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Determine a formula for the acceleration of the system in terms of mA, mB, θ, and g. Ignore the mass of the cord and pulley. Express your answer in terms of the variables mA, mB, θ, and g.

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opudodennis

Answer:

[tex]a=\frac{mBg-mAgSin\theta}{mA+mB}[/tex]

Explanation:

Given two mass on an incline code [tex]mA[/tex] and [tex]mB[/tex] and an angle of inclination [tex]\theta[/tex]. [tex]g[/tex]. Assume that [tex]mA[/tex] is the weight being pulled up and [tex]mB[/tex] the hanging weight.

-The equations of motion from Newton's Second Law are:

[tex]mBg-T=mBa[/tex] where a is the acceleration.

#Substituting for [tex]T[/tex] (tension) gives:

[tex]mBg-mAsin\theta-mAa=mBa[/tex]

#and solving for [tex]a:[/tex]

[tex]a=\frac{mBg-mAgSin\theta}{mA+mB}[/tex] which is the system's acceleration.

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