College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Exercise Explanation:**
Kayla, a fitness trainer, develops an exercise that involves pulling a heavy crate across a rough surface. The exercise involves using a rope to pull a crate of mass \( M = 45.0 \, \text{kg} \) along a carpeted track. Using her physics expertise, Kayla determines that the coefficients of kinetic and static friction between the crate and the carpet are \( \mu_k = 0.490 \) and \( \mu_s = 0.770 \), respectively.
**Problem Statement:**
Kayla uses one of her employees, Ramon, to test the exercise. If the rope makes an angle of \( \theta = 23.0^\circ \) with the floor, what is the minimum force \( F_{\text{min}} \) that Ramon must apply to set the crate in motion? Use \( g = 9.80 \, \text{m/s}^2 \).
\[ F_{\text{min}} = \, \text{______ N} \]
**Next Task:**
Next, Kayla has Ramon pull on the rope as hard as he can. If he pulls with a force of \( F = 295 \, \text{N} \) along the direction of the rope, and the rope makes the same angle of \( \theta = 23.0^\circ \) with the floor, what is the acceleration \( a \) of the box?
\[ a = \, \text{______ m/s}^2 \]
**Diagram Explanation:**
The diagram shows a crate being pulled by a rope at an angle \( \theta \) relative to the horizontal floor. The force \( F \) is applied at this angle. The crate's mass is labeled \( M \) and it rests on a surface with coefficients of friction \( \mu_k \) and \( \mu_s \). The diagram highlights the setup of the problem, showing the angle of the applied force and the position of the crate on the surface.](https://content.bartleby.com/qna-images/question/c58cb787-7e9f-401f-bc3b-4d11a9fe5e2a/cb2b4cf5-3ebb-4d28-9fd0-6dca173a069f/byf7vwc_processed.jpeg)
Transcribed Image Text:**Exercise Explanation:**
Kayla, a fitness trainer, develops an exercise that involves pulling a heavy crate across a rough surface. The exercise involves using a rope to pull a crate of mass \( M = 45.0 \, \text{kg} \) along a carpeted track. Using her physics expertise, Kayla determines that the coefficients of kinetic and static friction between the crate and the carpet are \( \mu_k = 0.490 \) and \( \mu_s = 0.770 \), respectively.
**Problem Statement:**
Kayla uses one of her employees, Ramon, to test the exercise. If the rope makes an angle of \( \theta = 23.0^\circ \) with the floor, what is the minimum force \( F_{\text{min}} \) that Ramon must apply to set the crate in motion? Use \( g = 9.80 \, \text{m/s}^2 \).
\[ F_{\text{min}} = \, \text{______ N} \]
**Next Task:**
Next, Kayla has Ramon pull on the rope as hard as he can. If he pulls with a force of \( F = 295 \, \text{N} \) along the direction of the rope, and the rope makes the same angle of \( \theta = 23.0^\circ \) with the floor, what is the acceleration \( a \) of the box?
\[ a = \, \text{______ m/s}^2 \]
**Diagram Explanation:**
The diagram shows a crate being pulled by a rope at an angle \( \theta \) relative to the horizontal floor. The force \( F \) is applied at this angle. The crate's mass is labeled \( M \) and it rests on a surface with coefficients of friction \( \mu_k \) and \( \mu_s \). The diagram highlights the setup of the problem, showing the angle of the applied force and the position of the crate on the surface.
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