phy11 lesson 3jhb momentum and collisions 2q1415

5/19/2018 PHY11 Lesson 3jhb Momentum and Collisions 2Q1415

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Momentum andCollisions

PHY11 Lesson 3


2/21

Newtons 2ndLaw

Consider a force F acting on a body of mass m withinitial velocity v

o

.

m F

vo

mF

v

From Newtons2ndLaw of Motion,

Linear Momentum (p)

dt

vmd

dt

vdmamF

)(

vmp unit: kgm/s


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Newtons 2ndLaw

dtpdF

Impulse

dtFpd

pdJ dtFJ


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Conservation of Linear Momentum

dt

pdF

If no net external acts on a system, the total linearmomentum of the system cannot change.

0,0 dt

pdthenFIf

The total momentum of the system is constant.

initial total momentum = final total momentum


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Conservation of Linear Momentum: Explosion

Consider a simple explosion, where a composite bodyexplodesinto two fragments of masses m

1

and m2

.

m2m1

initial total momentum of the system: 0)0()0( 21 mm

final total momentum of the system: 02211 vmvm

m2v2

m1v1

2211 vmvm


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Conservation of Linear Momentum: InelasticCollision

Consider an inelastic head-on collision between twomasses m1and m2.

initial total momentum of the system: oo vmvm 2211

final total momentum of the system: vmmvmvm )( 2121

m2v m1

m1v1o

vmmvmvm oo 212211

m2v2o


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Conservation of Linear Momentum: ElasticCollision



22112211 vmvmvmvm oo

m1v1o m2

v2o

Consider an elastic head-on collision between twomasses m1and m2.

m1v1 m2v2


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Conservation of Linear Momentum: ElasticCollision



22112211 vmvmvmvm oo

m1v1o m2

v2o

Consider an elastic head-on collision between twomasses m1and m2.

m1v1 m2v2


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Coefficient of Restitution (e)

Coefficient of restitution is the ratio of the relativevelocities colliding bodies after and before collision.

oo vv

vve

21

12

Coefficient of Restitution and Bouncing (e)

1

2

y

ye

y1= original height

y2= height of bounce


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Collisions in Two Dimensions (inelastic)

xoxox vmmvmvm 212211

conservation of momentumalong x-axis:

conservation of momentumalong y-axis:

22

yx vvv

Velocity after collision:

Consider two masses in an inelastic glancing collision.

x

y

m2

m1

v1o

V2o

v

m1m2

yoyoy vmmvmvm 212211

x

y

v

vtan


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Collisions in Two Dimensions (elastic)

Consider two masses in an elastic glancing collision.

x

y

m2m1

v1o

V2o=0

v1

v2

m1

m2

1

2

22211111 coscos vmvmvm o

222111 sinsin0 vmvm

conservation of momentumalong x-axis:

conservation of momentumalong y-axis:

2

22212

11212

10121 vmvmvm

conservation of kinetic energy


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Chapter 09, Problem 021A 0.28 kg softball has a velocity of 13 m/s at an angle of36 below the horizontal just before making contact withthe bat. What is the magnitude of the change in

momentum of the ball while it is in contact with the bat ifthe ball leaves the bat with a velocity of (a)18 m/s,vertically downward, and (b)18 m/s, horizontally backtoward the pitcher?

ANSWERS: (a) 4.1 kgm/s (b) 8.3 kgm/s


13/21

Chapter 09, Problem 037A soccer player kicks a soccer ball of mass 0.450 kg thatis initially at rest. The player's foot is in contact with theball for 1.40 10-3s, and the force of the kick is given

by F(t) = [(9.80 105)t - (1.20 108)t2] N for ,where t is in seconds. Find the magnitudes of thefollowing: (a) the impulse on the ball due to thekick, (b)the average force on the ball from the player'sfoot during the period of contact, (c)the maximum force

on the ball from the player's foot during the period ofcontact, and (d) the ball's speed immediately after itloses contact with the player's foot.

