Two rough planes, A and B, inclined at 30 degrees and 60 degrees to the horizont

Question

Two rough planes, A and B, inclined at 30 degrees and 60 degrees to the horizontal, respectively, and at the same vertical height, are placed back to back. A pulley of mass 1 kg and radius 10 cm is fixed to the top of the system. A string is passed over the pulley and attached to two masses, Ma=2 kg and Mb= 6 kg. The coefficient of kinetic friction between the masses and the planes is 0.2.

When released from rest, what is the acceleration of the system?

What is the tension in the string on side A?

What is the tension in the string on side B?

Explanation / Answer

ma=2kg

mb=6kg

u(coefficient of friction)=0.2

acceleration =(mbgsintheta2-magsintheta1+ug(macos30-mbsin60))/((mp/2)+mb-ma)

here theta1=30

theta2=60

mp=1kg

substituting the values we get

a=8.586m/s2

t1=(tension in string A)=mAa+mAgsin30+umAgcos30=30.4N

t2(tension in stringB)=mbg-umbgcos60-mbgsin60=6.47N

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