What is the acceleration of the block and trolley system show in the Fig. if the corfficient 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 .

Explanation

As the string in inextensible , and the pully is smooth , the 3 kg block and the 20 kg trolley both have same magnitude of acceleration .Applying second of law to motion of the block (Fig . (b) .
` 30 - T = 3a `
Applying the second law of the trolley (Fig (c ))
`T- f_(k) = 20 a `
Now , `f_(k) = mu_(k) N , `
Here `mu_(k) = 0.04`
`N = 20 xx 10 = 200 N `
Thus the equation for the motion of the trolley is
`T - 0.04 xx 200 = 20 a or T - 8 = 20 a `
These equations give a ` = 22/23 ms^(-2) = 0.96 m `
`s^(-2) and T = 27.1 N `