2 Linear MomentumMomentum can describe the motion of an object before and after a collision takes place.Examples:Bowling ball and the PinsAutomobile AccidentSportsRocketsEtc… (Basically anything that has movement)
3 Inertia and MomentumInertia is the tendency for an object to resist changeObject at rest, stays at restObject in motion, stays in motionMomentum is the tendency for an object to stay in motionMomentum = Inertia in motion
4 MomentumMomentum – A vector quantity that is the product of an object’s mass and its velocity.
5 p = mv Momentum Equation p = Momentum (lower case letter “p”) m = Mass v = VelocityThe symbol “p” comes from the word progress, which is defined as “The quantity of motion with which a body proceed in a certain direction.”
6 Momentum = mass x velocity SI Units For Momentump = mvMomentum = mass x velocity= (kg)(m/s)=kgm/sSI units for Momentum – “kgm/s”There is no short way around the units for momentum.
7 Momentum as a VectorThe direction of momentum is in the same direction as the velocity of the object.
8 Momentum & VelocityAn object that has no velocity (v=0 m/s) has no momentum.An object that picks up speed, picks up momentum.The more momentum an object has, the harder it is to make the object stop.An object that slows down, loses momentum.The less momentum an object has, the easier it is to make the object stop.Momentum is directly proportional to the velocity.
9 Momentum of Different Objects Can two different objects have the same momentum, such as a Mack truck and a roller skate?
10 Momentum of Different Objects Sure they can!In order for both to have the same momentum, the Mack truck would have to be moving really slow and the roller skate would have to be moving really fast in order for both objects to achieve the same momentum.Mack Truck = Roller Skatemv = mv
11 Momentum and MassEven objects with small masses can have a lot of momentum, as long as the velocity is very large.BulletsHailstonesHammerEtc…
12 Example ProblemAn astronaut with a mass of 45 kg wears a 32 kg suit and moves at 5.7 m/s on the moon. What is the total momentum of the astronaut and the suit?
13 Example Problem Answer p = mv= (77kg)(5.7m/s)= 440 kgm/sp = 440 kgm/s
14 Changing Momentum Takes a Force Catching a baseball thrown very fast might sting the hand.Catching a slow-moving baseball causes no discomfort when it is caught.When catching a ball, the velocity changes to zero once it is caught.Change in velocity is an acceleration and if there is acceleration, then there must be a force present.
15 Force = Change in momentum ÷ time interval Force and MomentumMomentum is closely related to force.In fact, Newton wrote his Second Law of Motion mathematically, he wrote it not as F=ma, but in the following form:F = Δp/ΔtForce = Change in momentum ÷ time interval
16 Impulse-Momentum Theorem FΔt = ΔpF = ForceΔt = Time intervalΔp = Change in momentum
17 Impulse-Momentum Theorem Explained The derived version of the equation. Ft = Δp Ft = mΔv Ft = m(vf – vi)
18 ImpulseImpulse – For a constant external force, the product of the force and the time over which it acts on an object.A large force will cause a change in an object’s momentum in a short time, but a small force will take a much longer time to cause the same change in momentum.
19 Everyday Use of The Theorem With out thinking, you use this theorem in everyday activities. What are some of these activities?
20 Example ProblemA 1400 kg car moving with a velocity of 15m/s due east collides with a utility pole and is brought to rest in 0.30 seconds. Find the magnitude of the force exerted on the car during the collision.
21 Example Problem Answer 70,000 N to the westPage 211 – Sample Problem 6B
22 Impulse For Stopping Times and Distances The impulse momentum theorem is the formula used by engineers and accident investigators.Larger mass objects have larger momentums, therefore it takes longer for a larger mass object to stop then a small mass.This directly affects the distance.Must use the kinematic equations
23 Example ProblemIf the maximum coefficient of kinetic friction between a 2300kg car and a road is 0.50, what is the minimum stopping distance for a car moving at 29m/s?