What is the acceleration of the block and trolley system shown in if the coefficient of kinetic friction between the trolley and the surface is 0 .04 ? What is the tension in the string ? Take `g = 10 ms^(-2)` Neglect the mass of the string
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Explanation

As the string is inextensible and the pulley is smooth the 3 kg block and the 20 kg trolley , both have same magnitude of motion to free body Applying Newton ' s second law of motion to free body diagram of W = 20 kg
` T - f_(k) = 20 a `
Now , ` f_(k) = mu_(k) R = mu_(k) mg = 0. 04 xx 20 xx 10 `
` = 8 N `
` :. T - 8 = 20 a `
Again applying Newton ' s second law of motion to free body diagram of W = 3 kg we get
` 30 - T = 3 a `
Adding (ii) and (iii) , we get
` 22 = 23 a `
`a = (22)/(23) = 0.96 ms^(-2)`
From (ii) , `T = 20 a + 8`
` T = 20 xx 0.96 + 8 = 19 .2 + 8 = 27 . 2 N`
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