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Linear momentum is a quantity associated with how a mass moves along a straight path. A force can change the linear momentum of a mass. If you hit a hockey puck with a stick, the puck will move forward and there is a linear momentum associated with it. If no forces are acting on the puck, it keeps moving in the same path with the same velocity forever or until it runs out of ice; in this case, the linear momentum stays the same.Linear Momentum Defined
Linear momentum is defined to be equal to the mass of an object times its velocity. A 10,000 kilogram (kg) truck moving at 2 meters per second (m/s) has a linear momentum of 20,000 kilogram-meters per second (kg m/s) while a 80 kg bicyclist moving at 2 m/s has a linear momentum of 160 kg m/s. The truck has a much larger linear momentum even though both are moving at the same velocity. It is easier to bring the bicyclist to a stop than it is to bring the truck to a stop. Similarly, it is easier to stop a bicyclist moving at 2 m/s than a bicyclist moving at 5 m/s.
If there are no external forces acting on a system, then the linear momentum of the system is conserved. The hockey puck sliding across the ice has no forces acting on it, so its linear momentum is conserved. Two billiard balls rolling toward each other each have some linear momentum and after they hit, their total linear momentum will be the same as their total linear momentum before the collision.Example: The Dog
Let's take an example. You are standing still when your dog runs up and jumps on you. Together, you and the dog fall backwards. Your mass is 40 kg and the dog is 20 kg. The dog is coming at you at 2 m/s. Since linear momentum is conserved in this situation, the total linear momentum before the collision must equal the total linear momentum afterwards.
The linear momentum before the collision is
You and the dog are basically stuck together as you are falling. The two of you are moving with the same velocity backwards. The linear momentum after the collisions is then
Setting these expressions equal and solving yields the velocity at which you and the dog will be moving backwards.
After the collision, you and the dog will be moving at 2/3 m/s backwards.
There is an interaction between you and the dog during the collision that causes you to start moving and the dog to slow down. When the dog hits you, he pushes on you and exerts a force on you. You start moving and gain some linear momentum. At the same time, you are exerting a force on the dog to slow him down. The force the dog exerts on you is exactly equal and opposite to the force you exert on the dog. Nothing influences you or the dog from the outside so linear momentum is said to be conserved.