Momentum and Impulse Ch 6

To answer these questions, we introduce the concept of momentum… Momentum (p) is defined as the product of an object’s ______ and _________. p =p = Units = _____ How is momentum related to force? = massvelocity mv vv tt F  t m  v

The “FAt mAv” Formula F  t is termed the ________ that is applied to an object, which is a combined measure of the ________ applied to the object and the length of _______ over which the force was applied. m  v is termed the _______ in __________ of the object. “ F  t = m  v ” in words … a ______ applied to an object for a particular length of _______ will produce a _______ in the object’s __________! impulse force time changemomentum force time changemomentum

Applications of “FAt mAv” 1. Back to our initial questions … a person may survive a long free fall IF they land on something that has “give” to it, like a snowbank or tree branches. The more “give”, the longer the ________ ______. Survival if ______ = m  v ( _______ collision time results in _______ force) Lethal if ______ = m  v ( _______ collision time results in _______ force) collision time tt F tt F Longer smaller Shorter larger

2. Bungee Jumping The bungee cord stretches for a _______ time (slowing the person down ________), resulting in a _______ (nonlethal!) force. ______ = m  v long gradually smaller tt F

3. Automobile Safety Air Bags and Crumple Zones both serve to ________ the collision time (again slowing the passenger down more gradually), resulting in a _______ impact force on them. _____ = m  v tt F lengthen smaller

4. Boxing “Riding with the punch” _______ the collision time. Moving into the punch _______ the collision time. image from lengthens reduces

The Law of Conservation of Momentum Review: According to, if an external force is applied to an object, the object will experience a change in its __________. It follows, then, that if there is NO external force on an object, its change in momentum would be _____, or its momentum would remain ________. = momentum zero constant pipi pfpf

Elastic and inelastic collisions in one dimension Momentum is conserved in any collision, elastic and inelastic. Mechanical Energy is only conserved in elastic collisions. Perfectly inelastic collision: After colliding, particles stick together. There is a loss of energy (deformation). Elastic collision: Particles bounce off each other without loss of energy. Inelastic collision: Particles collide with some loss of energy, but don’t stick together.

So, when does this happen? When are there no external forces on a system? Let’s examine a collision between two vehicles, neglecting the force of friction between the tires and road. Considering the car as the “system”, it’s clear that it experienced an external force (the push from the truck). This force caused the car’s momentum to _________. change

Now, considering the truck as the “system”, it’s clear that it also experienced an external force (the push from the car). This force caused the truck’s momentum to _________. But, if we consider the car and the truck together as the “system”, then there are ___ external forces acting on them (The forces that they apply to each other would be forces internal to the system). So, momentum is conserved in a collision!! change NO

Conservation of Momentum Animations What would happen if the car’s velocity had been 60 m/s? dead stop!

Perfectly inelastic collision of two particles (Particles stick together) Notice that p and v are vectors and, thus have a direction (+/-) There is a loss in energy E loss

Elastic collision of two particles (Particles bounce off each other without loss of energy. Energy is conserved : Momentum is conserved:

Another Example V f = ?

Recoil Examples When a gun fires a bullet, there are ___ external forces, so momentum is _________. Since the initial momentum is zero, the final momentum must equal _____! So… the gun must recoil the opposite direction! Rockets “recoil” up as exhaust gases are expelled down. Again, there are no “external forces”. NO conserved zero m 1 v 1 = -m 2 v 2