### Ball on Incline Dynamics#### Problem:A 10 kg ball is projected up a 10° incline with a speed of 20 m/s.1. **Free-Body Diagram** - Draw the free-body diagram as the ball moves along the incline. 2. **Maximum Distance Calculation** - Determine the maximum distance that the package will move up the incline assuming the coefficient of kinetic friction is 0.1. 3. **Velocity Calculation** - Determine the velocity of the package as it returns to its original position. 4. **Kinetic Energy Loss** - Calculate the loss in kinetic energy (KE) as it returns to its original position.#### Explanation:- **Free-Body Diagram**: Illustrate and label all forces acting on the ball as it moves up the incline. Typically, this includes weight (mg), normal force (N), applied force (if any), and friction (f). - **Weight (mg)**: Acts vertically downward. - **Normal Force (N)**: Perpendicular to the surface of the incline. - **Friction Force (f = μN)**: Opposes the motion of the ball, where μ is the coefficient of kinetic friction. - **Component of Weight along Incline (mg sin θ)**: Acts down the incline. - **Component of Weight perpendicular to Incline (mg cos θ)**: Acts into the incline.- **Maximum Distance Calculation**: - Use energy principles or kinematic equations to determine how far the ball travels along the incline before stopping, considering frictional forces.- **Velocity Calculation**: - After determining the maximum height, assess the velocity of the ball as it returns to the original position.- **Kinetic Energy Loss**: - Calculate initial kinetic energy \((KE_i = \frac{1}{2}mv^2)\) and compare it to the final kinetic energy (after considering work done against friction).These steps provide a comprehensive analysis of the ball's movement on the incline, considering all forces and energy principles involved.

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Description: ### Ball on Incline Dynamics#### Problem:A 10 kg ball is projected up a 10° incline with a speed of 20 m/s.1. **Free-Body Diagram** - Draw the free-body diagram as the ball moves along the incline. 2. **Maximum Distance Calculation** - Determi

A 10 kg ball is projected up a 100 inclined with a speed of 20m/s

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2. A 10 kg ball is projected up a 10°- incline with a speed of 20 m/s. i. Draw the free-body diagram as the ball moves along the incline. ii. Determine the maximum distance that the package will move up the incline assuming the coefficient of kinetic friction is 0.1. iii. The velocity of the package as it returns to its original position. iv. The loss in KE as it returns to its original position.

2. A 10 kg ball is projected up a 10°- incline with a speed of 20 m/s. i. Draw the free-body diagram as the ball moves along the incline. ii. Determine the maximum distance that the package will move up the incline assuming the coefficient of kinetic friction is 0.1. iii. The velocity of the package as it returns to its original position. iv. The loss in KE as it returns to its original position.

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Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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Question

### Ball on Incline Dynamics

#### Problem:
A 10 kg ball is projected up a 10° incline with a speed of 20 m/s.

1. **Free-Body Diagram**
- Draw the free-body diagram as the ball moves along the incline.

2. **Maximum Distance Calculation**
- Determine the maximum distance that the package will move up the incline assuming the coefficient of kinetic friction is 0.1.

3. **Velocity Calculation**
- Determine the velocity of the package as it returns to its original position.

4. **Kinetic Energy Loss**
- Calculate the loss in kinetic energy (KE) as it returns to its original position.

#### Explanation:
- **Free-Body Diagram**: Illustrate and label all forces acting on the ball as it moves up the incline. Typically, this includes weight (mg), normal force (N), applied force (if any), and friction (f).

- **Weight (mg)**: Acts vertically downward.
- **Normal Force (N)**: Perpendicular to the surface of the incline.
- **Friction Force (f = μN)**: Opposes the motion of the ball, where μ is the coefficient of kinetic friction.
- **Component of Weight along Incline (mg sin θ)**: Acts down the incline.
- **Component of Weight perpendicular to Incline (mg cos θ)**: Acts into the incline.

- **Maximum Distance Calculation**:
- Use energy principles or kinematic equations to determine how far the ball travels along the incline before stopping, considering frictional forces.

- **Velocity Calculation**:
- After determining the maximum height, assess the velocity of the ball as it returns to the original position.

- **Kinetic Energy Loss**:
- Calculate initial kinetic energy \((KE_i = \frac{1}{2}mv^2)\) and compare it to the final kinetic energy (after considering work done against friction).

These steps provide a comprehensive analysis of the ball's movement on the incline, considering all forces and energy principles involved.

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