Momentum and Collision

1. The Cart and The Brick - Part A The animation below portrays the collision between a 3.0-kg loaded cart and a 2-kg dropped brick. It will be assumed that there are no net external forces acting upon the two objects involved in the collision. The only net force acting upon the two objects (loaded cart and dropped brick) are internal forces - the force of friction between the loaded cart and the droped brick. The before- and after-collision velocities and momentum are shown in the data tables. Momentum and Collision

2. The Cart and The Brick - Part B In the collision between the cart and the dropped brick, total system momentum is conserved. Before the collision, the momentum of the cart is 60 kg*cm/s and the momentum of the dropped brick is 0 kg*cm/s; the total system momentum is 60 kg*cm/s. After the collision, the momentum of the cart is 20.0 kg*cm/s and the momentum of the dropped brick is 40.0 kg*cm/s; the total system momentum is 60 kg*cm/s. The momentum of the loaded cart-dropped brick system is conserved. The momentum lost by the loaded cart (40 kg*cm/s) is gained by the dropped brick.

3. The Diesel and Freight Car • The animation below portrays the inelastic collision between a very massive diesel and a less massive flatcar. Before the collision, the diesel is in motion with a velocity of 5 km/hr and the flatcar is at rest. The mass of the diesel is 8000 kg and the mass of the flatcar is 2000 kg. The diesel has four times the mass of the freight car. After the collision, both the diesel and the flatcar move together with the same velocity. (Collisions such as this where the two objects stick together and move with the same post-collision velocity are referred to as inelastic collisions.) What is the after-collision velocity of the two railroad cars?

4. Car Rear Ends Truck • Certain collisions are referred to as elastic collisions. Elastic collisions are collisions in which both momentum and kinetic energy are conserved. The total system kinetic energy before the collision equals the total system kinetic energy after the collision. If total kinetic energy is not conserved, then the collision is referred to as an inelastic collision. • The animation below portrays the inelastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown in the data tables.

5. Truck Rear Ends Car • The animation below portrays the elastic collision between a 3000-kg truck and a 1000-kg car. The before- and after-collision velocities and momentum are shown in the data tables.

6. Car and Truck in Head-on Collision In the collision between the truck and the car, total system momentum is conserved. Before the collision, the momentum of the car is +20 000 kg*m/s and the momentum of the truck is -60 000 kg*m/s; the total system momentum is -40 000 kg*m/s. After the collision, the momentum of the car is -40 000 kg*m/s and the momentum of the truck is 0 kg*m/s; the total system momentum is -40 000 kg*m/s. The total system momentum is conserved. The momentum change of the car (-40 000 kg*m/s) is equal in magnitude and opposite in direction to the momentum change of the truck (40 000 kg*m/s) . An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 800 000 Joules (200 000 J for the car plus 600 000 J for the truck). After the collision, the total system kinetic energy is 800 000 Joules (800 000 J for the car and 0 J for the truck). The total kinetic energy before the collision is equal to the total kinetic energy after the collision. A collision such as this in which total system kinetic energy is conserved is known as an elastic collision.

7. Truck Rear Ends Car The animation below portrays the inelastic collision between a 3000-kg truck and a 1000-kg car. The before- and after-collision velocities and momentum are shown in the data tables. In the collision between the truck and the car, total system momentum is conserved. Before the collision, the momentum of the truck is 60 000 kg*m/s and the momentum of the car is 0 kg*m/s; the total system momentum is 60 000 kg*m/s. After the collision, the momentum of the truck is 45 000 kg*m/s and the momentum of the car is 15 000 kg*m/s; the total system momentum is 60 000 kg*m/s. The total system momentum is conserved. The momentum lost by the truck (15 000 kg*m/s) is gained by the car.

8. Car Rear Ends Truck In the collision between the truck and the car, total system momentum is conserved. Before the collision, the momentum of the car is 20 000 kg*m/s and the momentum of the truck is 0 kg*m/s; the total system momentum is 20 000 kg*m/s. After the collision, the momentum of the car is -10 000 kg*m/s and the momentum of the truck is +30 000 kg*m/s; the total system momentum is 20 000 kg*m/s. The total system momentum is conserved. The momentum lost by the car (30 000 kg*m/s) is gained by the truck.

9. Car and Truck in Head-on Collision In the collision between the truck and the car, total system momentum is conserved. Before the collision, the momentum of the car is +20 000 kg*m/s and the momentum of the truck is -60 000 kg*m/s; the total system momentum is -40 000 kg*m/s. After the collision, the momentum of the car is -10 000 kg*m/s and the momentum of the truck is -30 000 kg*m/s; the total system momentum is -40 000 kg*m/s. The total system momentum is conserved. The momentum change of the car (-30 000 kg*m/s) is equal in magnitude and opposite in direction to the momentum change of the truck (30 000 kg*m/s) .

10. Two Cars in 2-Dimensional Collision The animation below portrays the inelastic collision between two 1000-kg cars. The before- and after-collision velocities and momentum are shown in the data tables.

11. Big Fish in Motion Catches Little Fish The mathematics of this problem is simplified by the fact that before the collision, there is only one object in motion and after the collision both objects have the same velocity. That is to say, a momentum analysis would show that all the momentum was concentrated in the big fish before the collision. And after the collision, all the momentum was the result of a single object (the combination of the big and little fish) moving at an easily predictable velocity.

12. Little Fish in Motion is Caught by Big Fish The mathematics of this problem is simplified by the fact that before the collision, there is only one object in motion and after the collision both objects have the same velocity. That is to say, a momentum analysis would show that all the momentum was concentrated in the little fish before the collision. And after the collision, all the momentum was the result of a single object (the combination of the big and little fish) moving at an easily predictable velocity.

13. Astronaut Catch Imagine that you are hovering next to the space shuttle in earth-orbit and your buddy of equal mass who is moving 4 m/s (with respect to the ship) bumps into you. If she holds onto you, then how fast do the two of you move after the collision? The mathematics of this problem is simplified by the fact that before the collision, there is only one object in motion and after the collision both objects have the same velocity. That is to say, a momentum analysis would show that all the momentum was concentrated in the moving astronaut before the collision. And after the collision, all the momentum was the result of a single object (the combination of the two astronauts) moving at an easily predictable velocity. Since there is twice as much mass in motion after the collision, it must be moving at one-half the velocity. Thus, the two astronauts move together with a velocity of 2 m/s after the collision.