What is the acceleration of the block and trolley system shown in a Fig.(a), 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 m s^(-2)` ). Neglect the mass of the string.

Explanation

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