Work-energy theorem , not sure what I am doing wrong.

AI Thread Summary
The discussion centers on applying the work-energy theorem to calculate the length of a rough patch on an ice rink that slows a skater from 6.0 m/s to 42% of that speed. The user initially attempts to calculate the length using a formula but arrives at an incorrect answer, questioning whether the result should be negative. Another participant clarifies that the change in kinetic energy should be calculated using the correct percentage, emphasizing that it should be 0.58 of the initial velocity rather than 0.42. The equation presented highlights the relationship between work done by friction and the change in kinetic energy. The conversation underscores the importance of accurately applying the work-energy theorem in physics problems.
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On an essentially frictionless, horizontal ice rink, a skater moving at 6.0 m/s encounters a rough patch that reduces her speed by 42 \% due to a friction force that is 20 \% of her weight.

Use the work-energy theorem to find the length of this rough patch.

i do: [.42 * (.5) * (6)^2]/ [.2 * 9.8]=3.85
but i get the wrong answer can anyone help, does the answer need to be negative, what am i doing wrong.
 
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What does the work-energy theorem state?

What is the change of the KE if the speed is reduced to 42% of the original 6 m/s ?

ehild
 
K_2-K_1 where k=1/2*m*v^2, thank you, it would be .58v not .42, in the equation
-.2gs = (1/2)mvf^2 - (1/2)mvi^2 where the m cancel
 
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