momentum and collisions momentum and collisions physics 2053 lecture notes

Momentum and Collisions


Physics 2053Lecture Notes


6-01 Momentum and Impulse

6-02 Conservation of Momentum

6-03 Collisions

Topics


mm

iv

F

tavv if

mF

fv

if mvmvtF

ImpulsetΔF )p( omentumMmv

Momentum is a vectormvtF

mvtF ptmF

vv if

pΔtΔF

Momentum and Impulse


t


A block moving with an initial velocity vi is acted on by

a constant force F for a time t.

maF

tΔmvΔ

F net


Newton’s 2nd Law

netFtΔvΔ

p

tΔvΔ

mF net

tΔpΔ

F net



A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail?

(b) What is the average force acting on the nail?

hamernail ppI

if mvmvI m/s 8.5 kg 120I m/skg 102

tp

Favg

s 0080.0

m/skg 102 N 750,12

Momentum and Collisions Problem


v

m

The area under the curve on a Force versus time (F vs. t) graph represents

A) impulse.

B) momentum.

C) work.

D) kinetic energy.

Momentum and Collisions 07-01


M m

FMFm

Fm = FM

Fmt = FMt

pm = pM

m(u2 u1) = M(v2 v1)

Conservation of

Momentum

v1 u1

M m

v = u

M m

v2 u2

mu2 m u1 = Mv2 Mv1

Mv1 + m u1 = Mv2 mu2

p(before) = p(after)

Conservation of Momentum

Collision between to moving objects


M m

v

before

after

mMMv

V

M m

V = ?

afterbefore PP

Mv VmM

VmMMv


Collision with a stationary block


A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car?



Mv

m

before after

V

mMmv

V

afterbefore PP

mv (M + m)V

VmMmv


Bullet fired into a block which is initially at rest.


A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car.What happens to the velocity of the car?

A) It increases.

B) It remains the same.

C) It decreases.

D) cannot be determined from the information given



Collisions

Elastic Collisions

Inelastic Collisions

Momentum and Kinetic Energy are both conserved

Only Momentum is conserved


m1 m2

v1

m1 m2

vf

before

after

An Inelastic Collision

v2

21

2211f mm

vmvmv

afterbefore pp

2211 vmvm f21 vmm

f212211 vmmvmvm

Collisions


In an inelastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy?

A) Kinetic energy is also conserved.

B) Kinetic energy is gained.

C) Kinetic energy is lost.

D) none of the above



Two objects collide and stick together. Kinetic energy

A) is definitely conserved.

B) is definitely not conserved.

C) is conserved only if the collision is elastic.

D) is conserved only if the environment is frictionless.



1 Eq vmm

m2v

mm

mmv 1B

BA

B1A

BA

BA2A

2 Eq vmm

mmv

mm

m2v 1B

BA

AB1A

BA

A2B

mBmA

vA1 vB1

mBmAvA2 vB2

Elastic Collision (General Equations)

Collisions


1BBA

B1A

BA

BA2A v

mm

m2v

mm

mmv

Elastic Collision (vB1 = 0) Ball B is initially at rest.

0 vmm

mmv 1A

BA

BA2A

mBmA

vA1

mBmAvA2 vB2

1BBA

AB1A

BA

A2B v

mm

mmv

mm

m2v

0 vmm

m2v 1A

BA

A2B

Collisions


mmvA1

mm

VB2

Elastic Collision (vB1 = 0 and mA= mB)

1ABA

BA2A v

mm

mmv

1ABA

A2B v

mm

m2v

0v 2A

1A2B vv

Collisions


In an elastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy?

A) Kinetic energy is also conserved.

B) Kinetic energy is gained.

C) Kinetic energy is lost.




When is kinetic energy conserved?

A) in inelastic collisions

B) in any collision in which the objects do not stick together

C) in all collisions

D) in elastic collisions



When a light beach ball rolling with a speed of 6.0 m/s collides with a heavy exercise ball at rest, the beach ball's speed after the collision will be, approximately,

A) 0.

B) 3.0 m/s.

C) 6.0 m/s.

D) 12 m/s.



Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision?



Ballistic Pendulum

m

vo M h

v

Cons. Momentum Cons. Energy

Collisions


Ballistic Pendulum

m

v M h

V

Cons. Momentum

VMmmv Mmmv

V

Find the speedof the bullet

afterbefore pp

Collisions


Ballistic Pendulum

M h

V

Cons. Energy

gh2 m

Mmv

Mm

mvV

0KU

2

Mmmv

21

gh

2

VMmgh Mm

2

Collisions


A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.



A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it?



Two objects collide and bounce off each other.Linear momentum

A) is definitely conserved.

B) is definitely not conserved.

C) is conserved only if the collision is elastic.

D) is conserved only if the environment is frictionless.



A 100 kg football linebacker moving at 2.0 m/s tackles head-on an 80 kg halfback running 3.0 m/s. Neglecting the effects due to digging in of cleats,

A) the linebacker will drive the halfback backward.

B) the halfback will drive the linebacker backward.

C) neither player will drive the other backward.

D) this is a simple example of an elastic collision.



cm

xcm

x1

x2

x

y

m1

m2

21

2211cm mm

xmxmx

ii

iii

cm m

xm

x

Center of Mass (cm)


21

2211cm mm

xmxmx

Location of the cm of the Earth-Moon system

xcmmemm

me

mmcm mm

Rmx

kg10x 7.3kg10x 6.0

m10x 3.8kg10x 7.3x

2224

822

cm

m10x 4.6 6

Rm

x

Center of Mass (cm)


Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass.


0.5 m 0.25 m

1.0 kg 1.5 kg 1.1 kgx

y


Consider two unequal masses, M and m. Which of the following statements is false?

A) The center of mass lies on the line joining the centers of each mass.

B) The center of mass is closer to the larger mass.

C) It is possible for the center of mass to lie within one of the objects.

D) If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present.



Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass?

A) It was always zero.

B) It was never zero.

C) It was not zero, but ended up zero.




mvp Momentum :

vΔmtΔF Impules:

Newton’s second law: tΔpΔ

F net

Total momentum of an isolated system of objects is conserved.

0pΔ

afterbefore pp

Momentum is conserved during collisions.

Chapter 7 Summary


In an elastic collision, total kinetic energy is also conserved

In a completely inelastic collision, the two objects stick together after the collision.

The center of mass of a system is the point at which external forces can be considered to act.

In an inelastic collision, some kinetic energy is lost.

Chapter 7 Summary


momentum and collisions momentum and collisions physics 2053 lecture notes

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