Favg = 2.5×10^4 N
7.5 - Conservation of momentum
Conservation of momentum: The total
momentum of an isolated system is constant.
Momentum is conserved in an isolated system. An isolated system is one that does not
interact with its environment. Momentum can transfer from object to object within this
system but the vector sum of the momenta of all the objects remains constant.
Excluding deep space, it can be difficult to find locations where a system has no
interaction with its environment. This makes it useful to state that momentum is
conserved in a system that has no net force acting on it.
We will use pool balls on a pool table to discuss the conservation of momentum. To put
it more formally, the pool balls are the system.
In pool, a player begins play by striking the white cue ball. To use the language of
physics, a player causes there to be a net external force acting on the cue ball.
Once the cue ball has been struck, it may collide with another ball, and more collisions
may ensue. However, there is no net external force acting on the balls after the cue ball
has been struck (ignoring friction which we will treat as negligible). The normal force of
the table balances the force of gravity on the balls. Since there is now no net external
force acting on the balls, the total amount of their momentum remains constant. When
they collide, the balls exert forces on one another, but this is a force internal to the
system, and does not change its total momentum.
In the scenario you see illustrated above, the cue ball and another ball are shown
before and after a collision. The cue ball initially has positive momentum since it is
moving to the right. The ball it is aimed at is initially stationary and has zero momentum.
When the cue ball strikes its target, the cue ball slows down and the other ball speeds
up. In fact, the cue ball may stop moving. You see this shown on the right side of the
illustration above. During the collision, momentum transfers from one ball to another.
The law of conservation of momentum states that the combined momentum of both
remains constant: One ball’s loss equals the other ball’s gain.
A rifle also provides a notable example of the conservation of momentum. Before it is
fired, the initial momentum of a rifle and the bullet it fires are both zero (since neither
has any velocity). When the rifle is fired, the bullet moves in one direction and the rifle
recoils in the opposite direction. The bullet and the rifle each now have nonzero
momentum, but the vector sum of their momenta must remain at zero.
Two factors account for this. First, the rifle and the bullet are moving in opposite
directions. In the case of the rifle and bullet, all the motion takes place along a line, so
we can use positive and negative to indicate direction. Let’s assume the bullet has
positive velocity; since the rifle moves (recoils) in the opposite direction, it has negative
velocity. The momentum vector of each object points in the same direction as its
velocity vector. This means the bullet has positive momentum while the rifle has
negative momentum.
Second, for momentum to be conserved, the sum of these momenta must equal zero,
since the sum was zero before the rifle was fired. The amount of momentum of the
faster moving but less massive bullet equals the amount of momentum of the more massive but slower moving rifle. When the two are added
together, the total momentum continues to equal zero.
Conservation of momentum
No net external force on system:
Total momentum is conserved