7.2 Conservation of Momentum in One Dimension
7.3 Conservation of Momentum in Two Dimensions
sion
- State the law of conservation of momentum.
- Use the conservation of momentum to solve one-dimensional collision problems.
For this whale to leap out of the water, something underwater must be moving in the opposite direction, and intuition
tells us it must be moving with relatively high velocity. The water that moves downward is pushed downward by the
whale’s tail, and that allows the whale to rise up.
Conservation of Momentum in One Dimension
When impulse and momentum were introduced, we used an example of a batted ball to discuss the impulse and
momentum change that occurred with the ball. At the time, we did not consider what had happened to the bat. Ac-
cording to Newton’s third law, however, when the bat exerted a force on the ball, the ball also exerted an equal and
opposite force on the bat. Since the time of the collision between bat and ball is the same for the bat and for the
ball, then we have equal forces (in opposite directions) exerted for equal times on the ball AND the bat. That means
that the impulse exerted on the bat is equal and opposite (-Ft) to the impulse on the ball (Ft) and that also means that
there was a change in momentum of the bat[−∆(mv)BAT]that was equal and opposite to the change in momentum
of the ball[∆(mv)BALL].
The change in momentum of the ball is quite obvious because it changes direction and flies off at greater speed.
However, the change in momentum of the bat is not obvious at all. This occurs primarily because the bat is more
massive than the ball. Additionally, the bat is held firmly by the batter, so the batter’s mass can be combined with
the mass of the bat. Since the bat’s mass is so much greater than that of the ball, but they have equal and opposite
forces, the bat’s final velocity is significantly smaller than that of the ball.
Consider another system: that of two ice skaters. If we have one of the ice skaters exert a force on the other skater,
the force is called aninternal forcebecause both the object exerting the force and the object receiving the force