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?

A question like this involves momentum principles. In any instance in which two objects collide and can be considered isolated from all other net forces, the conservation of momentum principle can be utilized to determine the post-collision velocities of the two objects. Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the two astronauts, the combined momentum of the two astronauts before the collision equals the combined momentum of the two astronauts 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.

 

 

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?

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the two cars, the momentum of the diesel and the flatcar before the collision equals the momentum of the diesel and the flatcar 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 diesel before the collision. And after the collision, all the momentum was the result of a single object (the combination of the diesel and flatcar) moving at an easily predictable velocity.

The prediction of the final velocity of the two cars involves determining the ratio by which the mass which is in motion changed; and then dividing the initial velocity by that ratio. That is if the amount of mass in motion increases by a factor of two, then the velocity would decrease by a factor of two (divid the original velocity by two). If the amount of mass in motion increases by a factor of five, then the velocity would decrease by a factor of five (divide the original velocity by five). In the case of the animation above, the amount of mass in motion increased by a factor of 5/4; a change from say 8000 kg for the diesel before the collision to 10 000 kg for the combination of the diesel and flatcar after the collision. Since the amount of mass in motion increased by a factor of 5/4, the velocity at which that mass is in motion must decrease by a factor of 5/4. That is, the original velocity of 5 km/hr must be divided by 5/4. Voila! The result is 4 km/hr; the diesel and flatcar move together with a velocity of 4 km/hr after the collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

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.

In the collision between the loaded cart and the dropped brick, total system momentum is conserved. Before the collision, the momentum of the loaded cart is 150 kg*cm/s and the momentum of the dropped brick is 0 kg*cm/s; the total system momentum is 150 kg*cm/s. After the collision, the momentum of the loaded cart is 90.0 kg*cm/s and the momentum of the dropped brick is 60.0 kg*cm/s; the total system momentum is 150 kg*cm/s. The momentum of the loaded cart-dropped brick system is conserved. The momentum lost by the loaded cart (60 kg*cm/s) is gained by the dropped brick.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

The animation below portrays the collision between a 1.0-kg 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 (the cart and the dropped brick) are internal forces - the force of friction between the cart and the droped brick. The before- and after-collision velocities and momentum are shown in the data tables.

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.

 

 

The animation below portrays the inelastic collision between a very massive fish and a less massive fish. Before the collision, the big fish is in motion with a velocity of 5 km/hr and the little fish is at rest. The big fish has four times the mass of the little fish. After the collision, both the big fish and the little fish 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 fish?

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the two fish, the momentum of the big and little fish before the collision equals the momentum of the big and little fish 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 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.

The prediction of the final velocity of the two fish involves determining the ratio by which the mass which is in motion changed; and then dividing the initial velocity by that ratio. That is, if the amount of mass in motion increases by a factor of two, then the velocity would decrease by a factor of two (divid the original velocity by two). If the amount of mass in motion increases by a factor of five, then the velocity would decrease by a factor of five (divide the original velocity by five). In the case of the animation above, the amount of mass in motion increased by a factor of 5/4; a change from say 4 kg for the big fish before the collision to 5 kg for the combination of the big and litlle fish after the collision (note that I can make up any numbers for mass as long as they meet the criteria that the big fish has four times the mass as the little fish). Since the amount of mass in motion increased by a factor of 5/4, the velocity at which that mass is in motion must decrease by a factor of 5/4. That is, the original velocity of 5 km/hr must be divided by 5/4. Voila! The result is 4 km/hr; the big and little fish move together with a velocity of 4 km/hr after the collision.

 

 

The animation below portrays the inelastic collision between a very massive fish and a less massive fish. Before the collision, the little fish is in motion with a velocity of 5 km/hr and the big fish is at rest. The big fish has four times the mass of the little fish. After the collision, both the big fish and the little fish 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 fish?

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the two fish, the momentum of the big and little fish before the collision equals the momentum of the big and little fish 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 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.

