# 50 Central Net Force Model Worksheet 3

## Introduction

Welcome to the Central Net Force Model Worksheet 3! In this worksheet, we will explore the concept of net force and how it applies to objects moving in a circular path. By understanding the central net force model, you will be able to analyze the forces acting on an object and determine its motion. Let's dive in!

### 1. What is the Central Net Force Model?

The central net force model is a mathematical model used to analyze the forces acting on an object moving in a circular path. It takes into account both the magnitude and direction of the forces to determine the net force acting on the object. The net force is the vector sum of all the forces acting on the object.

### 2. Understanding Centripetal Force

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is always perpendicular to the object's velocity. Without centripetal force, the object would move in a straight line tangent to the circle.

### 3. Calculating Centripetal Force

To calculate the centripetal force acting on an object, you can use the formula:

F = m * v^2 / r

Where:

- F is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circular path

By plugging in the values for mass, velocity, and radius into the formula, you can determine the centripetal force required to keep the object in its circular motion.

### 4. Analyzing the Forces

In the central net force model, it's important to consider all the forces acting on the object. These forces can include gravity, friction, tension, and any other external forces. By analyzing the magnitude and direction of these forces, you can determine their contributions to the net force.

### 5. Balancing Forces

In some cases, the forces acting on an object in circular motion may be balanced, resulting in a net force of zero. This means that the object is in equilibrium and will continue to move in a circular path at a constant speed. Balancing forces can occur when the centripetal force is equal to the force of gravity or any other opposing force.

### 6. Unbalanced Forces

When the forces acting on an object in circular motion are unbalanced, it will experience a net force. This net force will cause the object to accelerate or decelerate, depending on the direction of the force. The object may also change its direction or radius of motion.

### 7. Examples of Central Net Force Model

To better understand the central net force model, let's look at a few examples:

#### 7.1 Example 1: Car Turning a Corner

When a car turns a corner, the centripetal force is provided by the friction between the tires and the road. The friction force acts towards the center of the circular path, allowing the car to maintain its trajectory. If the car goes too fast or the road is slippery, the friction force may not be sufficient, causing the car to skid or lose control.

#### 7.2 Example 2: Roller Coaster Loop

When a roller coaster goes through a loop, the centripetal force is provided by the normal force exerted by the track on the car. The normal force acts towards the center of the loop, keeping the car in its circular path. If the speed of the roller coaster is too low, the normal force may not be enough to prevent the car from falling off the track.

#### 7.3 Example 3: Satellite Orbiting Earth

A satellite orbiting the Earth experiences a gravitational force that acts towards the center of the Earth. This gravitational force provides the centripetal force needed to keep the satellite in its circular orbit. If the satellite's speed is too low, it may fall towards the Earth, while if it's too high, it may escape Earth's gravitational pull.

### 8. Solving Central Net Force Problems

When solving central net force problems, it's important to follow a systematic approach:

#### 8.1 Step 1: Identify the Forces

Start by identifying all the forces acting on the object. Consider both external forces and internal forces, such as tension in a string or the force of gravity.

#### 8.2 Step 2: Determine the Net Force

Calculate the net force by adding up all the forces acting on the object. Pay attention to the direction of the forces and use vector addition to determine the resultant force.

#### 8.3 Step 3: Apply Newton's Second Law

Use Newton's second law of motion, F = ma, to relate the net force to the acceleration of the object. Rearrange the equation to solve for the unknown variable, whether it's the net force, mass, or acceleration.

#### 8.4 Step 4: Check for Equilibrium

If the net force is zero, the object is in equilibrium and will continue to move in a circular path at a constant speed. If the net force is non-zero, the object will accelerate or decelerate, and you may need to calculate other variables, such as velocity or radius.

### 9. Conclusion

The Central Net Force Model Worksheet 3 provides a comprehensive understanding of the forces acting on objects in circular motion. By applying this model, you can analyze and solve complex problems involving centripetal force and net force. Practice using this worksheet to sharpen your skills and deepen your understanding of this fundamental concept in physics.