What is the kinetic energy now?

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Homework Help Overview

The problem involves a body initially moving in one direction with a certain kinetic energy, which then changes direction and increases its speed. Participants are exploring how this change affects the kinetic energy of the body.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the kinetic energy formula and how changes in speed impact the kinetic energy. There are attempts to relate the initial and final kinetic energies, with some questioning the steps taken to arrive at conclusions.

Discussion Status

Some participants have provided insights into the relationship between the initial and final kinetic energies, while others are seeking clarification on the reasoning behind specific steps. The discussion is ongoing, with various interpretations being explored.

Contextual Notes

There is a focus on understanding the implications of speed changes on kinetic energy, and participants are encouraged to recognize the relationship between initial and final kinetic energies without reaching a definitive conclusion.

genu
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Homework Statement



Initially a body moves in one direction and has kinetic energy K. Then it moves in the opposite direction with three times its initial speed. What is the kinetic energy now?

Homework Equations



k =1/2mv^2

The Attempt at a Solution



k = 1/2m(3v)^2
k=1/2m(9v^2(
k=(m9v^2)/2
2k=m9v^2
2/9k=mv^2
...
?

answer: 9k
 
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You've actually found the answer within the first few steps.

As you've said, [tex]K = 1/2*mv^2[/tex]

And afterwards, [tex]K' = 1/2*m(-3v)^2[/tex]

so that [tex]K' = 9/2*mv^2[/tex]

What do you notice about K and K' when comparing them?

K' = 9K.
 
I'm not understanding how you've arrived to that last step...what happened to all the other variables?
 
genu said:
I'm not understanding how you've arrived to that last step...what happened to all the other variables?

You found that the final KE was 9 * (½mv²)

If you divide by the initial KE you get

Final KE = 9 * (Initial KE)

The suggestion was to encourage you to recognize the initial KE in the final KE expression.
 

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