A horizontal force of 40 N is required to start a 15-kg block sliding along a horizontal surface. What is the

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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
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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