Momo with mass m is sliding down an inclined plane that makes an angle Φ relative to the horizontal. The coefficient of kinetic friction between Momo and the inclined plane is μk. Obtain an expression for Momo's acceleration along the incline.

Principles of Physics: A Calculus-Based Text
5th Edition
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Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter5: More Applications Of Newton’s Laws
Section: Chapter Questions
Problem 64P: If a single constant force acts on an object that moves on a straight line, the objects velocity is...
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Momo with mass m is sliding down an inclined plane that makes an angle Φ relative to the horizontal. The coefficient of kinetic friction between Momo and the inclined plane is μk. Obtain an expression for Momo's acceleration along the incline.

Assign a rotated Cartesian plane so that the acceleration is along the positive x-axis and the normal force is along the positive y-axis.

The component of the weight parallel to Momo's acceleration is wx = mg ______ Φ

The magnitude of the frictional force is f = μk ______

The normal force on Momo is n = mg______Φ

With these expressions and applying Newton's second law, we arrive at an expression for Momo's acceleration:

a = ____ ( ____  - μk _____)

 

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