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Clifton Bluhm

“Inertia in Motion”

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define MOMENTUM

Define IMPULSE

determine which quantities affect momentum.

determine which quantities affect impulse.

quantify momentum with an equation.

quantify impulse with an equation.

I can . . .

differentiate elastic from inelastic collisions�using concepts of�CONSERVATION OF MOMENTUM.

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Which vehicle has more momentum?

Momentum is a Function of MASS

http://www.subaru-global.com/lineup/legacy/exterior/colour.html

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www.toyota.com

Which car has more momentum?

Momentum is a Function of VELOCITY

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Momentum ≡

UNITS

Momentum = kg · m/s

Momentum =

kg · m�s

Mass · Velocity

? ? ?

“Inertia in Motion”

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http://www.waynet.org/waynet/spotlight/2001/images/08/smileytruck-closeup640.jpg

Zero Velocity

Implies

Zero Momentum

Momentum ≡

Mass · Velocity

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http://brd3.chosun.com/bemil/files/BEMIL025/upload/A%20Tomahawk

Tomahawk Cruise Missile

Mass = 1000 kg�Velocity = 100 m/s

Semi Truck

Mass = 5000 kg�Velocity = 20 m/s

Momentum = 100,000 kg·m/s

Momentum = 100,000 kg·m/s

http://kesl.infocity.cz/img/truck.jpg

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http://www.rit.edu/~andpph/photofile-c/bullet-rifle-22-1a.jpg

http://wilsonscc.com/Giant%20Turtle%20copy.jpg

300 m/s�.01 kg

.03 m/s�100 kg

.22 Caliber Bullet

Giant Turtle

3 kg·m/s

3 kg·m/s

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.22 Caliber Bullet

Giant Turtle

http://www.rit.edu/~andpph/photofile-c/bullet-rifle-22-1a.jpg

http://wilsonscc.com/Giant%20Turtle%20copy.jpg

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1,000 kg(30 m/s)

1,000 kg(50 m/s)

30,000 kg·m/s

50,000 kg·m/s

Momentum Before

Momentum After

Change in Momentum (Δp)

Change in Momentum = m·ΔV �= 1000 kg (20 m/s)�= 20,000 kg·m/s

After – Before = 20,000 kg·m/s

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a =

f�m

a =

ΔV�t

f�m

ΔV�t

=

m · ΔV = f · t

ΔMomentum = f · t

Impulse = f · t

Newton’s 2nd Law

Definition of Acceleration

Impulse ≡ ΔMomentum

J = f · t

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An Impulse of�250 N·s�CAUSES a �change in Momentum of�250 kg·m/s

Impulse = ΔMomentum

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Push with 100 N for 1 s. Push with 50 N for 2 s.�Push with 25 N for 4 s.�Push with 10 N for 10 s.�Push with 5 N for 20 s.

​

List 5 ways to apply�an Impulse of 100 N·s

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Time (seconds)

Force (Newtons)

Time (seconds)

Force (Newtons)

Impulse = Force ·Time

Impulse = ½ Maximum Force ·Time

= Average Force ·Time

Time (seconds)

Force (Newtons)

Impulse = Area Under the Curve

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Time (seconds)

Force (Newtons)

40 N

​

​

30 N

​

​

20 N

​

​

10 N

​

​

​

​

​

​

​

​

-10 N

​

​

-20 N

​

​

​

1 s 2 s 3 s 4 s 5 s 6 s

​

Impulse = 80 N·s�

If the object had a change in velocity of 30 m/s, what was the object’s mass?

Δp = m · Δv�60 kg·m/s = m · 30 m/s

m = 2 kg

– 20 N·s � = 60 N·s

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Force Sensor

Sonic Ranger

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Which object would have a larger change in momentum if the man pushed for 3.0 s?

3.0 seconds

A) Car�B) Motorcycle�C) Neither

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Which object would have a larger change in momentum at the finish line?

A) Car�B) Motorcycle�C) Neither

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Who had the larger IMPULSE?

Momentum = mass ·velocity

= 70 kg · 30 m/s

= 2100 kg·m/s

Who had the larger Force of impact?

Who had the larger TIME of impact?

Momentum = ZERO

Impulse = f · t

Impulse = ∆ Momentum

Momentum = ZERO

Momentum = mass · velocity

= 70 kg · 30 m/s

= 2100 kg·m/s

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Impulse = f · t

Impulse = · t f ·

f

t

=

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http://www.netcar.co.il/img2/milon/25A%20front%20air%20bag.jpg

You stop in 0.5 seconds with an airbag, and you stop in 0.05 seconds without. �If without an airbag there is 2000 N of force on you, how much force will there be with an airbag?

200 N

Impulse = · t f ·

f

t

=

2000 · .05 = f · .5

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http://www.geocities.com/demeri_stunts/d-fall-1.jpg

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http://www.rescate.com/rappel.jpg

http://www.rock-climbing-courses.co.uk/images/galler4.jpg

Dynamic Rope

Static Rope

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http://www.bishopweb.com/photos/data/500/3701CL-al609.jpg

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Who had the larger IMPULSE?

Who had the larger Force of impact?

Who had the larger TIME of impact?

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Who had the larger IMPULSE?

Who had the larger Force of impact?

Who had the larger TIME of impact?

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Who received a larger FORCE?

Who had a larger IMPULSE?

Who had a larger CHANGE IN MOMENTUM?

