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### 2. A 75 kg box encounters 10 N of friction and slides down a hall with an acceleration of 3.60 m/s².

**a. Find the coefficient of kinetic friction between the box and the floor.**

We know:
- Mass of the box \( m = 75 \, \text{kg} \)
- Friction force \( F_f = 10 \, \text{N} \)
- Acceleration \( a = 3.60 \, \text{m/s}^2 \)

The friction force is related to the coefficient of kinetic friction \( \mu_k \) by the formula:
\[
F_f = \mu_k F_N
\]
where \( F_N \) is the normal force. Since the box is on a horizontal surface, the normal force \( F_N \) is equal to the weight of the box, which is given by:
\[
F_N = mg
\]
where \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity).

Thus,
\[
F_N = 75 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 735.75 \, \text{N}
\]

Now, using the friction force equation:
\[
\mu_k = \frac{F_f}{F_N} = \frac{10 \, \text{N}}{735.75 \, \text{N}} \approx 0.0136
\]

So, the coefficient of kinetic friction \( \mu_k \) is approximately **0.0136**.

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**b. What is the weight of this box?**

The weight of the box is calculated using:
\[
W = mg
\]
where \( m = 75 \, \text{kg} \) and \( g = 9.81 \, \text{m/s}^2 \).

Thus,
\[
W = 75 \times 9.81 = 735.75 \, \text{N}
\]

The weight of the box is **735.75 N**.

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Would you like further details or have any other questions? 

Here are five related questions to expand on the topic:
1. How would the coefficient of kinetic friction change if the friction force were doubled?
2. What would happen to the box’s acceleration if the coefficient of friction increased?
3. Can you derive the acceleration of the box using Newton’s second law?
4. How would the result differ if the surface were inclined at an angle?
5. What if the mass of the box were increased—how would that affect the friction and weight?

**Tip:** Always start by identifying the forces acting on an object before using the friction or Newton’s laws to solve for unknowns.

A 75 kg box encounters 10 N of friction and slides down a hall with an acceleration of 3.60 m/s². a. Find the coefficient of kinetic friction between the box and the floor. b. What is the weight of this box?

Learn how to calculate the coefficient of kinetic friction and weight for a 75 kg box sliding down with a 10 N friction force and acceleration of 3.60 m/s². Detailed steps involve friction force, weight calculation, and Newton's laws.

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