Initial Height h₁ m = 325 kg h₁ = 19.5 m 1 Car mass, with passengers = m No friction. 2 Bottom 3 Final Height h₂ h2=4.7 m A roller coaster car of mass m is rolling down the track, starting from rest, as shown in the figure. The initial height from the ground is h1 (Position-1), while the final height is h2 (Position-3). The system has no friction. What is the speed of the car when it reaches the bottom (Position-2) of the track.

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### Energy Conservation in a Roller Coaster Ride

#### Diagram Explanation:

A diagram of a roller coaster track is shown, divided into three key positions:

1. **Position 1 (Initial Height, \( h_1 \))**:
   - The roller coaster starts at the topmost point of the track with an initial height \( h_1 = 19.5 \) meters from the ground.
   
2. **Position 2 (Bottom)**:
   - The lowest point of the track, where we will calculate the speed of the roller coaster.
   
3. **Position 3 (Final Height, \( h_2 \))**:
   - Another elevated point on the track where the final height \( h_2 \) is given as 4.7 meters.
   
- **Roller Coaster Car Information**:
   - The mass of the roller coaster car, including passengers, is denoted as \( m = 325 \) kg.
   - The track has no friction, implying that mechanical energy is conserved throughout the ride.

#### Problem Statement:

A roller coaster car of mass \( m \) is rolling down the track, starting from rest, as shown in the figure. The initial height from the ground is \( h_1 \) (Position-1), while the final height is \( h_2 \) (Position-3). The system has no friction.

What is the speed of the car when it reaches the bottom (Position-2) of the track?

#### Given:
- \( m = 325 \) kg
- \( h_1 = 19.5 \) m
- \( h_2 = 4.7 \) m

#### Solution Approach:

Using the conservation of mechanical energy principle:

1. **Potential Energy at Initial Point (Position 1)**:
   - \( PE_1 = m \cdot g \cdot h_1 \)

2. **Kinetic Energy at Initial Point (Position 1)**:
   - Since the car starts from rest, \( KE_1 = 0 \)

3. **Potential Energy at Bottom (Position 2)**:
   - At the bottom, \( h = 0 \), so \( PE_2 = 0 \)

4. **Kinetic Energy at Bottom (Position 2)**:
   - \( KE_2 = \frac{1}{2} m v^2 \), where \( v \)
Transcribed Image Text:### Energy Conservation in a Roller Coaster Ride #### Diagram Explanation: A diagram of a roller coaster track is shown, divided into three key positions: 1. **Position 1 (Initial Height, \( h_1 \))**: - The roller coaster starts at the topmost point of the track with an initial height \( h_1 = 19.5 \) meters from the ground. 2. **Position 2 (Bottom)**: - The lowest point of the track, where we will calculate the speed of the roller coaster. 3. **Position 3 (Final Height, \( h_2 \))**: - Another elevated point on the track where the final height \( h_2 \) is given as 4.7 meters. - **Roller Coaster Car Information**: - The mass of the roller coaster car, including passengers, is denoted as \( m = 325 \) kg. - The track has no friction, implying that mechanical energy is conserved throughout the ride. #### Problem Statement: A roller coaster car of mass \( m \) is rolling down the track, starting from rest, as shown in the figure. The initial height from the ground is \( h_1 \) (Position-1), while the final height is \( h_2 \) (Position-3). The system has no friction. What is the speed of the car when it reaches the bottom (Position-2) of the track? #### Given: - \( m = 325 \) kg - \( h_1 = 19.5 \) m - \( h_2 = 4.7 \) m #### Solution Approach: Using the conservation of mechanical energy principle: 1. **Potential Energy at Initial Point (Position 1)**: - \( PE_1 = m \cdot g \cdot h_1 \) 2. **Kinetic Energy at Initial Point (Position 1)**: - Since the car starts from rest, \( KE_1 = 0 \) 3. **Potential Energy at Bottom (Position 2)**: - At the bottom, \( h = 0 \), so \( PE_2 = 0 \) 4. **Kinetic Energy at Bottom (Position 2)**: - \( KE_2 = \frac{1}{2} m v^2 \), where \( v \)
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