e coefficient of friction for a cart on an inclined track is 0.1, and theta is 15 degrees and the mass of the cart is 500 grams (0.5 kg). What mass is required for the hanging mass so that the cart moves up the track at a constant sp

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Chapter4: Motion In Two Dimensions
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If the coefficient of friction for a cart on an inclined track is 0.1, and theta is 15 degrees and the mass of the cart is 500 grams (0.5 kg). What mass is required for the hanging mass so that the cart moves up the track at a constant speed?

 

### Dynamics of a Trolley on an Incline with a Pulley System

#### Description and Explanation:

**Diagram Overview:**

The provided diagram illustrates a physics experiment setup commonly used to study the dynamics of motion involving a trolley and a pulley system.

**Components in the Diagram:**

1. **Inclined Plane:**
   - A sloped surface on which the trolley moves.
   - The angle of inclination is adjustable and is measured from the horizontal.

2. **Trolley:**
   - A small cart labeled with the mass \( M \).
   - This trolley can move up and down the inclined plane.
   - The trolley experiences a combination of gravitational force and friction.

3. **Pulley:**
   - Positioned at the top end of the inclined plane.
   - Allows a string to pass over it, connecting the trolley to the mass hanger.

4. **String:**
   - A string passes over the pulley.
   - One end of the string is attached to the trolley, and the other end is attached to the mass hanger.
   - The string transmits force between the trolley and the mass hanger.

5. **Mass Hanger:**
   - Depicted as a small object hanging vertically down, labeled with the mass \( m \).
   - This mass hanger can hold additional masses and acts as a counterweight to the trolley.

**Forces Involved:**

- **Gravitational Force:** Acts downward on both the trolley and the mass hanger.
- **Normal Force:** Perpendicular to the inclined plane acting on the trolley.
- **Tension Force:** In the string, it transmits force over the pulley.
- **Friction Force:** Acts opposite to the direction of motion on the inclined plane (often adjustable or negligible for some experiments).

**Purpose of the Experiment:**

This setup aims to study:

1. **Acceleration:** By observing the system’s response to different masses and inclinations.
2. **Forces in Motion:** Analyzing the interplay between gravitational force, tension, and friction.
3. **Newton’s Second Law:** Verifying the relationship \( F = ma \) by measuring the forces and acceleration.

**Procedure Example:**

1. Adjust the angle of the incline and note the angle.
2. Place the trolley at the starting position on the inclined plane.
3. Add known masses to the mass hanger and release the system.
4. Measure the time it takes for the trolley to travel a certain distance
Transcribed Image Text:### Dynamics of a Trolley on an Incline with a Pulley System #### Description and Explanation: **Diagram Overview:** The provided diagram illustrates a physics experiment setup commonly used to study the dynamics of motion involving a trolley and a pulley system. **Components in the Diagram:** 1. **Inclined Plane:** - A sloped surface on which the trolley moves. - The angle of inclination is adjustable and is measured from the horizontal. 2. **Trolley:** - A small cart labeled with the mass \( M \). - This trolley can move up and down the inclined plane. - The trolley experiences a combination of gravitational force and friction. 3. **Pulley:** - Positioned at the top end of the inclined plane. - Allows a string to pass over it, connecting the trolley to the mass hanger. 4. **String:** - A string passes over the pulley. - One end of the string is attached to the trolley, and the other end is attached to the mass hanger. - The string transmits force between the trolley and the mass hanger. 5. **Mass Hanger:** - Depicted as a small object hanging vertically down, labeled with the mass \( m \). - This mass hanger can hold additional masses and acts as a counterweight to the trolley. **Forces Involved:** - **Gravitational Force:** Acts downward on both the trolley and the mass hanger. - **Normal Force:** Perpendicular to the inclined plane acting on the trolley. - **Tension Force:** In the string, it transmits force over the pulley. - **Friction Force:** Acts opposite to the direction of motion on the inclined plane (often adjustable or negligible for some experiments). **Purpose of the Experiment:** This setup aims to study: 1. **Acceleration:** By observing the system’s response to different masses and inclinations. 2. **Forces in Motion:** Analyzing the interplay between gravitational force, tension, and friction. 3. **Newton’s Second Law:** Verifying the relationship \( F = ma \) by measuring the forces and acceleration. **Procedure Example:** 1. Adjust the angle of the incline and note the angle. 2. Place the trolley at the starting position on the inclined plane. 3. Add known masses to the mass hanger and release the system. 4. Measure the time it takes for the trolley to travel a certain distance
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