Calculate the coefficint of kinetic friction between the slide and the child

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SUMMARY

The problem involves calculating the coefficient of kinetic friction between a child and a slide with a 28-degree incline. The child’s speed at the bottom is half of what it would be on a frictionless slide. The correct coefficient of kinetic friction is established as 0.4, while the user’s calculations yield a maximum of 0.53. Key equations include the normal force and the forces acting along the incline, specifically N = -mgcos(28) and mgsin(28) + μmgcos(28) = ma.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of trigonometric functions in physics
  • Familiarity with the concepts of friction and normal force
  • Ability to solve equations involving acceleration and forces
NEXT STEPS
  • Review the derivation of the equations for forces on an incline
  • Study the principles of kinetic friction and its calculation
  • Practice problems involving inclined planes and friction
  • Learn about the role of acceleration in motion on inclined surfaces
USEFUL FOR

Students in physics courses, particularly those studying mechanics, as well as educators looking for examples of friction calculations in real-world scenarios.

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Homework Statement


A child slides down a slide with a 28 degree incline, and at the bottom her speed is precisely half of what it would had been if the slide had been frictionless. Calculate the coefficint of kinetic friction between the slide and the child.


Homework Equations



N= -mgcos =0
Fy= mgsin =ma

N= -mgcos(28)
-Fy + f = ma

mgsin(28) + Mu mgcos(28) = ma


The Attempt at a Solution



I have no attempt all my answers seem to be coming out wrong the books answer is .4 but the closest i can get is .53. I found acceleration but that didnt help much. I honestly lost on this problem. If you can please help me Id appreciate if very much. Thank you
 
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Be careful with the signs of the forces. Which way does friction act? (You're on the right track.)
 

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