Take out tables. On a separate sheet: Make a list of every equation we’ve not yet used in this class.

Here is your choice:. a. I toss a bullet at you. b Here is your choice: a. I toss a bullet at you. b. I shoot a bullet at you from a gun. Which is more dangerous to you? Why?

Linear Momentum & Impulse

Linear Momentum = mass in motion A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

Momentum (p) depends on: mass & velocity of object. p = mv m in kg v in m/s Units are … kg m no name. s

Momentum is a Vector Quantity Same direction as velocity All Energy KE too is a scalar

p = mv = (2250 kg)(25 m/s) = 5.6 x 104 kg m s Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum? p = mv = (2250 kg)(25 m/s) = 5.6 x 104 kg m s

Change in momentum - accl occurs any time an object changes velocity (speed or direction).

Momentum Change & Newton’s 2nd Law F = ma F = m(Dv/Dt) FDt =mDv m (vf - vi) for const mass. FDt = Dp Impulse. Dp = Change in momentum

Stand up Try to hit a home run. Try to drive a golf ball really far.

Equations of Momentum Change J =FDt = Dp Impulse = change momentum. pf – pi. Dp = mvf – mvi for velocity change with constant mass can factor out mass you can write, m (vf - vi) or mDv.

Force is required to change velocity or momentum of a body in motion Force is required to change velocity or momentum of a body in motion. Force must be in contact for some time.

Increased force & contact time on object give greatest impulse Dp = mDv.

Hit a homerun needs large impulse Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse D p.

Impulse (J) is the momentum change. It has the same units. kg m or Ns s It is like force but includes a contact time component!

Ex 2. How long does it take an. upward 100N force acting on Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?

F = 100 N Dv = 50 m/s m = 50 kg Ft = mDv t = mDv F 50 kg(50 m/s) 100 kg m/s2 = 25 s.

Concept: A pitcher throws a fastball to a catcher  Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.

Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.

Examples of Impulse/ Change in Momentum Baseball batter swinging through ball. Applying brakes of car over time to stop.

Ex 3. How long does it take a. 250 N force to increase to Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?

Ft = mDv. t = mDv. F F = 250 N m= 100 kg Dv =190 m/s t = 100kg(190m/s) Ft = mDv t = mDv F F = 250 N m= 100 kg Dv =190 m/s t = 100kg(190m/s) 250 kg m/s2. = 76 s.

Ex 4. The speed of a 1200 kg car. increases from 5 to 29 m/s in 12 s Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car? 2400 - N

Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s: a) what was its Dv? b) What was its Dp?

Dv = vf – vi. -12 m/s – (15 m/s) = - 27 m/s. Dp = mDv = 0.4kg(27m/s) =10.8 kg m/s

How many water balloons does it take to stop a bullet? 3:30 http://www.unwindly.com/i/772-How-Many-Water-Balloons-Does-It-Take-To-Stop-A-Bullet

Running with momentum. 15 min. https://www.youtube.com/watch?v=jLIyDfkQcsk Relaxing with impulse.13 minutes. https://www.youtube.com/watch?v=0nOHLThv2mw

Understanding Car Crashes 22 min start 8:53 http://www.youtube.com/watch?v=yUpiV2I_IRI Hewitt Momentum 4:20 https://www.youtube.com/watch?v=2FwhjUuzUDg

Hwk read text 208 – 211 do pg 214 #1- 4 concepts do p 211 #1 - 4 Hwk read text 208 – 211 do pg 214 #1- 4 concepts do p 211 #1 - 4. Impulse prbs. Also worksheet “Impulse Momentum”

Which are units of Impulse?   Nm N/s Ns N/m A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is: 1.5 kgm/s 1.8 kgm/s 2.4 kgm/s 4.8 kgm/s

A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball?   0.36 kgm/s 0.72 kgm/s 1.1 kgm/s 1.8 kgm/s

Graphs

Constant force f - t graph: Dp /Impulse is area under curve FDt. Force N

Non-Constant Force Force vs. time graph Non-Constant Force Force vs. time graph. The area under the curve = impulse or Dp change in momentum. What is the impulse during the 9 seconds of contact? 225 Ns

Consv Momentum Demos.

Conservation of Momentum If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.

What is a system? Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s). Common examples: collisions, explosions.

One Ball transfers all its momentum.

The astronaut transfers part of his momentum to the second astronaut.

