Consider the 65.0 kg ice skater being pushed by two others shown in the figure. F₁ Ftot F₁ Free-body diagram F₂ F₁

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:**

Consider the 65.0 kg ice skater being pushed by two others as shown in the figure.

**Figure Explanation:**

- The diagram illustrates three individuals on an ice surface.
- Person A exerts force \( F_1 \) horizontally to the right.
- Person B exerts force \( F_2 \) vertically upward.
- The resultant force \( F_{\text{tot}} \) is depicted by an arrow diagonally upward and to the right, representing the vector sum of \( F_1 \) and \( F_2 \).
- There is also a free-body diagram showing the vectors \( F_1 \) and \( F_2 \).

---

**Questions:**

(a) **Find the direction (in degrees) and magnitude (in N) of \( F_{\text{tot}} \),** the total force exerted on her by the others, given that the magnitudes \( F_1 \) and \( F_2 \) are 28.8 N and 18.6 N, respectively.

- \(\text{Direction:} \, \_\_\_\_^\circ \, (\text{counterclockwise from the direction of } F_1 \text{ is positive})\)
- \(\text{Magnitude:} \, \_\_\_\_ \, \text{N}\)

(b) **What is her initial acceleration (in m/s\(^2\))** if she is initially stationary and wearing steel-bladed skates that point in the direction of \( F_{\text{tot}} \)? (Assume the value of \(\mu_s\) for steel on ice is 0.04.)

- \(\_\_\_\_ \, \text{m/s}^2\)

(c) **What is her acceleration (in m/s\(^2\))** assuming she is already moving in the direction of \( F_{\text{tot}} \)? Remember that friction is always in the opposite direction of motion or attempted motion between surfaces in contact.

- \(\_\_\_\_ \, \text{m/s}^2 \, (\text{in the direction of } F_{\text{tot}})\)
Transcribed Image Text:**Problem Statement:** Consider the 65.0 kg ice skater being pushed by two others as shown in the figure. **Figure Explanation:** - The diagram illustrates three individuals on an ice surface. - Person A exerts force \( F_1 \) horizontally to the right. - Person B exerts force \( F_2 \) vertically upward. - The resultant force \( F_{\text{tot}} \) is depicted by an arrow diagonally upward and to the right, representing the vector sum of \( F_1 \) and \( F_2 \). - There is also a free-body diagram showing the vectors \( F_1 \) and \( F_2 \). --- **Questions:** (a) **Find the direction (in degrees) and magnitude (in N) of \( F_{\text{tot}} \),** the total force exerted on her by the others, given that the magnitudes \( F_1 \) and \( F_2 \) are 28.8 N and 18.6 N, respectively. - \(\text{Direction:} \, \_\_\_\_^\circ \, (\text{counterclockwise from the direction of } F_1 \text{ is positive})\) - \(\text{Magnitude:} \, \_\_\_\_ \, \text{N}\) (b) **What is her initial acceleration (in m/s\(^2\))** if she is initially stationary and wearing steel-bladed skates that point in the direction of \( F_{\text{tot}} \)? (Assume the value of \(\mu_s\) for steel on ice is 0.04.) - \(\_\_\_\_ \, \text{m/s}^2\) (c) **What is her acceleration (in m/s\(^2\))** assuming she is already moving in the direction of \( F_{\text{tot}} \)? Remember that friction is always in the opposite direction of motion or attempted motion between surfaces in contact. - \(\_\_\_\_ \, \text{m/s}^2 \, (\text{in the direction of } F_{\text{tot}})\)
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