INELASTIC PROBLEM two masses collide inelastically and stick together. A 3kg mas

Question

INELASTIC PROBLEM two masses collide inelastically and stick together. A 3kg mass is at rest. A 5kg mass collides at 2m/s. 1) what is conserved? 2) what is not conserved? 3) initial momentum of each masses stuck together? 4) final momentum of the two masses stuck together? 5) velocity of the two masses stuck together? ELASTIC PROBLEM two masses collide elastically but dont stick together. A 3kg mass is at rest. A 5kg mass collides at 2 m/s. 1) what is conserved? 2) what is conserved? 3) what special equation do you need to use? 4) initial and final momentum energy of the two masses ( show that the total, before and after dont change)? 5) intial and final kinetic energy of te two mass not stuck together ( show that the total, before and after dont change )? 6) velocity of the two masses but not stuck together.   INELASTIC PROBLEM two masses collide inelastically and stick together. A 3kg mass is at rest. A 5kg mass collides at 2m/s. 1) what is conserved? 2) what is not conserved? 3) initial momentum of each masses stuck together? 4) final momentum of the two masses stuck together? 5) velocity of the two masses stuck together? ELASTIC PROBLEM two masses collide elastically but dont stick together. A 3kg mass is at rest. A 5kg mass collides at 2 m/s. 1) what is conserved? 2) what is conserved? 3) what special equation do you need to use? 4) initial and final momentum energy of the two masses ( show that the total, before and after dont change)? 5) intial and final kinetic energy of te two mass not stuck together ( show that the total, before and after dont change )? 6) velocity of the two masses but not stuck together.  

Explanation / Answer

INELASTIC PROBLEM
two masses collide inelastically and stick together. A 3kg mass is at rest. A 5kg mass collides at 2m/s.
1) what is conserved?
Momentum, insofar as net external forces (like friction)=0

2) what is not conserved?

Kinetic energy is not conserved,

3) initial momentum of each masses stuck together?

The masses won't stick together until they collide, so their respective momentums will equal
MaVai=(3)(0)=0
and
MbVbi=(5)(2)=10


4) final momentum of the two masses stuck together?

(Ma + Mb)vf --> this is the same as oridinary momentum, but we need to add the masses because the objects stick together.

5) velocity of the two masses stuck together?

MaVai + MbVbi=(Ma + Mb)vf

0 + 10=(8)vf
vf=10/8=1.25

ELASTIC PROBLEM
two masses collide elastically but dont stick together. A 3kg mass is at rest. A 5kg mass collides at 2 m/s.

1) what is conserved?

Momentum, isofar as net external forces (like friction) =0

2) what is conserved?

If completely elastic, Kinetic Energy is conserved.

3) what special equation do you need to use?

elastic:MaVai + MbVbf=MaVaf + MbVbf
Completely elastic=KEai +KEbi=KEaf + KEbf (KE=1/2mv^2)

4) initial and final momentum energy of the two masses ( show that the total, before
and after dont change)?

Pi=Pai + Pbi=MaVai + MbVbi=(3x0) + (5x2)=10
Pf=Paf + Pbf=3vaf + 5vbf

say Vbf=2m/s

(3)(0) + (5)(2)=(3)(2) + 5vf
10=6 + 5vf
10-6=5vf
4/5=vf
vf=.8

Now, substitute this into Pf to see if it equals Pi(10):

(3)(2) + (5)(.8)=6 + 4=10

Pi=Pf, so the energy is conserved


5) intial and final kinetic energy of te two mass not stuck together ( show that the total, before and after dont change )?

KEai + KEbi=KEaf + KEbf

KEi=1/2(3)(0)^2 + 1/2(5)(2)^2=0 + 10= 10Joules
KEf=1/2(3)(Vaf)^2 + 1/2(5)(VbF)^2 Do the same thing: substitute a value into either Vaf or Vbf, determine the value of the of the unsolved velocity. Insert this velocity into KEf and prove that it equals KEi.6) velocity of the two masses but not stuck together. You would need Vaf or Vbf to solve for this. The velocity of Mb will affect the final velocity of Ma, so you can't treat its final velocity independently.   All you can determine are the initial momentums: Pima=(3)(0)=0 Pimb=(5)(2)=10

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