Please solve Question 4 **Physics Collision Problems and Solutions**1. **Proton Collision:** - A proton with a speed of 500 m/s collides elastically with another proton at rest. The projectile proton is scattered 60° from its initial trajectory. - a) What is the direction of the target proton after the collision? - b) What are the speeds of the two protons after the collision? **Answers:** - a) 30° - b) 250 m/s and 433 m/s2. **Inelastic Collision of Equal Mass Particles:** - Two particles of equal mass and the same initial speed collide in a completely inelastic collision. After the collision, the two are found to move away together at half their initial speed. Find the angle between the initial velocities of the two particles. **Answer:** 120°3. **Railroad Car Collision:** - 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 - 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/s4. **Alpha Particle Collision:** - 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% loss5. **Box Sled New Speed:** - A 6.0 kg box sled is moving across frictionless ice at a speed of 9.0 m/s when a 12 kg package is dropped onto it from above. What is the new speed of the sled? **Answer:** 3.0 m/s6. **Barge Collision:** - A barge of mass 1.50 x 10^5 kg is proceeding eastward on a

4) As per the conservation law of momentum. Here, p, m, u, and v represent the momentum, the mass, initial velocity, and final velocity, respectively. The subscript a and n represent the alpha particle and the nucleus, respectively. Since initially, the gold nucleus was at the rest, its initial velocity is zero. Thus, Now, as the per conservation law of energy, As the nucleus’s initial velocity is zero. Solving the quadratic equation gives, From 1 and 2. Now, the percentage loss in the original value of alpha particle’s kinetic energy can be given as, From equation (3). Substitute the relevant values. Thus, the loss in the alpha particle’s original kinetic energy is about 7.8%.

Science

Physics

4. 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