Consider an object on an incline where friction is present. The angle between the incline and the horizontal is θ and the coefficient of kinetic friction is μk.a.)  Find an algebraic expression for the acceleration of this object. Treat down the incline as the positive direction.b.) Calculate the acceleration, in meters per second squared, of this object if θ = 31° and μk = 0.34. Treat down the incline as the positive direction.

Question
Asked Oct 13, 2019

Consider an object on an incline where friction is present. The angle between the incline and the horizontal is θ and the coefficient of kinetic friction is μk.

a.)  Find an algebraic expression for the acceleration of this object. Treat down the incline as the positive direction.

b.) Calculate the acceleration, in meters per second squared, of this object if θ = 31° and μk = 0.34. Treat down the incline as the positive direction.

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Expert Answer

Step 1

Given,

Angle between incline and horizontal = 0
Coefficient of kinetic friction-u
0 31°
4=0.34
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Angle between incline and horizontal = 0 Coefficient of kinetic friction-u 0 31° 4=0.34

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Step 2

Free Body Diagram of such system having motion toward incline as positive has been represented below,

Friction
Force
ma
,mgsine
mgros
mg
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Friction Force ma ,mgsine mgros mg

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Step 3

Part (a):

By using Newton&rs...

Friction Force,F = uN
N mg cose
mg sin 0-mg cos0 = ma
a gsin 0- ug cos
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Friction Force,F = uN N mg cose mg sin 0-mg cos0 = ma a gsin 0- ug cos

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