In the figure shown, surface is smooth whereas, coefficient of friction between 10 kg and 5 kg block is μ = 1 . A force F = 15 t acts on 10 kg in horizontal direction. Find time (in seconds) by which

Question

In the figure shown, surface is smooth whereas, coefficient of friction between 10 kg and 5 kg block is μ = 1 . A force F = 15 t acts on 10 kg in horizontal direction. Find time (in seconds) by which work done by friction on 5 kg block is 10 joule.

TestHub · Accepted Answer

While blocks move together: a = 15 15 t ​ = t m/s 2 . Valid while friction on the 5 kg block ( 5 t N ) stays below μ N = 50 N, i.e. t ≤ 10 s. Only friction does work on the 5 kg block: v = 2 t 2 ​ . W = 2 1 ​ ⋅ 5 ⋅ ( t 2 /2 ) 2 = 10 , so t 4 = 16 , t = 2 s. Answer: 2.

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