The skiing duo of Brian (81 kg ) and Ashley (54 kg ) is always a crowd pleaser. In one routine, Brian, wearing wood skis, starts at the top of a 290-m-long, 20° slope. Ashley waits for him halfway down. As he skis past, she leaps into his arms and he carries her the rest of the way down. Hint. Use coefficient of kinetic friction from Table 6.1 in Part A the textbook. What is their speed at the bottom of the slope? Express your answer to two significant figures and include the appropriate units. HÀ v = Value Units Submit Request Answer

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Two sig figs, please. I have included table 6.1, needed for the problem. 

**The Skiing Duo Performance: Understanding Physics in Motion**

The skiing duo of Brian (81 kg) and Ashley (54 kg) always captivates audiences with their thrilling routine. Brian, equipped with wood skis, begins his descent from the top of a 290-meter-long slope with a 20° incline. Midway down, Ashley joins him. As she skis past, she leaps into his arms, and Brian carries her for the remainder of the slope. 

**Question:**
What is their speed at the bottom of the slope?

**Instructions:**
Express your answer to two significant figures and include the appropriate units.

**Hint:**
Use the coefficient of kinetic friction from Table 6.1 in the textbook.

```plaintext
v = [       ] [Units]
```

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**Note:** To solve this question, consider the principles of physics including gravitational force, friction, and momentum.
Transcribed Image Text:**The Skiing Duo Performance: Understanding Physics in Motion** The skiing duo of Brian (81 kg) and Ashley (54 kg) always captivates audiences with their thrilling routine. Brian, equipped with wood skis, begins his descent from the top of a 290-meter-long slope with a 20° incline. Midway down, Ashley joins him. As she skis past, she leaps into his arms, and Brian carries her for the remainder of the slope. **Question:** What is their speed at the bottom of the slope? **Instructions:** Express your answer to two significant figures and include the appropriate units. **Hint:** Use the coefficient of kinetic friction from Table 6.1 in the textbook. ```plaintext v = [ ] [Units] ``` **Submission Tools:** - Submit Button - Request Answer Option **Note:** To solve this question, consider the principles of physics including gravitational force, friction, and momentum.
**A Model of Friction**

These ideas can be summarized in a model of friction:

- **Static:** \( \vec{f}_s \leq (\mu_s n, \text{ direction as necessary to prevent motion}) \)
- **Kinetic:** \( \vec{f}_k = (\mu_k n, \text{ direction opposite the motion}) \)
- **Rolling:** \( \vec{f}_r = (\mu_r n, \text{ direction opposite the motion}) \)

*(6.15)*

Here, “motion” means “motion relative to the surface.” The maximum value of static friction \( f_{s \, \text{max}} = \mu_s n \) occurs at the point where the object slips and begins to move.

**Note:** Equations 6.15 are a “model” of friction, not a “law” of friction. These equations—a simplification of reality—provide a reasonably accurate, but not perfect, description of how friction forces act. They are not a “law of nature” on a level with Newton’s laws.

**Table 6.1 Coefficients of Friction:**

| Materials               | Static \( \mu_s \) | Kinetic \( \mu_k \) | Rolling \( \mu_r \) |
|-------------------------|-------------------|--------------------|-------------------|
| Rubber on concrete      | 1.00              | 0.80               | 0.02              |
| Steel on steel (dry)    | 0.80              | 0.60               | 0.002             |
| Steel on steel (lubricated) | 0.10           | 0.05               |                   |
| Wood on wood            | 0.50              | 0.20               |                   |
| Wood on snow            | 0.12              | 0.06               |                   |
| Ice on ice              | 0.10              | 0.03               |                   |

This table provides a list of coefficients of friction for different material combinations, illustrating how friction varies between static, kinetic, and rolling conditions.
Transcribed Image Text:**A Model of Friction** These ideas can be summarized in a model of friction: - **Static:** \( \vec{f}_s \leq (\mu_s n, \text{ direction as necessary to prevent motion}) \) - **Kinetic:** \( \vec{f}_k = (\mu_k n, \text{ direction opposite the motion}) \) - **Rolling:** \( \vec{f}_r = (\mu_r n, \text{ direction opposite the motion}) \) *(6.15)* Here, “motion” means “motion relative to the surface.” The maximum value of static friction \( f_{s \, \text{max}} = \mu_s n \) occurs at the point where the object slips and begins to move. **Note:** Equations 6.15 are a “model” of friction, not a “law” of friction. These equations—a simplification of reality—provide a reasonably accurate, but not perfect, description of how friction forces act. They are not a “law of nature” on a level with Newton’s laws. **Table 6.1 Coefficients of Friction:** | Materials | Static \( \mu_s \) | Kinetic \( \mu_k \) | Rolling \( \mu_r \) | |-------------------------|-------------------|--------------------|-------------------| | Rubber on concrete | 1.00 | 0.80 | 0.02 | | Steel on steel (dry) | 0.80 | 0.60 | 0.002 | | Steel on steel (lubricated) | 0.10 | 0.05 | | | Wood on wood | 0.50 | 0.20 | | | Wood on snow | 0.12 | 0.06 | | | Ice on ice | 0.10 | 0.03 | | This table provides a list of coefficients of friction for different material combinations, illustrating how friction varies between static, kinetic, and rolling conditions.
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