Two railroad cars, each of mass 5819kg and traveling 108km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collision?

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Chapter1: Units, Trigonometry. And Vectors
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**Physics Problem:**

**Problem Statement:**
Two railroad cars, each of mass 5819 kg and traveling 108 km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collision?

**Explanation:**
This problem involves the concepts of conservation of momentum and energy. When the two railroad cars collide and come to rest, the kinetic energy of the system converts to thermal energy, sound, and other forms of energy.

**Step-by-Step Solution:**

1. **Convert the velocities to meters per second (m/s):**
   108 km/h × (1000 m/km) / (3600 s/h) = 30 m/s
  
2. **Calculate the initial kinetic energy of each railroad car:**
   K.E. = 1/2 * m * v^2
   For one car: 
   K.E. = 1/2 * 5819 kg * (30 m/s)^2
   K.E. ≈ 2,617,650 Joules

3. **Calculate the total initial kinetic energy of both cars:**
   Total K.E. = K.E. (car 1) + K.E. (car 2)
   Total K.E. = 2,617,650 J + 2,617,650 J
   Total K.E. ≈ 5,235,300 Joules

Since the final kinetic energy is zero (the cars come to rest), all the initial kinetic energy is converted into thermal energy, among other energy forms.

**Result:**
The total thermal energy produced in the collision is approximately 5,235,300 Joules.

**Graphical/Diagram Explanation:**
While the problem does not provide a graph or diagram, one could illustrate:
- **Initial States:** Two arrows pointing towards each other representing the velocities of the railroad cars.
- **Collision:** A point where the arreows meet indicating the collision.
- **Final State:** Both arrows stop, indicating the trains are at rest.
Transcribed Image Text:**Physics Problem:** **Problem Statement:** Two railroad cars, each of mass 5819 kg and traveling 108 km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collision? **Explanation:** This problem involves the concepts of conservation of momentum and energy. When the two railroad cars collide and come to rest, the kinetic energy of the system converts to thermal energy, sound, and other forms of energy. **Step-by-Step Solution:** 1. **Convert the velocities to meters per second (m/s):** 108 km/h × (1000 m/km) / (3600 s/h) = 30 m/s 2. **Calculate the initial kinetic energy of each railroad car:** K.E. = 1/2 * m * v^2 For one car: K.E. = 1/2 * 5819 kg * (30 m/s)^2 K.E. ≈ 2,617,650 Joules 3. **Calculate the total initial kinetic energy of both cars:** Total K.E. = K.E. (car 1) + K.E. (car 2) Total K.E. = 2,617,650 J + 2,617,650 J Total K.E. ≈ 5,235,300 Joules Since the final kinetic energy is zero (the cars come to rest), all the initial kinetic energy is converted into thermal energy, among other energy forms. **Result:** The total thermal energy produced in the collision is approximately 5,235,300 Joules. **Graphical/Diagram Explanation:** While the problem does not provide a graph or diagram, one could illustrate: - **Initial States:** Two arrows pointing towards each other representing the velocities of the railroad cars. - **Collision:** A point where the arreows meet indicating the collision. - **Final State:** Both arrows stop, indicating the trains are at rest.
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