What is the acceleration of the blockandtrolley 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.

What is the acceleration of the blockandtrolley system shown in a Fig.

1.	What is the acceleration of the blockandtrolley 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.
Answer» <html><body><p></p>Solution :As the string is <a href="https://interviewquestions.tuteehub.com/tag/inextensible-2736845" style="font-weight:bold;" target="_blank" title="Click to know more about INEXTENSIBLE">INEXTENSIBLE</a> and the pully is smooth, the <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> kg block and the 20 kg trolley both have same magnitude of acceleration.Applying second law to motion of the block (Fig. (b))<br/> `30 - T = 3a` <br/> Apply the second law to motion of the trolley (Fig. (c)),<br/>`T - f_k = 20a` <br/>`f_k = mu_k N`<br/> ` mu_k = 0.04` <br/>`N = 20 xx 10` <br/> = <a href="https://interviewquestions.tuteehub.com/tag/200n-290170" style="font-weight:bold;" target="_blank" title="Click to know more about 200N">200N</a> <br/> Thus the equation for the motion of the trolley is<br/> `T - 0.04 xx 200 = 20 a " or" T - 8 = 20a ` <br/> These <a href="https://interviewquestions.tuteehub.com/tag/equations-452536" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATIONS">EQUATIONS</a> give a ` = 22/23 ms^(-2) = 0.96 ms^(-2)`and T = 27.1 N</body></html>