A person with a mass of 63 kg walks by applying 176. N of force on the ground while pushing a 14-kg object.  If the person accelerates at 1.8 m/s2, what is the force of friction between the object and the floor

To find the force of friction between the object and the floor, we can approach the problem step by step using Newton's second law, which is \( F = ma \).

### Given Information:
- Mass of the person: \( m_p = 63 \, \text{kg} \)
- Force applied by the person: \( F_{\text{applied}} = 176 \, \text{N} \)
- Mass of the object: \( m_o = 14 \, \text{kg} \)
- Acceleration of the person and object: \( a = 1.8 \, \text{m/s}^2 \)

We need to find the force of friction, \( F_f \), between the object and the floor.

### Step 1: Determine the net force on the object
Using Newton’s second law, we can calculate the net force \( F_{\text{net}} \) acting on the object:

\[
F_{\text{net}} = m_o \cdot a
\]

Substitute the values:

\[
F_{\text{net}} = 14 \, \text{kg} \times 1.8 \, \text{m/s}^2 = 25.2 \, \text{N}
\]

### Step 2: Find the friction force
The net force \( F_{\text{net}} \) acting on the object is the difference between the applied force on the object and the force of friction. Since the object is moving in the same direction as the person, the force of friction opposes the motion.

\[
F_{\text{applied\_on\_object}} - F_f = F_{\text{net}}
\]

Rearrange to solve for \( F_f \):

\[
F_f = F_{\text{applied\_on\_object}} - F_{\text{net}}
\]

However, we don’t have the exact force applied by the person directly on the object from the 176 N. The 176 N applied by the person is divided between moving their own body and pushing the object. But using only the object's net force, the friction can be approximated:

\[
F_f = F_{\text{applied}} - F_{\text{net}} \quad (\text{if we assume friction balances it})
\]

If further refinement is needed, a breakdown of person/object interactions can help!

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Would you like details on resolving interactions or simplification?

**Relative Questions:**
1. How do we calculate friction force in cases with multiple objects?
2. What role does Newton’s third law play in analyzing this scenario?
3. What if the person’s mass was different? How would it affect friction?
4. How does the friction coefficient relate to this force of friction?
5. How could we calculate the force applied specifically to the object?

**Tip**: Friction force depends heavily on both the normal force and the surface's properties (like the coefficient of friction).

A person with a mass of 63 kg walks by applying 176 N of force on the ground while pushing a 14-kg object. If the person accelerates at 1.8 m/s², what is the force of friction between the object and the floor?

Learn how to calculate the force of friction between a 14-kg object and the floor when pushed by a person applying 176 N of force. This solution uses Newton's Second Law (F = ma) to determine the net force and solve for the force of friction. Suitable for high school students in Grades 9-12.

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