A.P. PHYSICS --- CHAPTER 6 Momentum and Collisions Chapter 6 ...

A.P. PHYSICS --- CHAPTER 6Momentum and Collisions1Chapter 6 textbook hw#1,3,4,6,9,15,16,20,21,23,26,27,25,34,63,70,716 – 1 What is momentum?Momentum is a _____________ quantity.The instantaneous momentum of an object isdefined as p = _______Since momentum is a ________ quantity, wecan break it into its components:p x =and p y =Ex 1A 5 kg flowerpot falls out of a window 50 mabove the ground. Find the momentum of theflowerpot at the instant it hits the ground.

What is Impulse?2What happens when a ball hits a wall? Is theforce on the ball constant during impact?_ _Thus, F = m a(in this course, since we only deal withuniform acceleration, the averageacceleration will therefore equal the uniform,or constant acceleration)_ _from F = m a and a = Äv/tderive the formulas for impulse.

EX 2A 50 g golf ball sits on a tee and is struck bya golf club. The balls leaves the club at44 m/s.3V i = 0 m/sA) What is the impulse due to the collision?B) What is the average force on the ball ifthe club is in contact with the ball for1 x 10 -3 s?

EX 3A ball of 0.1 kg is dropped from a height 2 mabove the ground. It rebounds to a height of1.5 m after colliding with the floor.A) Find the momentum of the ball at theinstant before it hits the ground.B) Find momentum of the ball at the instantafter it leaves the ground.C) Find impulse of the ball during thecollision.D) If average force on the ball during thecollision is 200 N, find the time ball is incontact with ground.42m1.5m

EX 4A 1500kg car collides and rebounds off of awall as shown. The car is in contact with thewall for .15s.A) Find the impulse during the collision.B) Find average force the wall exerts on thecar5Before CollisionAfter CollisionV= 15 m/s V= 2.6 m/sHW – 1,3,4,6,9

6 – 2 Conservation of Momentum6When two objects collide, according toNewton’s 3 rd law, the force that object 1exerts on object 2, is ________ the forcethat object 2 exerts on object 1.Hence F 1 = -F 2Also, the time that object 1 is in contactwith object 2 is _________ as the timeobject 2 is in contact with object 1.Thus, Ät 1 =Ät 2Therefore, the impulse (or change inmomentum) is _________________.Now derive the formula forConservation of Momentum(Also, when can we use this equation?)

EX 5A 1000 kg car traveling 10 m/s collideswith a 5000 kg truck at rest.A) If the car bounces off the truck at2 m/s(Opposite direction), what is thevelocity of the truck after the collision?B) How much momentum did the truckgain in collision?C) How much momentum did the carlose?7After CollisionV= 0 m/sV= 10 m/s V= 2 m/sV= ?

EX 6What is the recoil velocity of a 4kg rifle thatshoots a 0.05 kg bullet at 280m/s?8V= 280 m/s V= ?(Discuss mV = Mv )When can we use this?

9Ex 7A boy is standing at rest on a frozen pond.He fires a 50 g bullet at 400m/s from a gunthat has a mass of 5 kg. If the boy has a massof 60 kg and the coefficient of kinetic frictionis 0.01, does the boy reach the shore? If not,where does he stop?V= 400 m/sm bullet = 50 gm boy = 60 kgm gun = 5 kg50mEX 8A 65 kg boy and a 40 kg girl, both wearingice skates face each other in the middle of theskating rink. The boy pushes the girl sendingher away from him at 4 m/s. What happensto the boy? (neglect friction)HW – 15,16,20,21µ k = .01

10TYPES OF COLLISIONS (or Explosions)Before CollisionAfter CollisionIn this example use conservation ofmomentum to find V 2fV 1i = 3 m/sV 2i = -3 m/sV 1f = -3 m/s V 2f =Now find:KE 1i = KE 1f =KE 2i = KE 2f =Is the total energy before the collision equalto the total energy after the collision?ELASTIC COLLISION∑P bc = ∑P ac and ∑KE bc = ∑KE ac

EX 911Before CollisionIf the cue ball hits the 8 ballELASTICALLY, find the speed of each ballafter the collision.EX 10 (now m 1 ≠ m 2 )Before CollisionIf the cue ball hits the 8 ballELASTICALLY, find the speed of each ballafter the collision.

Ex1112V 1i = V o2mV 2i = 0 m/s3m(V 1f = ½ V o )A car of mass 2m has a speed of V o as itstrikes another car of mass 3m initially atrest. If after the collision, the first car slowsto half of its speed,A) Find V 2f in terms of V 0 .B) Is this collision elastic?Show why/why notC) If the collision is not elastic, how muchenergy was lost in the collision?INELASTIC COLLISION∑P bc = ∑P ac and ∑KE bc ≠ ∑KE ac(Hence Energy Lost = _________________)(in collision)

Ex1213V 1i = V oV 2i = 0 m/s2m3mA car of mass 2m has a speed of V o as itstrikes another car of mass 3m initially atrest. If after the collision, the two cars couple(stick together)A) Find the common speed V com that the twocars go off with, after the collision interms of V 0 .B) Is this collision elastic/inelastic?Show why/why notC) If the collision is not elastic, how muchenergy was lost in the collision?PERFECT INELASTIC COLLISIONA collision in which the objects coupleduring the collision and go off together witha common speed.∑P bc = ∑P ac and ∑KE bc ≠ ∑KE ac

EX 13 (Ballistic Pendulum)14m bullet = .05 kgV i = 500 m/s2kgA 0.05 kg bullet is fired into a block at500 m/s and gets stuck in the 2 kg block thatis initially at rest and suspended by a 10.5 mrope.A) Find height that system rises to.B) Find Energy lost in collision.

EX 14A steel ball of mass m is fastened to a lightcord of length L and released when the cordis horizontal. At the bottom of the path, theball ELASTICALLY strikes a hard plasticblock of mass 4m, initially at rest on africtionless horizontal surface.mL15A) Find the speed of block immediatelyafter the collision.B) To what height h will the ball reboundafter the collision?HW – 23, 26, 274mM

Glancing CollisionsSince conservation of momentum says that∑P bc = ∑P ac and since momentum is avector, we can break the momentum into itscomponents.16Hence ∑P bcx = ∑P acx∑P bcy = ∑P acyEx15The cars collide in a perfect inelasticcollision.A) Find the common velocity they go offwith. (also include angle)B) Find energy lost in collision.m 1 = 1500 kgV 1 = 25 m/sm 2 = 2500 kgV 2 = 20 m/s

EX 16A cue ball hits the 8 ball in billiards asshown. The mass of each ball is 100 g.17Before CollisionAfter CollisionA) Find angle and speed of the 8 ball afterthe collision.B)What type of collision is it?HW – 25, 34, 63, 70, 71

EX 17Find velocity of the 2000kg car after thecollision.18Before CollisionV 1i = 20 m/sè = 30°V 2i = 30 m/sAfter CollisionV 1f = 15 m/sè = 45°