3. A railroad car weighing 32 tons and travelling at 5.0 ft/s overtakes another car weighing 24 tons and travelling at 3.0 ft/s in the same direction. If the cars couple together when they meet, find a) the speed of the cars after collision, and b) the loss of kinetic energy during the collision. c) If the collision is, though unlikely, completely elastic, find the speed of the cars after the collision. Answers: a) 4.1 ft/s b) 2332 ft -lbs c) 5.3 ft/s, 3.3 ft/s

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Please solve 3A,B,and C

### Physics Problems on Collisions

1. **Elastic Collision of Protons**  
   A proton moving at 500 m/s collides elastically with another proton at rest. The projectile proton is scattered at a 60° angle from its initial trajectory.  
   - a) Direction of the target proton after collision?  
   - b) Speeds of the two protons after the collision?  
   **Answers:**  
   a) \(30^\circ\)  
   b) 250 m/s and 433 m/s  

2. **Inelastic Collision of Equal Mass Particles**  
   Two particles of equal mass and the same initial speed collide completely inelastically. After the collision, they move together at half their initial speed. Find the angle between the initial velocities of the two particles.  
   **Answer:** 120°

3. **Collision of Railroad Cars**  
   A railroad car weighing 32 tons and traveling at 5.0 ft/s overtakes another car weighing 24 tons and traveling at 3.0 ft/s in the same direction. If the cars couple together upon meeting, find:  
   - a) Speed of the cars after the collision.  
   - b) Loss of kinetic energy during the collision.  
   - c) If the collision is completely elastic, find the speed of the cars after the collision.  
   **Answers:**  
   a) 4.1 ft/s  
   b) 2332 ft-lbs  
   c) 5.3 ft/s, 3.3 ft/s  

4. **Elastic Collision with Nucleus**  
   An alpha particle of mass 4 u experiences an elastic head-on collision with a gold nucleus of mass 197 u initially at rest. What percentage of its original kinetic energy does the alpha particle lose?  
   **Answer:** 7.8% loss

5. **Box Sled on Frictionless Ice**  
   A 6.0 kg box sled moving at 9.0 m/s on frictionless ice has a 12 kg package dropped onto it from above. What is the new speed of the sled?  
   **Answer:** 3.0 m/s

6. **Collision of Barges**  
   A barge of mass \(1.50 \times 10^5\) kg proceeds eastward at 6.2 m/s and collides with another barge moving north
Transcribed Image Text:### Physics Problems on Collisions 1. **Elastic Collision of Protons** A proton moving at 500 m/s collides elastically with another proton at rest. The projectile proton is scattered at a 60° angle from its initial trajectory. - a) Direction of the target proton after collision? - b) Speeds of the two protons after the collision? **Answers:** a) \(30^\circ\) b) 250 m/s and 433 m/s 2. **Inelastic Collision of Equal Mass Particles** Two particles of equal mass and the same initial speed collide completely inelastically. After the collision, they move together at half their initial speed. Find the angle between the initial velocities of the two particles. **Answer:** 120° 3. **Collision of Railroad Cars** A railroad car weighing 32 tons and traveling at 5.0 ft/s overtakes another car weighing 24 tons and traveling at 3.0 ft/s in the same direction. If the cars couple together upon meeting, find: - a) Speed of the cars after the collision. - b) Loss of kinetic energy during the collision. - c) If the collision is completely elastic, find the speed of the cars after the collision. **Answers:** a) 4.1 ft/s b) 2332 ft-lbs c) 5.3 ft/s, 3.3 ft/s 4. **Elastic Collision with Nucleus** An alpha particle of mass 4 u experiences an elastic head-on collision with a gold nucleus of mass 197 u initially at rest. What percentage of its original kinetic energy does the alpha particle lose? **Answer:** 7.8% loss 5. **Box Sled on Frictionless Ice** A 6.0 kg box sled moving at 9.0 m/s on frictionless ice has a 12 kg package dropped onto it from above. What is the new speed of the sled? **Answer:** 3.0 m/s 6. **Collision of Barges** A barge of mass \(1.50 \times 10^5\) kg proceeds eastward at 6.2 m/s and collides with another barge moving north
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