Momentum and Newton’s Laws Section 5.4

Momentum aka the big “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 involving momentum Collisions Explosions Recoil

Defining Momentum The 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 Momentum Momentum 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 Problems A fully loaded Redi-Mix cement truck has mass 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/s p = kg * 19.4 m/s p = kgm/s [N] p = 8.1 x 10 5 kgm/s [N] b) p = mv so v = p/m = kgm/s /1270 kg v = 642 m/s [N]  640 m/s [N]

Practice Problems Saku 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 problem p= mv  (90. kg)( m/s) = 1.0 x 10 3 kgm/s (toward Biron) v = p/(m 1 + m 2 ) = ( kgm/s)/(190 kg) v = 5.26 m/s  5.3 m/s ( in the original direction of motion)

Defining Impulse Originally, 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 Impulse From the previous equation, F∆t = m∆v The 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 Theorem Because the impulse of a force causes the momentum of an object to change, F∆t = m∆v and Ns = kg · m/s See text example p. 201

Impulse and Auto Safety Reducing 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.