Two packing crates of masses 10.0 kg and 5.00 kg are connected by alight string

Question

Two packing crates of masses 10.0 kg and 5.00 kg are connected by alight string that passes over a frictionless pulley as in FigureP4.20. The 5.00 kg crate lies on a smooth incline of angle40.0 degrees. Find the acceleration of the 5.00 kg crate.
a) Find the tension in the rope.

Explanation / Answer

From fig we can write      For m1 = 5 kg crate :        T - m1gsin =m1a   ......1 For m2 = 10kg crate        m2g - T =m2a       ==> T = m2(g -a)......2 From 1 and 2 we get          m2(g-a)- m1gsin = m1a ==> ( m2g - m1gsin ) /(m1+m2) = a ==> a = (10*9.8 - 5*9.8*sin40) / (15)            = 4.43 m/s2 Tension in the rope         T = 10 (9.8 - 4.43) =53.66 N

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