UNIT 5 – Momentum and Impulse Chapter 8 Inertia in Motion Need Eggs – several hard boiled

momentum = mass x velocity p = mv momentum = mass x velocity vector units: kgm/s car truck supertanker bullet What’s the difference between a Mack truck and a skateboarder? (mass) Would you rather stand in front of a bullet some one throws at you or one someone shoots at you? (velocity) We combine these two idea into mass in motion – inertia in motion … momentum. car = m v truck = 20m v supertanker = 100,000m (1/6v) bullet = (1/100,000) m x 10v no – truck not moving check question: Will a truck always have more momentum than a skateboarder?

What is the momentum of a 0.5 kg baseball thrown at 40 m/s? What is the mass of a car that has a momentum of 10,000 kgm/s when moving at 10 m/s? 20 kgm/s 1000 kg 4 m/s 5x A canoe has a momentum of 1,200 kgm/s when loaded with 300 kg of gear. What is its velocity? check question: A truck has 10x the mass and half the speed of a car – compare p.

time during which the force acts Impulse = force x time I= Ft time during which the force acts units = Ns F t 10 5 F t 5 10 F t 20 10 video: impulse - tennis ball video: impulse - baseball ball video: impulse – golf ball Video: impulse – real golf ball 150 mph Photo: impulse – bat & ball Impulse = 50 Ns Impulse ~ 160 Ns (Rectangle = 200, Triangle = 100) DEMO: force plate answer: longer time -> lower force check question: Why do you aim for the haystack rather than the brick wall?

𝐹𝑡=𝑚∆𝑣 𝐽= ∆𝑝 Δp = change in momentum = Δ(mv) = m(Δv) an ________ leads to a __________________________ 𝐹𝑡=𝑚∆𝑣 𝐽= ∆𝑝 Increase v (m const): Decrease F (m and v const): Increase F: Impulse Change in Momentum Write: “Impulse Momentum Equation” in front of boxed equation Optional: derive Ft = mv from Newton’s 2nd Law Increase v: cannon, archery Write exaggerated eqn with big F and t and Δv Video: increase speed - carrier launch Decrease Force: pulling hand back when catching, boxing, air bags, traffic safety, egg toss Write exaggerated eqn with big F and small t Video: decrease force – traffic barrels, skateboarder, carrier landing DEMO: egg toss into sheet Increase F: hammering, self defense Write exaggerated eqn with big m and Δv and small t Video: increase force - ????

What is the force exerted on the pole? A 4,500 kg truck moving east at 5 m/s hits a utility pole and is brought to rest in 0.90 sec. Find the force exerted on the truck. What is the force exerted on the pole? F(0.9) = 4500(-5) F = - 25,000 N or 25,000 N West F = +25,000 N or 25,000 N East (Newton’s 3rd Law!) +20 m/s -25 m/s Check questions: Will pushing on dash of car make it go faster? (no) Will pulling up on shoe laces make you weigh less? (no) A car speeds up from 5 to 25 m/s. What’s the Δv? A car accelerates from 30 to 5 m/s. What’s the Δv?

Bouncing The ball hits the ground at 10 m/s and splats. Δv? The ball hits the ground at 10 m/s and bounces up at 8 m/s. Δv? The ball is pitched at 30 m/s and is hit back toward the pitcher at 40 m/s. Δv? Demo: bounce vs. no bounce balls Δv = 10 m/s Δv = 18 m/s Δv = 70 m/s Video: bounce - football helmet tech (go to 1:20) Ans: splat (delta v = v, not 2v, so lower force) check question: When designing a container to protect eggs from breaking, do you want it to splat or bounce off the floor?

What is the change in momentum of the car during this time? 2000 kg car traveling to the east slows down uniformly from 20 m/s to 5 m/s. How long does it take the car to decelerate if the force on the car is 3000 N to the west? What is the change in momentum of the car during this time? What is the impulse on the car during this time? How far does the car travel during the deceleration? Δv = -15 m/s Ft = mΔv -3000 (t) = 2000(-15) t = 10 sec Δp= mΔv = 2000 (-15) = -30,000 kg m/s Impulse = Ft = - 3000 (10) = -30,000 Ns (Impulse = Change in Momentum!) d = ? d = 1/2 (vi +vf) t vi = 20 m/s d = 1/2 (20 + 5) (10) vf = 5 m/s d = 125 m t = 10 s

Short Barrel: Long Barrel: Water Balloon Catch Good Catch: Bad Catch: Paint Ball Gun Short Barrel: Long Barrel: Check Question: Why are cars designed with “crumple zones” (increases time and decreases force) Note: Avoid saying “it absorbs force or energy” – neither are true Falling on: Concrete: Gymnastics Mat:

Conservation of Momentum Collisions Elastic Inelastic Explosions Conservation of Momentum pi = pf Elastic: 10 kg ball moving at 20 m/s collides elastically with a 5 kg ball moving in the same direction at 5 m/s. After collision 10 kg ball continues moving forward at 10 m/s, what is the velocity of the 5 kg ball? Demo: tennis ball (elastic) vs. ball of clay (inelastic) Video: elastic – football hits Video: inelastic – train vs car Video: expolsion – pumpkin 10(20) + 5(5) = 10(10) + 5(v) v = 25 m/s DEMO: air track or cart on track

What is their momentum after? How do their two momenta compare? Inelastic: 5 kg fish swimming at 4 m/s eats a 1 kg fish swimming at 2 m/s . What their velocity after lunch? Explosion: The cannon has a mass of 100 kg and the cannon ball has a mass of 5 kg. What is their momentum before the explosion? What is their momentum after? How do their two momenta compare? If the cannon ball fires at 100 m/s, what is the velocity of the cannon? 5(4) + 1(-2) = (5+1) v 20 – 2 = 6v v = 3 m/s DEMO: air track or cart on track same 100(v) = 5(100) v = 5 m/s

0 m/s 0 m/s 4 m/s _____ m/s 0 m/s 12 m/s _____ m/s 0 m/s 0 m/s

More complicated collisions: Do NOT print this slide If p = mv [down] before, what is p after explosion?

Do not print Ans: 200/80 = 2.5 kgm/s

Ft=mΔv more t = more change in velocity