Momentum (and related stuff) Kellee Nicholas Kevin “Kev” Williams Dave Garbe

IMPULSE AND MOMENTUM “Momentum-The product of the mass of a moving particle multiplied by its linear velocity”—MSN onlinemass velocity -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) mv f - mv i -- change in velocity caused by an impulse Examples: Air bags in automobiles Padded dashboards Egg 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 kg v = 0 km/hr MEDICINE BALL m = 15 kg v = 20 km/hr AFTER PERSON m = 60 kg v = ? km/hr MEDICINE BALL m = 15 kg v = ?

SAMPLE PROBLEM #1 (CONTINUED…) BEFOREAFTER PERSON(60)(0) = 060v BALL (15)(20) = v TOTAL300 60v + 15v = v = 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 COLLISIONS Elastic 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 kg v = 10 m/s CAR m= 1000 kg v = 0 m/s AFTER TRUCK m = 3000 kg v = ? m/s CAR m = 1000 v = 15 m/s

SAMPLE PROBLEM WITH WORK (ELASTIC COLLISIONS) 3000v = v = v = 5 m/s BEFOREAFTER VAN(3000)(10)= v CAR0(1000)(15)= TOTAL30000

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 kg v = 6 m./s AMBROSE m = 40 kg v = 0 m/s AFTER GRANNY m = 80 kg v = ? m/s AMBROSE m = 40 kg v = ? m/s

QUIZ QUESTION #1 (ANSWER) BEFOREAFTER GRANNY (80)(6)=48080v AMBROSE (40)(0)=040v TOTAL 480+0=48080v+40v= v = 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/s CAR B: 600 kg; 20 m/s The two cars stick together and continue in motion A. What type of collision is this? B. What is the final speed of the two cars?

ANSWER (QUIZ QUESTION #2) A: Inelastic Collision B: m 1 v 1 + m 2 v 2 = m n v n 500(30) + 600(20) = ( )v = 1100v v = 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 kg V = 6 m/s NAIL M =.16 kg V = 0 m/s AFTER HAMMER M = 2.5 kg V = ? m/s NAIL M =.16 kg V = ? m/s

ANSWER (QUIZ QUESTION #3) 2.5v+.16v= = 15 TOTAL.16v(.16)(0) = 0 NAIL 2.5v(2.5)(6) = 15 HAMMER AFTERBEFORE P = mv 2.5v +.16v = v = 15 v = 5.64 m/s

QUIZ QUESTION #4 A 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 kg V = ? m/s BLCOK M = 5 kg V = 0 m/s AFTER BULLET M =.035 kg V = 8.6 m/s BLOCK M = 5 kg V = 8.6 m/s

ANSWER (QUIZ QUESTION #4) TOTAL 5*8.6=430 BLOCK 0.035*8.6= v BULLET AFTERBEFORE 0.035v = v = 1237 m/s

SOURCES momentum/U4L2d.html stic_collisions.html hysics32.htm Physics Textbook