Masses M1,M2 and M3 are connected by string of negligible mass which pass over massless and frictionless pulley P1 and P2 as shown in the figure. The masses move such that the portion of the inclined plane and the portion of the string between P1 and P2 is parallel to the incline plane and the portion of the sting between P2 and M3 is horizontal. The masses M2 and M3 are 4.0kg each and the coefficient of kinetic friction between the masses and the surface is 0.25. The inclined plane makes an angle of 37o with the horizontal. If the mass M1 moves downward with a uniform velocity find the (a) mass of M1 (b) tension in the horizontal portion of the string. (9=9.8m/s2 and sin37o≈3/5)
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Solution
Let T1 be the tension in the string connecting m1 and m2 and T2 be the tension in the string connecting m2 and m3. Form the figure. M1g=T1 T2=μm3g=(0.5)4g Or, T2=g=9.8N Also T1=T2+(0.25)×4gcos37o+4gsin37o =g(1+45+4×35) T1=215g Or, M1g=215g ∴M1=215=4.2kg