ANSWERS:

(a) 0.851 Ns(b) 608 N(c) 1140 N(d) 1.89 m/s


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Chapter 09, Problem 044In the figure here, a stationary block explodes into twopieces Land Rthat slide across a frictionless floor andthen into regions with friction, where they stop. Piece L,

with a mass of 2.8 kg, encounters a coefficient of kineticfriction L= 0.45 and slides to a stop in distance dL=0.48 m. Piece Rencounters a coefficient of kineticfriction R= 0.37 and slides to a stop in distance dR=0.41 m. What was the mass of the block?

ANSWERS: 6.1 kg


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Chapter 09, Problem 048Particle A and particle B are held together with acompressed spring between them. When they arereleased, the spring pushes them apart and they then fly

off in opposite directions, free of the spring. The massofAis 2.00 times the mass of B, and the energy stored inthe spring was 35 J. Assume that the spring has negligiblemass and that all its stored energy is transferred to theparticles. Once that transfer is complete, what are the

kinetic energies of (a)particleAand (b)particle B?

ANSWERS: (a) 11.7 J (b) 23.3 J


16/21

Chapter 09, Problem 051In Figure (1), a 3.50 g bullet is fired horizontally at twoblocks at rest on a frictionless table. The bullet passesthrough block 1 (mass 1.34 kg) and embeds itself in block

2 (mass 1.80 kg). The blocks end up with speeds v1 =0.600 m/s and v2= 1.35 m/s (see Figure (2)). Neglectingthe material removed from block 1 by the bullet, find thespeed of the bullet as it (a) leaves and (b)enters block1.

ANSWERS: (a) 696 m/s (b) 925 m/s


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Chapter 09, Problem 058In the figure, block 2 (mass 1.70 kg) is at rest on africtionless surface and touching the end of anunstretched spring of spring constant 216 N/m. The other

end of the spring is fixed to a wall. Block 1 (mass 1.70kg), traveling at speed v1= 5.80 m/s, collides with block2, and the two blocks stick together. When the blocksmomentarily stop, by what distance is the springcompressed?

ANSWER: 0.364 m


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Chapter 09, Problem 066Block 1, with mass m1 and speed 2.9 m/s, slides alonganxaxis on a frictionless floor and then undergoes a one-dimensional elastic collision with stationary block 2, with

mass m2 = 0.35m1. The two blocks then slide into aregion where the coefficient of kinetic friction is 0.33;there they stop. How far into that region do (a)block 1and (b)block 2 slide?

ANSWERS: (a) 0.301 m (b) 2.85 m


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Chapter 09, Problem 071In the figure, projectile particle 1 is an alpha particle andtarget particle 2 is an oxygen nucleus. The alpha particleis scattered at angle 1= 64.0 and the oxygen nucleus

recoils with speed 1.90 105 m/s and at angle 2 =51.0. In atomic mass units, the mass of the alphaparticle is 4.00 u and the mass of the oxygen nucleus is16.0 u. What are the (a) final and (b) initial speeds ofthe alpha particle?

ANSWERS:(a) 657000 m/s(b) 766000 m/s


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Chapter 09, Problem 075A projectile proton with a speed of 1200 m/s collideselastically with a target proton initially at rest. The twoprotons then move along perpendicular paths, with the

projectile path at 40 from the original direction. After thecollision, what are the speeds of (a) the target protonand (b)the projectile proton?

ANSWERS:

(a) 770 m/s (b) 920 m/s


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Chapter 09, Problem 100In a game of pool, the cue ball strikes another ball of thesame mass and initially at rest. After the collision, the cueball moves at1.90 m/s along a line making an angle

of 32.0 with its original direction of motion, and thesecond ball has a speed of 1.70 m/s. Find(a) the anglebetween the direction of motion of the second ball andthe original direction of motion of the cue ball and (b)theoriginal speed of the cue ball.

ANSWERS:

(a) 36.3o

(b) 2.98 m/s

phy11 lesson 3jhb momentum and collisions 2q1415

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