Motion 3.2 Solving Collision & Explosion Problems

Motion 3.2 Solving Collision & Explosion Problems 1. Which one or more of the following are correct for a 400g ball is moving at 10ms1. The momentum of the ball is 40000kgms-1. The momentum of the ball is 4J The momentum of the ball is 4kgms-1. The momentum of the ball is 40kgms-1. The momentum of the ball is 4000kgms-1. The kinetic energy of the ball is 2J The kinetic energy of the ball is 2kgms-1. The kinetic energy of the ball is 20kgms-1. The kinetic energy of the ball is 20J The kinetic energy of the ball is 20000J

Motion 3.2 Solving Collision & Explosion Problems 2. Which one or more of the following are correct for a collision between two bodies? The momentum must be conserved. The final momentum must be equal to or less than the initial momentum. The total kinetic energy is conserved. The final kinetic energy must be equal to or less than the initial kinetic energy.

Motion 3.2 Solving Collision & Explosion Problems 3. Which one or more of the following are correct for an elastic collision between two bodies? The momentum must be conserved. The final momentum must be equal to or less than the initial momentum. The total kinetic energy is conserved. The final kinetic energy must be equal to or less than the initial kinetic energy.

Motion 3.2 Solving Collision & Explosion Problems 4. Which one or more of the following are correct for “sticky” collision (where the separate colliding bodies move off together)? The final total momentum ist he same as the initial total momentum.. The final total momentum must be less than the initial total momentum. The final total kinetic energy is the same as the initial total kinetic energy.. The final total kinetic energy is less than the initial total kinetic energy.

Motion 3.2 Solving Collision & Explosion Problems 5. Which one or more of the following are correct regarding a putty collides and sticks to a wall? Momentum is lost from the system because the putty comes to rest. The momentum lost from the putty is transferred to the wall Earth by increasing the speed of the wall & earth through space The momentum lost from the putty is transferred to the Earth by heating up the earth’s surface.

Motion 3.2 Solving Collision & Explosion Problems 6. Which one or more of the following are correct regarding a car that gradually comes to rest by applying its brakes? Momentum is lost from the system because the car comes to rest. The momentum lost from the car is transferred to the Earth by increasing the speed of the earth through space The momentum lost from the car is transferred to the Earth by heating up the earth’s surface.

Motion 3.2 Solving Collision & Explosion Problems 7. A 1.0kg cart travelling at 2.0ms1 collides head on with stationary cart weighing 3.0kg. If they stick together after the collision, what speed v will the two carts be travelling at? Initial Final ptoti = ptotf 1 × 2 + 0 = 4 × v 2 = 4v 0.50 = v v = 0.50ms-1 +

Motion 3.2 Solving Collision & Explosion Problems 8. A 1.0kg cart travelling at 6.0ms1 collides head on with 2.0kg cart travelling in the same direction at 3.0ms1. If they stick together after the collision, what speed will they be travelling at? Initial Final ptoti = ptotf 1 × 6 + 2 × 3 = 3 × v 12 = 3v 4.0 = v v = 4.0ms-1 +

Motion 3.2 Solving Collision & Explosion Problems 9. Is the collision in the previous question elastic or inelastic? Prove your answer Initial Final Eki = ½ × 1 × 62 + ½ × 2 × 32 Ekf = ½ × 3 × 42 Eki = 27J Ekf = 24J Since Eki  Ekf the collision is not elastic

Motion 3.2 Solving Collision & Explosion Problems 10. A 2.0t rail car travelling at 6.0ms1 collides head on with 4.0t rail car travelling in the same direction at v ms1. If they stick together after the collision and travel at 6.0ms1, what was the initial speed of the 4.0kg rail car? Initial Final ptoti = ptotf 2000 × 6 + 4000 × v = 6000 × 4 12000 + 4000v = 24000 4000v = 12000 v = 3.0ms-1 +

Motion 3.2 Solving Collision & Explosion Problems 11. For the two carts in the previous question: Initial Final (a) What was the impulse on the 4.0t cart? I = ? m = 4000kg v = 1ms-1 I = mv I = 4000 × 1 I = 4000 I = 4.0 × 103 Ns to the right (b) What was the impulse on the 2.0t cart? From Newton’s 3rd Law (Action-Reaction) the impulse on the 2.0t cart will be I = 4.0 × 103 Ns to the left +

Motion 3.2 Solving Collision & Explosion Problems 12. Work out the value of v in the situation below where the two carts stick together in the collision? Initial Final ptoti = ptotf 2 × 8 – 1 × 1 = 3 × v 16 – 1 = 3v 15 = 3v 5 = v v = 5.0ms-1 to the right +

Motion 3.2 Solving Collision & Explosion Problems 13. For the two carts in the previous question: Initial Final (a) What was the impulse on the 1.0kg cart? I = ? m = 1.0kg v = 6ms-1 I = mv I = 1 × 6 I = 6.0 Ns to the right (b) What was the impulse on the 2.0kg cart? From Newton’s 3rd Law (Action-Reaction) the impulse on the 2.0kg cart will be I = 6.0 Ns to the left +

Motion 3.2 Solving Collision & Explosion Problems 14. The two carts below have a compressed spring between them. If the spring is released and the 2.0kg car moves to the left at 2.0 ms1, what will be the speed of the 4.0kg car? Initial Final ptoti = ptotf 0 = 2 × –2 + 4 × v 0 = –4 + 4v 4 = 4v 1 = v v = 1.0ms-1 to the right +

