Momentum and Newton’s Momentum and Newton’s LawsLawsSection 5.4

Momentum aka the big Momentum aka the big “Mo”“Mo”Newton first thought of the

concept of a “quantity of motion” made up of mass and velocity. We call it momentum.

p=mv ( a vector quantity )A train moving slowly and a

bullet moving quickly both have a lot of momentum

Some typical interactions Some typical interactions involving momentuminvolving momentumCollisionsExplosionsRecoil

Defining MomentumDefining MomentumThe product of an object’s mass

and its velocity. The direction of the momentum of an object is the same as the direction of its velocity.

Since p = mv, the units for momentum are kg·m/s

Example: a 10.0 kg mass travelling [E] at 20.0 m/s has a momentum of

200. kgm/s [E]

Defining MomentumMomentum is really a measure of the

difficulty encountered in bringing an object to rest. The greater the mass or velocity of an object, the bigger its momentum.

Momentum is a “conserved” quantity. Through repeated investigation, it has been determined that in a closed system, the total momentum before the interaction takes place equals the total momentum after the interaction. This is referred to as the Law of Conservation of Momentum

Practice ProblemsA fully loaded Redi-Mix cement

truck has mass 42 000 kg travels north at 70. km/h. a) Calculate its momentum.

b) How fast must a Toyota Matrix of mass 1270 kg travel in order to have the same momentum as the truck?

Solution to problem a)p = mv 70. km/h 19.4 m/sp = 42 000 kg * 19.4 m/sp = 814 800 kgm/s [N]p = 8.1 x 105 kgm/s [N]

b) p = mv so v = p/m = 814 800 kgm/s /1270 kgv = 642 m/s [N] 640 m/s [N]

Practice ProblemsSaku Koivu has mass 90. kg

skates towards Biron who has mass 100. kg. If Koivu is skating at 40. km/h, how much momentum does he have when he crashes into Biron? If they become entangled i.e. stick together, how fast do they travel?

Solution to practice problemp= mv (90. kg)(11.111 m/s) =

1.0 x 103 kgm/s (toward Biron)

v = p/(m1 + m2) = (999.999 kgm/s)/(190 kg)

v = 5.26 m/s 5.3 m/s ( in the original direction of motion)

Defining ImpulseDefining ImpulseOriginally, Newton thought that a

force was needed to bring about a change in an object’ s motion i.e a force is required to produce a change in an object’s momentum. Symbolically, this can be represented as

F= ∆p/ ∆t F = m∆v/ ∆t F = ma

Defining ImpulseDefining ImpulseFrom the previous equation,F∆t = m∆vThe product of a force and the

time interval over which it acts is called the “impulse” of the force. The symbol for impulse is J

J = F∆t ( a vector quantity) units are Ns

The Impulse Momentum The Impulse Momentum TheoremTheoremBecause the impulse of a force

causes the momentum of an object to change,

F∆t = m∆v and Ns = kg·m/sSee text example p. 201

Impulse and Auto SafetyImpulse and Auto SafetyReducing forces during car crashes can sometimes save lives and reduce

the severity of injuries. This can be accomplished by designing cars with crumple zones. While the front or back zone is crumpling, time is passing, energy is being dissipated and the impact on the passengers is reduced.

Other features such as air bags also help. By increasing ∆t, F is decreased.