Is Conservation of Energy the Key to Solving This Tricky Problem?

AI Thread Summary
The discussion focuses on the relationship between momentum and kinetic energy in the context of a car and the Earth. It highlights that while the momentum change of the car is equal to that of the Earth, the kinetic energy is not the same due to the Earth's significantly larger mass. The formula for kinetic energy (Ek=1/2*m*v^2) is compared with momentum (p=m*v), leading to the conclusion that the kinetic energy gained by the Earth is much lower. This analysis suggests that option c is likely correct based on the calculations presented. The conversation emphasizes the importance of understanding these physical principles in solving related problems.
Tim Wu
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I find this problem kind of tricky. I think it must be a, since a change in momentum of the car causes the same change in momentum of the earth.
 
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Tim Wu said:
a change in momentum of the car causes the same change in momentum of the earth
That part is correct. But does that imply that the kinetic energy is the same? Compare the formulas for momentum and kinetic energy.
 
Doc Al said:
That part is correct. But does that imply that the kinetic energy is the same? Compare the formulas for momentum and kinetic energy.
Oh yeah! Ek=1/2*m*v^2, and v = p/m, therefore Ek= p^2/2m. Since p is the same for car and Earth but the Earth's mass is way bigger the kinetic energy gained by Earth wud be much lower! So would option c be right?
 
Tim Wu said:
Oh yeah! Ek=1/2*m*v^2, and v = p/m, therefore Ek= p^2/2m. Since p is the same for car and Earth but the Earth's mass is way bigger the kinetic energy gained by Earth wud be much lower! So would option c be right?
You got it. Good thinking!
 

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