The prediction of the final velocity of the two fish involves determining the ratio by which the mass which is in motion changed; and then dividing the initial velocity by that ratio. That is, if the amount of mass in motion increases by a factor of two, then the velocity would decrease by a factor of two (divide the original velocity by two). If the amount of mass in motion increases by a factor of five, then the velocity would decrease by a factor of five (divid the original velocity by five). In the case of the animation above, the amount of mass in motion increased by a factor of 5; a change from say 1 kg for the little fish before the collision to 5 kg for the combination of the big and litlle fish after the collision (note that I can make up any numbers for mass as long as they meet the criteria that the big fish has four times the mass as the little fish). Since the amount of mass in motion increased by a factor of 5, the velocity at which that mass is in motion must decrease by a factor of 5. That is, the original velocity of 5 km/hr must be divided by 5. Voila! The result is 1 km/hr; the big and little fish move together with a velocity of 1 km/hr after the collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

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.

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 5 000 kg*m/s and the momentum of the truck is 15 000 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 (15 000 kg*m/s) is gained by the truck.

An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 200 000 Joules (200 000 J for the car plus 0 J for the truck). After the collision, the total system kinetic energy is 50 000 Joules (12 500 J for the car and 37 500 J for the truck). The total kinetic energy before the collision is not equal to the total kinetic energy after the collision. A portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

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 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.

An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 600 000 Joules (600 000 J for the truck plus 0 J for the car). After the collision, the total system kinetic energy is 450 000 Joules (337 500 J for the truck and 112 500 J for the car). The total kinetic energy before the collision is not equal to the total kinetic energy after the collision. A portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

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 elastic 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.

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.

An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 200 000 Joules (200 000 J for the car plus 0 J for the truck). After the collision, the total system kinetic energy is 200 000 Joules (50 000 J for the car and 150 000 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.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum lost by one object equals the momentum gained by the other object.

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 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.

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 30 000 kg*m/s and the momentum of the car is 30 000 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 (30 000 kg*m/s) is gained by the car.

An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 600 000 Joules (600 000 J for the truck plus 0 J for the car). After the collision, the total system kinetic energy is 600 000 Joules (150 000 J for the truck and 450 000 J for the car). The total kinetic energy before the collision is equal to the total kinetic energy after the collision. A collision in which total system kinetic energy is conserved is known as an elastic collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum change of the individual objects are equal in magnitude and opposite in direction.

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.

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) .

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 200 000 Joules (50 000 J for the car and 150 000 J for the truck). The total kinetic energy before the collision is not equal to the total kinetic energy after the collision. A large portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum change of the individual objects are equal in magnitude and opposite in direction.

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 elastic 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.

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.

 

 

Collisions between objects are governed by laws of momentum and energy. When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision. If there are only two objects involved in the collision, then the momentum change of the individual objects are equal in magnitude and opposite in direction.

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 two 1000-kg cars. The before- and after-collision velocities and momentum are shown in the data tables.

In the collision between the two cars, total system momentum is conserved. Yet this might not be apparent without an understanding of the vector nature of momentum. Momenum, like all vector quantities, has both a magnitude (size) and a direction. When considering the total momentum of the system before the collision, the individual momentum of the two cars must be added as vectors. That is, 20 000 kg*m/s, East must be added to 10 000 kg*m/s, North. The sum of these two vectors is not 30 000 kg*m/s; this would only be the case if the two momentum vectors had the same direction. Instead, the sum of 20 000 kg*m/s, East and 10 000 kg*m/s, North is 22 361 kg*m/s at an angle of 26.6 North of East. Since the two momentum vectors are at right angles, their sum can be found using the Pythagorean theorem; the direction can be found using SOH CAH TOA (specifically, the tangent function). The value 22 361 kg*m/s is the total momentum of the system before the collision; and since momentum is conserved, it is also the total momentum of the system after the collision. In order to determine the momentum of either individual car, this total system momentum must be divided by two (approx. 11 200 kg*m/s). Once the momentum of the individual cars are known, the after-collision velocity is determined by simply dividing momentum by mass (v=p/m).

An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is 250 000 Joules (200 000 J for the eastbound car plus 50 000 J for the northbound car). After the collision, the total system kinetic energy is 125 000 Joules (62 500 J for each car). The total kinetic energy before the collision is not equal to the total kinetic energy after the collision. A large portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision.