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## Section 6 – 1 Momentum and Impulse

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**Momentum (p)**A vector quantity defined as the product of an object’s mass and velocity. Describes an object’s motion.**Why “p”?**• Pulse (Date: 14th century) • from Latin pulsus, literally, beating, from pellere to drive, push, beat http://www.madsci.org/posts/archives/dec99/945106537.Ph.r.html**Momentum = mass x velocity**p = mv Units: kg-m/s**Conceptualizing momentum**Question – Which has more momentum; a semi-truck or a Mini Cooper cruising the road at 10 mph? Answer – The semi-truck has more mass. Since the velocities are the same, the semi has more momentum.**Conceptualizing momentum**Question – Which has more momentum; a parked semi-truck or a Mini Cooper moving at 10 mph? Answer – The velocity of the semi is 0 mph. That means its momentum is 0 and this time the Mini Cooper has more momentum.**Conceptualizing momentum**Question – Which has more momentum, a train moving at 1 mph or a bullet moving at 2000 mph? Answer – The mass of a train is very large, while the mass of a bullet is relatively small. Despite the large speed of the bullet, the train has more momentum.**Ex 1: Gary is driving a 2500 kg vehicle, what is his**momentum if his velocity is 24 m/s?**G: m = 2500 kg, v = 24 m/s**U: p =? E: p = mv S: p = S: p =**Ex 2: Ryan throws a 1.5 kg football, giving it a momentum of**23.5 kg-m/s. What is the velocity of the football?**G: m = 1.5 kg, p = 23.5 kg-m/s**U: v = ? E: p = mv or v = p/m S: v = S: v =**A change in momentum**Dp (Dp = mDv) Takes force and time.**Momentums do not always stay the same. When a force is**applied to a moving object, the momentum changes.**Impulse (J)**The product of the force and the time over which it acts on an object, for a constant external force. J = FDt**Impulse – Momentum Theorem**Impulse causes a change in momentum**J = Dp**or FDt = mvf - mvi**Ex 3: What is the impulse on a football when Greg kicks it,**if he imparts a force of 70 N over 0.25 seconds? Also, what is the change in momentum?**G: F = 70 N, Dt = 0.25 s**U: J = ? E: J = FDt S: J = S: J = Dp = FDt =**Ex 4: How long does it take a force of 100 N acting on a**50-kg rocket to increase its speed from 100 m/s to 150 m/s?**G: F = 100 N, vf = 150 m/s, vi = 100m/s, m = 50 kg**U: Dt = ? E: Dt = m(vf - vi)/F S:Dt = S: Dt =**Stopping times and distances depend upon impulse-momentum**theorem.**Ex 5: Crystal is driving a 2250 kg car west, she slows down**from 20 m/s to 5 m/s. How long does it take the car to stop if the force is 8450 N to the east? How far does the car travel during this deceleration?**G: m = 2250 kg F = 8450 N east = 8450 N**vi = 20 m/s west = - 20 m/s vf = 5 m/s west = - 5 m/s U: Dt =? E: F Dt = J = Dp = m (vf - vi) Dt = m (vf - vi) / F**S:**Dt =**S:**Dt = S: Dt =**B)**U: Dx = ? E: Dx = ½(vi + vf )Dt S:Dx = S: Dx = - ___ m or Dx = ___ m west**Frictional forces will be disregarded in most of the**problems unless otherwise stated.**Law of Conservation of Momentum**The total momentum of all objects interacting with one another, in an isolated system remains constant regardless of the nature of the forces between them.**What this means:**Any momentum lost by one object in the system is gained by one or more of the other objects in the system.**total initial momentum**total final momentum =**total initial momentum**total final momentum =**total initial momentum**total final momentum =**For objects that collide:**The momentum of the individual object(s) does not remain constant, but the total momentum does.**Momentum is conserved when objects push away from each**other. Ex 1: Jumping, Initially there is no momentum, but after you jump, the momentum of the you and the earth are equal and opposite.**Ex 2: 2 skateboarders pushing away from each other.**Initially neither has momentum. After pushing off one another they both have the same momentum, but in opposite direction.**Which skateboarder has the higher velocity?**The one with the smaller mass.**Ex 6: John, whose mass is 76 kg, is initially at rest in a**stationary 45 kg boat, steps out of the boat and onto the dock with an a velocity of 2.5 m/s to the right. What is the final velocity of the boat?**G: mjohn=76 kg, mboat= 45kg, vjohn, i = vboat,i = 0 m/s,**vjohn,f = 2.5 m/s U: vboat = ? E: Momentum is conserved. PJ,i + pb,i = pJ,f + pb,f mjvJ,i + mbvb,i = mjvJ,f + mbvb,f 0 + 0 = mjvJ,f + mbvb,f**vb,f = (mJvJ,f) /-mb**S: vb,f =**vb,f = (mJvJ,f) /-mb**S: vb,f = S: vb,f =**vb,f = (mJvJ,f) /-mb**S: vb,f = S: vb,f = - ____ m/s or ___ m/s to the left**Newton’s 3rd Law leads to a conservation of momentum.**Open books to HPg. 219-220**Forces in real collisions are not constant. They vary**throughout the collision, but are still opposite and equal.**Perfectly Inelastic Collisions**A collision in which two objects stick together and move with a common velocity.