Calculating Percentage Change in Kinetic Energy with Increased Speed

  • Thread starter Thread starter dimens
  • Start date Start date
  • Tags Tags
    Calculus Change
Click For Summary

Homework Help Overview

The discussion revolves around calculating the percentage change in kinetic energy when the speed of a body is increased by 2%. The kinetic energy is defined by the equation K = 1/2mv², and participants are exploring how this change in speed affects kinetic energy.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to use derivatives to approximate the change in kinetic energy based on the change in speed. Questions arise regarding the derivation of variables and the interpretation of the percentage change.

Discussion Status

Some participants are restating previous contributions and seeking clarification on the variables involved. There is a suggestion that the necessary information is already available, and the focus should shift to algebraic manipulation. Multiple interpretations of the problem are being explored, but no consensus has been reached.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a specific emphasis on understanding the relationship between speed and kinetic energy without deriving a final answer.

dimens
Messages
43
Reaction score
0

Homework Statement


The kinetic energy K of a body of mass m is moving with speed v is given by..

K = 1/2mv^2

If a body's speed is increased by 2%, what is the approximate percentage change in it's kinetic energy...


The Attempt at a Solution



Δy ≈ f'(x) Δx

... f'(K) = mv Δx

mv* 2?

?

Don't know how to find the other values. Lol
 
Physics news on Phys.org
Hi dimens. Let's write the equation: E= ½mv²

and we are asked to consider the case where (∆v)/v = 0.02

You have determined dE/dv = m⋅v

and we will approximate the actual ∆E/∆v by using dE/dv.

So far I have just restated what you provided. Can you complete this now?

Solution:
We use the equation: ∆E/∆v = ... http://smilearchive.com/s/cwm/3dlil/idea.gif
 
sorry i don't really get where you get the other variables from? E/0.02?
 
dimens said:
sorry i don't really get where you get the other variables from? E/0.02?
I just preferred E for K.E. because I thought E sounded more like an energy symbol! :smile:

As for where did I get that 0.02 from? I got it here:
If a body's speed is increased by 2%

:wink:
 
but the answer is 4% i don't know where to get the other variables from :s
 
We don't need to get any more variables, we have all that is needed. The hard work has already been done. :smile: All that remains is some algebraic manipulation. So go back to my first post, follow through the steps as I've written them, and see whether you can complete the equation where I've indicated.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
810
  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 8 ·
Replies
8
Views
1K