Now that you know how to calculate the torque using components of vector r, plug in values from a trial of your choice. The mass of the weights in each trial are: Trial 1,3,5,6: 4.54 kg Trial 2,4,6,8: 15.95 kg Hint: How can you use the tools available to measure the perpendicular component of r? (Ruler, Protractor, Vertical Line)
Now that you know how to calculate the torque using components of vector r, plug in values from a trial of your choice. The mass of the weights in each trial are: Trial 1,3,5,6: 4.54 kg Trial 2,4,6,8: 15.95 kg Hint: How can you use the tools available to measure the perpendicular component of r? (Ruler, Protractor, Vertical Line)
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Chapter1: Units, Trigonometry. And Vectors
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Now that you know how to calculate the torque using components of vector r, plug in values from a trial of your choice.
-
The mass of the weights in each trial are:
- Trial 1,3,5,6: 4.54 kg
- Trial 2,4,6,8: 15.95 kg
Hint:
How can you use the tools available to measure the perpendicular component of r? (Ruler, Protractor, Vertical Line)
![In this image, a mechanical setup is used to demonstrate concepts in physics related to force vectors and torque.
### Description:
- **Mechanical Arm**: Attached to a pivot point on a vertical support structure, the arm is shown extending outward at an angle.
- **Vectors**:
- **\[ \vec{r} \] (Position Vector)**: This is the vector from the pivot point to the point where the force \[ \vec{F} \] is applied.
- **\[ \vec{r}_\perp \] (Perpendicular Component)**: It is depicted as a dashed red arrow that is perpendicular to the line of action of the force. This component is critical in calculating torque since torque is maximized when force is applied perpendicularly.
- **\[ \vec{r}_\parallel \] (Parallel Component)**: This is another dashed red arrow, representing the component of \[ \vec{r} \] that is parallel to the force line, which does not contribute to torque.
- **\[ \vec{F} \] (Force Vector)**: Illustrated as a blue arrow pointing downwards from the end of the arm, it represents the force being applied.
- **Line of Action of the Force**: Shown as a dashed line extending from \[ \vec{F} \] in the direction of the force. This line helps in visualizing where the force would continue if unobstructed.
### Concepts:
- **Torque (\[ \tau \])**: It is the rotational equivalent of force, calculated as \[ \tau = \vec{r}_\perp \times \vec{F} \]. Only the perpendicular distance contributes to the torque.
- **Vector Components**: Decomposing \[ \vec{r} \] into perpendicular (\[ \vec{r}_\perp \]) and parallel (\[ \vec{r}_\parallel \]) components helps in understanding how torque and linear force interact.
This setup is useful for educational insights into balancing forces, understanding torque, and analyzing vector components in rotational dynamics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F564f6caa-72b9-4830-9068-7e6c4ac461c2%2Ffc2560fc-e86f-4509-b450-3bdf109291b1%2Fzm2o8s_processed.png&w=3840&q=75)
Transcribed Image Text:In this image, a mechanical setup is used to demonstrate concepts in physics related to force vectors and torque.
### Description:
- **Mechanical Arm**: Attached to a pivot point on a vertical support structure, the arm is shown extending outward at an angle.
- **Vectors**:
- **\[ \vec{r} \] (Position Vector)**: This is the vector from the pivot point to the point where the force \[ \vec{F} \] is applied.
- **\[ \vec{r}_\perp \] (Perpendicular Component)**: It is depicted as a dashed red arrow that is perpendicular to the line of action of the force. This component is critical in calculating torque since torque is maximized when force is applied perpendicularly.
- **\[ \vec{r}_\parallel \] (Parallel Component)**: This is another dashed red arrow, representing the component of \[ \vec{r} \] that is parallel to the force line, which does not contribute to torque.
- **\[ \vec{F} \] (Force Vector)**: Illustrated as a blue arrow pointing downwards from the end of the arm, it represents the force being applied.
- **Line of Action of the Force**: Shown as a dashed line extending from \[ \vec{F} \] in the direction of the force. This line helps in visualizing where the force would continue if unobstructed.
### Concepts:
- **Torque (\[ \tau \])**: It is the rotational equivalent of force, calculated as \[ \tau = \vec{r}_\perp \times \vec{F} \]. Only the perpendicular distance contributes to the torque.
- **Vector Components**: Decomposing \[ \vec{r} \] into perpendicular (\[ \vec{r}_\perp \]) and parallel (\[ \vec{r}_\parallel \]) components helps in understanding how torque and linear force interact.
This setup is useful for educational insights into balancing forces, understanding torque, and analyzing vector components in rotational dynamics.
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