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tell me all the helpful formula to use to solve this thank you


To solve the problems in the image provided, here are the key formulas and concepts that are useful:

---

### **1. Newton's Second Law of Motion:**
\[ F_{\text{net}} = m \cdot a \]
- \( F_{\text{net}} \): Net force acting on the object (in Newtons, \(N\)).
- \( m \): Mass of the object (in kilograms, \(kg\)).
- \( a \): Acceleration of the object (in meters per second squared, \(m/s^2\)).

**Net Force:**  
\[
F_{\text{net}} = F_{\text{app}} - F_{\text{frict}}
\]
Where:  
- \( F_{\text{app}} \): Applied force (in \(N\)).
- \( F_{\text{frict}} \): Frictional force (in \(N\)).

---

### **2. Friction Force Formula:**
\[ F_{\text{frict}} = \mu \cdot F_{\text{norm}} \]
Where:  
- \( F_{\text{frict}} \): Frictional force (in \(N\)).  
- \( \mu \): Coefficient of friction (unitless).  
- \( F_{\text{norm}} \): Normal force (in \(N\)).

For horizontal surfaces:  
\[
F_{\text{norm}} = F_{\text{grav}}
\]
Where:  
- \( F_{\text{grav}} \): Gravitational force (in \(N\)).  
- \( F_{\text{grav}} = m \cdot g \), with \( g = 9.8 \, m/s^2 \) (acceleration due to gravity).

---

### **3. Solving for Acceleration:**
If friction and applied forces are known, acceleration can be calculated as:  
\[
a = \frac{F_{\text{net}}}{m}
\]

---

### **4. Coefficient of Friction:**
Rearranging the friction force formula, the coefficient of friction can be calculated as:  
\[
\mu = \frac{F_{\text{frict}}}{F_{\text{norm}}}
\]

---

### **Steps to Solve Each Situation:**
1. Identify the forces given in the problem (\( F_{\text{app}}, F_{\text{frict}}, F_{\text{norm}}, F_{\text{grav}} \)).
2. Calculate the missing force or acceleration using the formulas above.
3. If acceleration is \( 0 \), frictional force exactly balances the applied force:  
   \[
   F_{\text{frict}} = F_{\text{app}}
   \]
4. Use \( \mu \) formula when necessary.

Let me know if you'd like a detailed walkthrough of one or more parts of the problem!

tell me all the helpful formula to use to solve this thank you

Explore key formulas and concepts like Newton's Second Law, friction force equations, and coefficient of friction to solve problems involving applied forces, friction, and acceleration. Perfect for Grades 9-12 physics students.

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