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In the Fig 7.89 shown , m_(2) = 2.5 kg, h = 1.5 m , the system is released fromrest at t = 0 and the mass m_(2) strikes ground at t = 0.82s . The system is placed in its initial position and a 1.2 kgmass is placed on top of the block of mass m_(1) . Released from rest , the mass m_(2) now strikes the ground 1.3 s later .Determine the mass m_(1)and the coefficient of kinetic friction between m_(1) and the shelf .

Answer» <html><body><p><br/></p>Solution :Initial acceleration of system when `1.<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>` kg mass is not placedover `m_(1)` kg block <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/GRB_AM_PHY_C07_E01_010_S01.png" width="80%"/> <br/> `a_(0) = sqrt((2h)/(t^(2))) =sqrt((2 xx 1.5)/(0.82 xx 0.82))` <br/>As , `"" m_(2) <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> - T = m_(2)a_(0) ""…… (i) ` <br/> `T - mu m_(1) g = m_(1) a_(0) "" ...... (ii)` <br/> Adding Eqns. (i) and (ii) <br/> `g (m_(2) - mum_(1)) = a_(0) (m_(1) + m_(2)) "" ..... (iii)` <br/> Now when `1.2` kg mass is placed , then <br/> `a= sqrt((2h)/(t'^(2))) = sqrt((2 xx 1.5)/(1.3xx 1.3))` <br/> as `m_(2)g - T = m_(2)a "" ...... (iv)` <br/> `T - mu(m_(1) + 1.2)g = a [m_(2) + m_(1) + 1.2] "".....(<a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>)` <br/> Adding Eqns. (iv) and (v) <br/>`m_(2)g - mu_(g) (m_(1) + 1.2) = a[m_(2) + m_(1) + 1.2] "" .... (vi)` <br/> <a href="https://interviewquestions.tuteehub.com/tag/solving-1217196" style="font-weight:bold;" target="_blank" title="Click to know more about SOLVING">SOLVING</a> Eqns. (iii) and (vi) , <br/> we get <a href="https://interviewquestions.tuteehub.com/tag/values-25920" style="font-weight:bold;" target="_blank" title="Click to know more about VALUES">VALUES</a> of `mu` and`m_(1)`.</body></html>


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