Does Equal Kinetic Energy Imply Different Momenta for Cars with Varying Masses?

  • #1
avenkat0
59
0

Homework Statement



Car A has a greater mass than car B. Let:

- KA = the kinetic energy of car A
- KB = the kinetic energy of car B
- pA = the magnitude of the momentum of car A
- pB = the magnitude of the momentum of car B
- vA = the speed of car A
- vB = the speed of car B

a) If car A and car B have the same kinetic energy (KA = KB), then

Homework Equations


p=mv
Ke= .5(m)(v^2)

The Attempt at a Solution


I tried to set up a situation:
Car A- 10 kg Car B- 5kg Ke=20 J
.5(10)(v^2) = 20 .5(5)(v^2)=20
v= 2 m/s v= 2.828 THEREFORE Vb > Va
Pa=10(2) = 20 Pb=5(2.828) THEREFORE Pb < Pa

But the selection Pb<Pa and Vb>Va is wrong
Is there a flaw in my reasoning
thank you for your help
 
Last edited:
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  • #2
with Ma=2 and Mb=1 and Ke=10
im getting

Va=3.162
Vb=4.47

MVa=6.92
MVb=4.47

Vb>Va and MVb<MVa

same result as earlier and its wrong
 
  • #3
avenkat0 said:
with Ma=2 and Mb=1 and Ke=10
im getting

Va=3.162
Vb=4.47

MVa=6.92
MVb=4.47

Vb>Va and MVb<MVa

same result as earlier and its wrong
I deleted my previous post because you edited your post after I had replied and therefore my previous post didn't make sense.
 
  • #4
sorry about that it was a typo
 
  • #5
Your answers look fine. You should, though, try to prove the relations in general, not just for particular values of mass, speed, etc.
 
  • #6
the answer itself is wrong.
But i tried graphing the m: ke function and it shows that when the mass increases the Velocity decreases
and when the mass increases the momentum increases...
im confuzed haha what am i doing wrong here

pB < pA and vB > vA

was the answer i selected and it came out to be wrong
 
  • #7
pB<pA and vB>vA are the correct answers. Who says it's wrong?
 
  • #8
the professor... thanks for your help now that i know that i have someone to confirm it i guess i can email him
 
  • #9
good luck :-)
 
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