College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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:**
A horizontal force of 40 N is required to start a 15-kg block sliding along a horizontal surface. What is the coefficient of static friction?
---
To solve this problem, you'll need to understand the relationship between the force of static friction, the normal force, and the coefficient of static friction.
### Important Concepts:
1. **Force of Static Friction (F_s):** The force that must be overcome to start the motion of an object at rest. It is given by the formula:
\[ F_s = \mu_s \cdot N \]
where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force.
2. **Normal Force (N):** For an object resting on a horizontal surface, the normal force is equal to the weight of the object, which is calculated by:
\[ N = m \cdot g \]
where \( m \) is the mass of the object (in kg) and \( g \) is the acceleration due to gravity (~9.8 m/s²).
### Calculation Steps:
1. **Determine the normal force (N):**
Given:
\[ m = 15 \, \text{kg} \]
\[ g = 9.8 \, \text{m/s}^2 \]
Calculation:
\[ N = 15 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ N = 147 \, \text{N} \]
2. **Determine the coefficient of static friction (μ_s):**
Given:
\[ F_s = 40 \, \text{N} \]
\[ N = 147 \, \text{N} \]
Using the formula:
\[ F_s = \mu_s \cdot N \]
Rearranging for \( \mu_s \):
\[ \mu_s = \frac{F_s}{N} \]
Calculation:
\[ \mu_s = \frac{40 \, \text{N}}{147 \, \text{N}} \]
\[ \mu_s \approx 0.272 \]
---
**Conclusion:**
The coefficient of static friction (\( \mu_s \)) between the block and the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a2e60b5-531b-408d-ad87-91178dbcae31%2F1aea58f2-9f6e-46b0-801e-12d73628c6cd%2Fpcv1ynb_processed.gif&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A horizontal force of 40 N is required to start a 15-kg block sliding along a horizontal surface. What is the coefficient of static friction?
---
To solve this problem, you'll need to understand the relationship between the force of static friction, the normal force, and the coefficient of static friction.
### Important Concepts:
1. **Force of Static Friction (F_s):** The force that must be overcome to start the motion of an object at rest. It is given by the formula:
\[ F_s = \mu_s \cdot N \]
where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force.
2. **Normal Force (N):** For an object resting on a horizontal surface, the normal force is equal to the weight of the object, which is calculated by:
\[ N = m \cdot g \]
where \( m \) is the mass of the object (in kg) and \( g \) is the acceleration due to gravity (~9.8 m/s²).
### Calculation Steps:
1. **Determine the normal force (N):**
Given:
\[ m = 15 \, \text{kg} \]
\[ g = 9.8 \, \text{m/s}^2 \]
Calculation:
\[ N = 15 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ N = 147 \, \text{N} \]
2. **Determine the coefficient of static friction (μ_s):**
Given:
\[ F_s = 40 \, \text{N} \]
\[ N = 147 \, \text{N} \]
Using the formula:
\[ F_s = \mu_s \cdot N \]
Rearranging for \( \mu_s \):
\[ \mu_s = \frac{F_s}{N} \]
Calculation:
\[ \mu_s = \frac{40 \, \text{N}}{147 \, \text{N}} \]
\[ \mu_s \approx 0.272 \]
---
**Conclusion:**
The coefficient of static friction (\( \mu_s \)) between the block and the
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