What is the maximum acceleration a runner can achieve with 90% friction?

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SUMMARY

The maximum acceleration a runner can achieve when the friction between her shoes and the pavement is 90% of her weight is 8.82 m/s². This conclusion is derived from applying Newton's Second Law, where the net force is calculated as 90% of the runner's weight, leading to the acceleration formula a = Fnet/m. The discussion emphasizes the importance of correctly interpreting the relationship between force, mass, and acceleration in physics problems.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Basic knowledge of friction and its role in motion
  • Familiarity with acceleration and its units (m/s²)
  • Concept of weight as a force (weight = mass × gravity)
NEXT STEPS
  • Study the implications of friction coefficients in motion analysis
  • Explore advanced applications of Newton's Laws in real-world scenarios
  • Learn about the effects of mass on acceleration in different contexts
  • Investigate the relationship between force, mass, and acceleration in circular motion
USEFUL FOR

Students transitioning into physics, particularly those interested in mechanics, as well as educators looking for clear examples of applying Newton's Laws in practical situations.

Kaleb
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Hey all, I am new to Physics. Recently changed majors from technical writing to physics for the amount of interest I have in the subject. I have been doing ok but I missed a couple of questions on my last homework and I feel that I should have had somebody check my general solved statements after I finished to make sure that I was correct. Anyways, enough about me!

Homework Statement


What is the greatest acceleration a runner can muster if the friction between her shoes and the pavement is 90% of her weight?

Homework Equations


F = ma
.9%*9.8 m/s

http://img183.imageshack.us/img183/8439/accelerationrn5.png

The Attempt at a Solution


I figure since the force is her body moving at a constant velocity that the greatest acceleration she could reach would be 8.82 m/s. I also tried to make this using Newtons Second Law of a = Fnet/m but what would the net force be equal to? 90%? Any and all help is appreciated, but please post in user friendly terms as I am not that familiar with heavy physics terms yet as I have seen in some other topics(but not all).
 
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I'm not sure how your paper was graded, but maybe you got it wrong because of a little confusion in units and terminology?

Kaleb said:
I figure since the force is her body moving at a constant velocity that the greatest acceleration she could reach would be 8.82 m/s. I also tried to make this using Newtons Second Law of a = Fnet/m but what would the net force be equal to? 90%?

The force of her movement is her body's mass moving at a constant acceleration, not velocity. Also the greatest acceleration would be 8.82 m/s^2. I can't see a mistake otherwise.
 
Thanks Sarujin, your help is appreciated as well as the corrections to my terms. I see why I go it wrong now.
 

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