4 Newton's Laws of Motion - BC Science Physics 11

Quick Check
1. (a) What is the momentum of a 112 kg football player running with a velocity of 3.6 m/s?
(b) What impulse must a tackler impart to the football player to bring him to a stop?
(c) If the tackle was completed in 0.80 s, what average force did the tackler exert on the other player?
(d) Why is the force negative in question 1(c)?
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Law of Conservation
of Momentum
Any moving body has momentum equal to the product of the body’s mass and its
velocity. What makes momentum such an important quantity in nature is the fact that in
a closed system, momentum is conserved. A closed system is one where no outside forces
act on the system. This is the law of conservation of momentum. In other words, the
total change in momentum within the closed, two-body system is zero. This means that
the total momentum is constant, or that momentum is conserved.
Scientists have done many, many experiments with momentum and are convinced
that momentum truly is a conserved quantity in nature. At the subatomic level in
experiments done with high-energy particle accelerators, physicists rely heavily on the
law of conservation of momentum in interpreting the results of collisions of particles.
Conservation of Momentum and Newton’s Third Law
Newton’s third law is a special case of the law of conservation of momentum. This can be
shown by using a proof. A proof is a mathematical solution that logically demonstrates
something to be true. The following is a proof showing that Newton’s third law is a special
case of the law of conservation of momentum.
Consider two bodies interacting such that body A exerts a force on body B, and
body B exerts an equal force on body A, but in the opposite direction.
F = – F
A on B B on A
action force = – reaction force
The minus sign indicates that the direction of the reaction force is opposite to that
of the action force. Using Newton’s second law, written in terms of momentum:
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m B v B
t
= – m A v A
t