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Consider Example 6.8 taking the coefficient of friction, u, to be 0.5 and calculate the maximum compression of the spring.

Answer» <html><body><p></p>Solution :In presence of friction, both the spring force and the frictional force act so as to oppose the compression of the spring as shown in Fig. 6.9. <br/> We invoke the work-energy theorem, rather than the conservation of mechanical energy. <br/> The change in kinetic energy is <br/> `triangleK= K_(f)-K_(t)= 0-(1)/(2)mv^(2)`<br/> The work done by the net force is <br/> `W= -(1)/(2)kx_(m)^(2)- mu mg x_(m)` <br/> Equatting we have <br/> `(1)/(2)mv^(2)= (1)/(2)k x_(m)^(2)+ mu mg x_(m)` <br/> Now `mu mg= 0.5xx10^(3)xx10= 5xx 10^(3)N` (<a href="https://interviewquestions.tuteehub.com/tag/taking-1238585" style="font-weight:bold;" target="_blank" title="Click to know more about TAKING">TAKING</a> `g= 10.0 ms^(-2)`). After rearranging the above equation we obtain the following quadratic equation in the unknown `x_(m)`. <br/> `kx_(m)^(2)+ 2 mu mg x_(m)- mv^(2)= O` <br/> `x_(m)=(-mu mg+[mu^(2)m^(2)g^(2)+mkv^(2)]^(1/2))/(k)` <br/> where we take the <a href="https://interviewquestions.tuteehub.com/tag/positive-1159908" style="font-weight:bold;" target="_blank" title="Click to know more about POSITIVE">POSITIVE</a> square root since `x_(m)` is positive. <a href="https://interviewquestions.tuteehub.com/tag/putting-2963476" style="font-weight:bold;" target="_blank" title="Click to know more about PUTTING">PUTTING</a> in numerical values we obtain `x_(m)= 1.35m` <br/> which, as expected, is less than the result in Example 6.8. <br/> If the <a href="https://interviewquestions.tuteehub.com/tag/two-714195" style="font-weight:bold;" target="_blank" title="Click to know more about TWO">TWO</a> forces on the body consist of a conservative force `F_(c )` and a non-conservative force `F_(nc)`, the conservation of mechanical energy formula will have to be modified. By the WE theorem <br/> `(F_(c )+F_(nc)) trianglex= triangleK` <br/> But `F_(c ) triangle x= -triangle V` <br/> Hence, `triangle(K+V)= F_(nc) triangle x` <br/> `triangle E= F_(nc) trianglex` <br/> where E is the total mechanical energy. Over the path this <a href="https://interviewquestions.tuteehub.com/tag/assumes-886174" style="font-weight:bold;" target="_blank" title="Click to know more about ASSUMES">ASSUMES</a> the form <br/> `E_(f)-E_(t)= W_(nc)` <br/> where `W_(nc)` is the total work done by the non-conservative forces over the path. Note that unlike the conservative force, `W_(nc)` depends on the particular path i to f. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_TAM_PHY_XI_P1_C06_SLV_013_S01.png" width="80%"/></body></html>


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