Motion 3.2 Solving Collision & Explosion Problems 15. Work out the value of v in the situation below? Initial Final ptoti = ptotf 2 × 4 + 0 = 2 × 2 + 1 × v 8 = 4 + v 4 = v v = 8.0ms-1 to the right +

Motion 3.2 Solving Collision & Explosion Problems 16. Is the collision in the previous question elastic or inelastic? Prove your answer Initial Final Eki = ½ × 2 × 42 + 0 Ekf = ½ × 2 × 22 + ½ × 1 × 42 Eki = 16J Ekf = 12J Since Eki  Ekf the collision is not elastic

Motion 3.2 Solving Collision & Explosion Problems 17. If the head-on collision below is elastic, what will be the values of v1 and v2? Initial Final v1 = 0ms-1 v2 = 3.0ms-1 In head on elastic collisions between to identical masses, the masses simply: SWAP velocities

Motion 3.2 Solving Collision & Explosion Problems 18. If the head-on collision below is elastic, what will be the values of v1 and v2? Initial Final v1 = –1.0 ms-1 v2 = 3.0ms-1 In head on elastic collisions between to identical masses, the masses simply: SWAP velocities

Motion 3.2 Solving Collision & Explosion Problems 19. A 5.0 tonne space capsule is travelling through space at 100ms1 attached to a 195tonne booster. A small explosion is used to separate the capsule from the booster and the booster is then moving at 98ms1. What will be the speed of the capsule? Initial Final ptoti = ptotf 200 × 100 = 195 × 98 + 5 × v 20000 = 19110 + 5v 890 = 5v 178 = v v = 178ms-1 to the right +

Motion 3.2 Solving Collision & Explosion Problems 20. As a 2.0tonne coal cart passes under a coal shute, coal is dropped into it. If the cart was free wheeling at 4.0ms1 before the coal was dropped and is free wheeling at 3.0ms1 after, how much coal was dropped into the cart? Initial Final ptoti = ptotf 2000 × 4 = (2000 + m) × 3 8000 = 6000 + 3m 2000 = 3m 666.6667 = m so  667 kg of coal was added to the 2000 + m +

Motion 3.2 Solving Collision & Explosion Problems The Total Energy of a System remains constant unless energy is transferred to a body outside of the system Motion 3.2 Solving Collision & Explosion Problems 21. If two objects undergo an elastic collision: (a) Which of the graphs represents the total energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems An Elastic Collision means that the Total Kinetic Energy at the start of the collision is the same as at the end. During the collision kinetic energy is converted to potential energy and then all that potential energy is then converted back to Ek. Motion 3.2 Solving Collision & Explosion Problems 21. If two objects undergo an elastic collision: (b) Which of the previous graphs represents the total kinetic energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems During an elastic collision kinetic energy is converted to potential energy and then all that potential energy is then converted back to kinetic energy. The potential energy at any time is the same as the decrease in total kinetic energy. Motion 3.2 Solving Collision & Explosion Problems 21. If two objects undergo an elastic collision: (c) Which of the previous graphs represents the potential energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems The Total Energy of a System remains constant unless energy is transferred to a body outside of the system Motion 3.2 Solving Collision & Explosion Problems 22. If two objects undergo an inelastic collision where the objects remain separate: (a) Which of the graphs represents the total energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems In an Inelastic Collision where the objects remain separate, there is a loss of kinetic energy in the system. During the collision kinetic energy is converted to potential energy and heat and then some of the that potential energy is then converted to heat and the rest to kinetic energy. Motion 3.2 Solving Collision & Explosion Problems 22. If two objects undergo an inelastic collision where the objects remain separate: (b) Which of the previous graphs represents the total kinetic energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems In an Inelastic Collision where the objects remain separate, heat losses mean that: the peak potential energy is less than the difference between initial Ektot and minimum Ektot the peak potential energy is more than the difference between initial Ektot and final Ektot Motion 3.2 Solving Collision & Explosion Problems 22. If two objects undergo an inelastic collision where the objects remain separate : (c) Which of the previous graphs represents the potential energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems The Total Energy of a System remains constant unless energy is transferred to a body outside of the system Motion 3.2 Solving Collision & Explosion Problems 23. If two objects undergo a collision where the objects become stuck together : (a) Which of the graphs represents the total energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems In a collision where the objects become stuck together, no significant conversion to potential energy that is then converted back to potential energy. This means that there is not significant increase in the total kinetic energy after it reaches its minimum. Motion 3.2 Solving Collision & Explosion Problems 23. If two objects undergo a collision where the objects become stuck together : (b) Which of the previous graphs represents the total kinetic energy for the situation? D A B E F none of above

Motion 3.2 Solving Collision & Explosion Problems In a collision where the objects become stuck together, Ek is essentially converted to heat. Depending on the dampening between the objects there may be some pot energy produced that then converts back to vibration between the objects but the vibration will eventually be converted to heat. Motion 3.2 Solving Collision & Explosion Problems 23. If two objects undergo a collision where the objects become stuck together : (c) Which of the previous graphs represents the potential energy for the situation? D A B E F none of above