Momentum (and related stuff)

Kellee NicholasKevin “Kev” Williams

Dave Garbe

IMPULSE AND MOMENTUM

“Momentum-The product of the mass of a moving particle multiplied by its linear velocity”—MSN online

-P(momentum)=m(mass)v(velocity) Impulse- A force applied over a period of

time.

-F(force)t(change in time)

IMPULSE AND MOMENTUM

(CONTINUED…)All moving

objects have momentum.

Momentum is conserved when no outside forces act on a system (sparknotes.com)

mvf - mvi -- change in velocity caused by an impulse

Examples:Air bags in

automobilesPadded

dashboardsEgg thrown into

sheet

INELASTIC COLLISIONS

Inelastic collision: a collision in which the kinetic energy of the system is not conserved

Kinetic energy of the colliding objects is transformed into other non-mechanical energy heat energy sound energy

In an inelastic collision, the two colliding objects stick together and move with the same post-collision speed.

Examples: Two billiard balls Golf club and ball Hammer and nail head Two coupled railroad

cars Falling object and

ground

SAMPLE PROBLEM #1(INELASTIC COLLISIONS)

A 15-kg medicine ball is thrown at a velocity of 20 km/hr to a 60-kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision.

BEFORE PERSON

m = 60 kgv = 0 km/hr

MEDICINE BALLm = 15 kgv = 20 km/hr

AFTER PERSON

m = 60 kgv = ? km/hr

MEDICINE BALLm = 15 kgv = ?

SAMPLE PROBLEM #1(CONTINUED…)

BEFORE AFTER

PERSON (60)(0) = 0 60v

BALL (15)(20) = 300

15v

TOTAL 300 30060v + 15v = 300

75v = 300

v = 4 km/hr

Since momentum is conserved, the total momentum after the collision is equal to the total momentum before the collision.

ELASTIC COLLISIONSElastic Collision:

when objects collide without being permanently deformed and without generating heat

Sum of momentum vectors are the same before and after each collision

Colliding objects bounce perfectly in perfect elastic collisions

Example: A moving billiard ball

collides head-on with a ball at rest and causes the second ball to move away with a velocity equal to the initial velocity of the first ball

SAMPLE PROBLEM (ELASTIC COLLISION)

A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck after the collision if the car moves off at 15 m/s.

BEFORE TRUCK

m = 3000 kgv = 10 m/s

CARm= 1000 kgv = 0 m/s

AFTER TRUCK

m = 3000 kgv = ? m/s

CARm = 1000v = 15 m/s

SAMPLE PROBLEM WITH WORK

(ELASTIC COLLISIONS)

3000v + 15000 = 30000

3000v = 15000

v = 5 m/s

BEFORE AFTER

VAN (3000)(10)=3000

0

3000v

CAR 0 (1000)(15)=1500

0

TOTAL 30000 30000

QUIZ QUESTION #1

Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without “braking.” Determine the velocity of Granny and Ambrose.

BEFORE GRANNY

m = 80 kgv = 6 m./s

AMBROSEm = 40 kgv = 0 m/s

AFTER GRANNY

m = 80 kgv = ? m/s

AMBROSEm = 40 kgv = ? m/s

QUIZ QUESTION #1(ANSWER)

BEFORE AFTER

GRANNY (80)(6)=480 80v

AMBROSE (40)(0)=0 40v

TOTAL 480+0=480 80v+40v=480

80v + 40v = 480

120v = 480

v = 4 m/s

The total momentum before the collision (possessed solely by Granny) equals the total momentum after the collision (shared by Granny and Ambrose).

QUIZ QUESTION #2

CAR A: 500 kg; 30 m/sCAR B: 600 kg; 20 m/s

The two cars stick together and continue in motionA. What type of collision is this?B. What is the final speed of the two

cars?

ANSWER (QUIZ QUESTION #2)

A: Inelastic CollisionB: m1v1 + m2v2 = mnvn

500(30) + 600(20) = (500 + 600)v

15000 + 12000 = 1100vv = 24.5454 m/s

QUIZ QUESTION #3 Jack is building a new

deck in his backyard. He is hammering each nail (which is at rest on top of each board and has a mass of .16 kg) with a hammer moving at 6 m/s and weighing 2.5 kg. Since the nail moves with the hammer once it is hit, what is the new velocity of the nail and hammer?

BEFORE HAMMER

M = 2.5 kgV = 6 m/s

NAILM = .16 kgV = 0 m/s

AFTER HAMMER

M = 2.5 kgV = ? m/s

NAILM = .16 kgV = ? m/s

ANSWER(QUIZ QUESTION #3)

2.5v+.16v=1515 + 0 = 15TOTAL

.16v(.16)(0) = 0NAIL

2.5v(2.5)(6) = 15HAMMER

AFTERBEFORE

P = mv

2.5v + .16v = 15

2.66v = 15

v = 5.64 m/s

QUIZ QUESTION #4A 35.0-g bullet

strikes a 5.0-kg stationary wooden block and embeds itself in the block. The block and bullet move together at 8.6 m/s. What was the original velocity of the bullet? (CAUTION: Be careful of the units on velocity.)

BEFORE BULLET

M = .035 kgV = ? m/s

BLCOKM = 5 kgV = 0 m/s

AFTER BULLET

M = .035 kgV = 8.6 m/s

BLOCKM = 5 kgV = 8.6 m/s

ANSWER(QUIZ QUESTION #4)

43.30143.301TOTAL

5*8.6=430BLOCK

0.035*8.6=.3010.035vBULLET

AFTERBEFORE

0.035v = 43.301

v = 1237 m/s

SOURCEShttp://www.physicsclasssroom.com/

Class/momentum/U4L2d.html

http://zebu.uoregon.edu/~js/glossary/inelastic_collisions.html

http://www.tpub.com/doephysics/classicalphysics32.htm

Physics Textbook