�Impulse = m·ΔV = f · t�

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�Impulse = m·ΔV = f · t�

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www.thephysicsguy.com

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http://www.turbosquid.com/HTMLClient/FullPreview/Index.cfm/ID/197797/Action/FullPreview

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Clifton Bluhm

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Clifton Bluhm

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Clifton Bluhm

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Clifton Bluhm

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Clifton Bluhm

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+

-

+

-

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+ 30,000 kg·m/s

- 30,000 kg·m/s

Positive and Negative Momenta

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+ 30,000 kg·m/s

- 30,000 kg·m/s

Positive and Negative Momenta

What was the IMPULSE on the car.

-50,000

-40,000

-30,000

-20,000

0

+10,000

+20,000

+30,000

+40,000

+50,000

-10,000

60,000 N·s

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Which ball had a larger IMPULSE?

+10 kg·m/s

-10 kg·m/s

0 kg·m/s

+10 kg·m/s

0 kg·m/s

∆Momentum = 20 kg·m/s

∆Momentum = 10 kg·m/s

Impulse = 20 N·s

Impulse = 10 N·s

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Impulse = f · t

2·Impulse = 2(f · t)

2·Impulse = 2·f · t

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http://www.theamericangym.com/BYtramps.htm

http://www.cartwheelfactory.com/mats.html

http://ofquiet.com/portland/pages/portland-balcony.html

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CONSERVATION:

Preservation from loss

kŏn׳sûr-vā ׳ shən

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CONSERVATION:

Preservation from loss

kŏn׳sûr-vā ׳ shən

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Conservation of Momentum

Total MomentumBefore = Total MomentumAfter

pABefore+ pBBefore = pAAfter+ pBAfter

mA·vA + mB·vB = mA·vA + mB·vB

A

B

BEFORE

AFTER

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Total MomentumBefore = Total MomentumAfter

2 kg(0 m/s) + .01 kg(0 m/s) = 2 kg(-1 m/s) + (.01 kg · 200 m/s)

pgun + pBullet = pgun + pBullet

Zero + Zero = -2 kg·m/s + 2 kg·m/s

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www.gauden.com

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Zero BEFORE = Zero AFTER

Total Momentum Before = Total Momentum After

+10 kg·m/s

-10 kg·m/s

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Zero BEFORE = Zero AFTER

Total Momentum Before = Total Momentum After

-10 kg·m/s

+10 kg·m/s

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Zero BEFORE = Zero AFTER

Total Momentum Before = Total Momentum After

3 kg·(-1 m/s)

1 kg·(+ 3 m/s)

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m1·v1 + m2·v2 = (m1 + m2)·v

Inelastic Collisions�(Sticking)

stick

Total MomentumBefore = Total MomentumAfter

BEFORE

AFTER

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m1·v1 + m2·v2 = (m1 + m2)·v

Total Momentum Before = Total Momentum After

1 · 1 + 1 · 0 = (1 + 1) · v

v = ½

1 = (2) · v

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m1·v1 + m2·v2 = (m1 + m2)·v

Total Momentum Before = Total Momentum After

1 · 1 + 2 · 0 = (1 + 2) · v

v = ⅓

1 = (3) · v

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m1·v1 + m2·v2 = (m1 + m2)·v

Total Momentum Before = Total Momentum After

2 · 1 + 1 · -1 = (2 + 1) · v

v = ⅓

1 = (3) · v

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http://www.atlasrr.com

http://www.maths.tcd.ie/~eoin/photoDB/newshow.php?collection=desert&id=12

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http://www.atlasrr.com

http://www.maths.tcd.ie/~eoin/photoDB/newshow.php?collection=desert&id=12

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http://www.atlasrr.com

http://www.maths.tcd.ie/~eoin/photoDB/newshow.php?collection=desert&id=12

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m1·v1 + m2·v2 = m1·v1 + m2·v2

Elastic Collisions�(Bouncing)

Total MomentumBefore = Total MomentumAfter

BEFORE

AFTER

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m1·v1 + m2·v2 = m1·v1 + m2·v2

Total Momentum Before = Total Momentum After

1 · ½ + 1 · -1 = 1 · v1 + 1 · v2

v1 = -1

v2 = +½

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m1·v1 + m2·v2 = m1·v1 + m2·v2

Total Momentum Before = Total Momentum After

1 · 1 + 1 · 0 = 1 · v1 + 1 · v2

v1 = 0

v2 = 1

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m1·v1 + m2·v2 = m1·v1 + m2·v2

Total Momentum Before = Total Momentum After

1 · 1 + 2 · 0 = 1 · v1 + 2 · v2

v1 = -⅓

v2 = ⅔

1 · 1 + 2 · 0 = 1 · v1 + 2 · v2

m1·v1 + m2·v2 = m1·v1 + m2·v2

½m1·v12 + ½m2·v22 = ½m1·v12 + ½m2·v22

½1·12 + ½2·02 = ½1·v12 + ½2·v22

v1 = 1 - 2v2

½ = ½v12 + v22

½ = ½(1 - 2v2)2 + v22

0 = -2v2 + 3v22

⅔= v2

v1 = 1 - 2 ⅔

v1 = -⅓

Conservation of Momentum

Conservation of Energy

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m1·v1 + m2·v2 = m1·v1 + m2·v2

Total Momentum Before = Total Momentum After

2 · 1 + 1 · 0 = 2 · v1 + 1 · v2

v1 = ⅓

v2 = 43

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define MOMENTUM

Define IMPULSE

determine which quantities affect momentum.

determine which quantities affect impulse.

quantify momentum with an equation.

quantify impulse with an equation.

I can . . .

differentiate elastic from inelastic collisions�using concepts of�CONSERVATION OF MOMENTUM.