Conservation of Momentum Calc’s Total momentum before = total after interactions. Collisions. Explosions Pushing apart.

SPbefore = Spafter m1v1 + m2v2 = m1fv1f + m2fv2f To Calculate: SPbefore = Spafter m1v1 + m2v2 = m1fv1f + m2fv2f v1 and v2 velocities for objects one and two. m1 and m2 masses of objects

Recoil From Explosions

Recoil illustrates conservation of momentum where initial and final momentum = 0. 0 = p1 + p2.

1. Two spring loaded lab carts A and B, explode apart from rest 1. Two spring loaded lab carts A and B, explode apart from rest. Cart A is twice the mass of cart B. The final velocity of cart A is 2 m/s. What is the final momentum of the system?

2. The cannon is 100kg and the cannonball is 5 kg 2. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon. - 5 m/s = vcf

Before Firing. After Firing m1v1 + m2v2 = m1fv1f + m2fv2f Before Firing After Firing m1v1 + m2v2 = m1fv1f + m2fv2f 0 = (100kg)vcf + (5kg)(100m/s) -500 kgm/s = (100 kg) vcf - 5 m/s = vcf recoil velocity of cannon

3. A 63-kg astronaut is in spacewalk when the tether breaks 3. A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank? 1.9 m/s

Hwk. Consv Momentum wksht

Collisions Sticky Bouncy

Stick em together problems Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final velocity? (4 kg)

Bg fish sm.fish Bg fish sm.fish m1v1 + m2v2 = m1fv1f + m2fv2f (4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2 But the final velocities are equal so factor out the vf: 20 kg m/s = vf (4+1kg) vf = (20 kg m/s) / (5kg) = 4m/s

Find the final velocity of the cart and brick together 4. A 2 kg brick not moving horizontally is dropped on a 3 kg cart moving at 5.0 m/s. Find the final velocity of the cart and brick together

cart. brick. cart. brick m1v1 + m2v2 = m1fv1f + m2fv2f (3kg)(5 cart brick cart brick m1v1 + m2v2 = m1fv1f + m2fv2f (3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2 150 kg m/s = v (3kg + 2 kg) (150 kg m/s )/5 kg = 3.0 m/s aaa

Elastic & Inelastic Collisions Elastic: no KE lost at all (to heat, light, sound etc.) Usu. Involves objects that don’t make contact or bounce off. Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.

Which is totally elastic? Inelastic?

6. A 1000 kg car moving east at 20 m/s rear ends a stationary truck 6. A 1000 kg car moving east at 20 m/s rear ends a stationary truck. The truck’s mass is 3000-kg. If the bumpers lock on impact, what is the final velocity of truck/car wreck? Inelastic Collision mc = 1000 kg mt = 3000 kg vc = 20 m/s vt = 0 pc = pt =

m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000)v + (3000)v (20000 kg m/s) = (1000kg + 3000kg)v (20000 kg m/s) = (4000 kg)v (20000 kg m/s) = v 4000 kg v = 5 m/s

Elastic Collision mc = 1000 kg. mt = 3000 kg vc. = 20 m/s. vt. =. 0 7 Elastic Collision mc = 1000 kg mt = 3000 kg vc = 20 m/s vt = 0 7. Find final velocity of the car if truck has final velocity of 10 m/s.

m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000kg)vc+(3000kg)(10m/s) 20,000 kg m/s = (1000kg)vc+30000 kg m/s 20,000 kg m/s – 30,000 kg m/s = vc (1000kg) - 10 m/s = vc

Do Now: On July 4th my family likes to shoot off fireworks Do Now: On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point. Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes: How does the rocket’s momentum compare before & after the explosion? How does its KE compare compare before & after the explosion?

Inelastic Collisions Stick em together KE “lost” converted Elastic Collisions – no KE lost. Bounce off each other.

Hwk Read Rev Book pg 57 – 58 Do sheet 1-8

Hwk Prob’s in momentum sheet Film Understanding Car Crashes 23 min http://www.youtube.com/watch?v=yUpiV2I_IRI Hwk Prob’s in momentum sheet

Fish lunch Hewitt 4:00 https://www.youtube.com/watch?v=MK0B5hEU7OI Hewitt Cons Momentum 6:30 https://www.youtube.com/watch?v=1-s8NZ8xKW0 Fish lunch Hewitt 4:00 https://www.youtube.com/watch?v=MK0B5hEU7OI