Momentum Defined as inertia in motion Equation: p = m v units: kg m/s So if the object’s at rest, then its p = 0 no matter how massive it is. Since momentum is based on an object’s velocity, which is a vector quantity, it too is an vector quantity – direction matters!

Change in Momentum Δp very different from just p of an object! Δp = pf – pi where each term has different values. = mvf – mvi = m (vf – vi ) [which = m Δv, but don’t use that in a math problem] since Δp most commonly from a Δv but it can also be from a Δm Ex: full vs empty salt truck rocket ship burning fuel

True or False? If an object’s Δp = 0, then its p = 0 as well. False Ex: Any moving object with a constant velocity If an object’s p = 0, then its Δp = 0 as well. Also false, although not as often Only if p = 0 only lasts for an instant during the time when we’re determining Δp Ex: a ball at the top its free fall climb

The Cause of a Change in Momentum Δp caused by a net force applied for a period of time This is called impulse (J) equations: J = Δp = F Δt = m (vf – vi) units: N s = kg m/s (kg m/s2) s = kg m/s where Δt – called impact time – the time it takes the collision to take place – is often very short . Watch: balloon time warp baseball breaks bat

Impending Collisions Notice, since Δp = m (vf – vi) = J = F Δt, If an object is destined to undergo a particular Δp (usually because it is going to crash or collide with something else…) then force and time are inversely proportional to each other for that situation. Since most often it is a lot of force that causes damage to things, we often want to minimize that force, so we try to extend the amount of time the change in momentum (collision) takes place in because, The longer the time an object takes to change momentum, the less force will be needed, therefore the less damage to the object. Ex: hard floor vs carpet riding with a punch landing bent legged vs stiff

Ex: Run-away truck ramps Air bags in vehicles (Show crash test Time Warp video)

Ex: hammering a nail into a wall But sometimes we want to “damage” the object, so a lot of force for a short time is ok Ex: hammering a nail into a wall nail gun on Time Warp

The Significance of Bouncing When an object bounces, not only did something have to get the object stopped from its original motion, but then it also needed to get it moving again from rest (opposite direction). This requires a greater Δp then to simply stop the object from moving -- therefore, a greater J and that usually comes from a larger force. Examples Pelton paddle wheel Rubber bumpers on cars?? (like those on Grande Prix) karate chop that doesn’t work karate chop to break boards

The Law of Conservation of Momentum The momentum of any isolated system remains constant. system refers to the objects you’ve chosen to be included isolated – a system that has no net force being applied from objects outside the defined system In an isolated system, for example, if one object loses p, then another one must gain = p Ex: Billiard balls in a game of pool , Newton’s Cradle if one object starts moving one way, then another will move the opposite way with = p Ex: 2 students face off on skateboards

Conservation of Momentum When it comes to defining your system, you get to pick the objects included in the system If something’s not included, but it applies a force, it’s an external force, so then it’s no longer an isolated system, so we can’t expect momentum to be conserved. So then Δpsys ≠ 0, and instead: Δpsys = J = Fext Δt = m (vf – vi) Ex: 1. push on car from outside of it 2. drop ball – it accelerates to ground 3. any interaction from 9.1! These are not exceptions to the law of conservation of momentum, we just aren’t satisfying the requirements of the law!

When it comes to defining your system, you get to pick the objects included in the system If something is included and it applies a force, it’s an internal force, so Δpsys = 0 for the system as a whole, even though objects inside may be changing their individual p’s Ex: 1. 2 students face off on skateboards 2. push on car from inside it 3. push car from outside, but include earth 4. watch ball drop, but include earth Does the Earth really gain = & - momentum? Yes – but too small to measure No – since it probably isn’t even a net force

Elastic vs Inelastic Elastic Collisions – book says it’s when there’s no heat loss, no permanent deformation, but that’s too simple. There’s always some energy lost to heat through friction and also to sound, so a true elastic collision doesn’t really exist at the macro level – we only deal in close approximations: Ex: billiard balls in a game of pool steel balls on Newton’s cradle spring bumpers on gliders on air track Inelastic Collisions – where there is obvious loss of energy in the form of permanent deformation, and sometimes the objects even entangle / stick together.

Momentum Conservation in 2 or 3 Dimensions The law of conservation of momentum is not restricted to objects interacting in a line – it also applies to 2 & 3D Consider the individual momentum vectors of the various objects within a system that are scattered in 2 & 3D: pisys = pfsys if you a combine the momentum of the pieces by vector addition

The math for the law of conservation of p: Use appropriate subscripts to ID given/unknown Start by staing: pisys = pfsys for an isolated system 2nd use some form of mivi = mfvf that best applies Watch signs on velocities – could be negative Let’s try a few…

The math for the law of conservation of p: for an isolated system pisys = pfsys [pi1 + pi2 + … = pf1 + pf2 + …] m1vi1 + m2vi2 = m1vf1 + m2vf2 m1 = m2 = vi1 = vi2 = vf1 = vf2 = ID the given carefully! instead of subscripts 1 & 2, use letters that represent specific objects in the problem if something starts from or goes to rest, then that entire term = 0 if the objects are stuck together, then they have = v’s so you can pull it out as a common factor: use (m1+ m2) vi , not m1vi1 + m2vi2 watch signs on the v’s – may be negative