled \(L/2\).
- The distance between point B and point C is also labeled \(L/2\).
- Combined, the total length of the wrench \(A \rightarrow C\) is represented as \(L\).
**Explanation:**
This diagram illustrates the principle of torque, which is calculated as the product of force and the lever arm distance from the pivot point. Torque (\(\tau\)) is given by:
\[
\tau = F \times L
\]
In this case, the forces \(-F\) and \(F\) create a rotational effect on the wheel's bolt, with the total lever arm length being \(L\). This setup is commonly used for changing wheels or tightening bolts and demonstrates how leverage can be used to apply a significant amount of rotational force with relatively small input force.
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