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A-wedge-has-two-equally-rough-faces-each-inclined-at-30-to-the-horizontal-Masses-of-5kg-and-2kg-one-on-each-face-are-connected-by-a-light-string-passing-over-a-smooth-pulley-at-the-top-of-the-wedge-




Question Number 22893 by NECx last updated on 23/Oct/17
A wedge has two equally rough  faces each inclined at 30° to the  horizontal.Masses of 5kg and 2kg  ,one on each face,are connected  by a light string passing over a  smooth pulley at the top of the  wedge.The coefficient of friction   μ, between each masses and the  surface of the wedge is 0.2.Find  the acceleration of the masses  when they are released.
$${A}\:{wedge}\:{has}\:{two}\:{equally}\:{rough} \\ $$$${faces}\:{each}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the} \\ $$$${horizontal}.{Masses}\:{of}\:\mathrm{5}{kg}\:{and}\:\mathrm{2}{kg} \\ $$$$,{one}\:{on}\:{each}\:{face},{are}\:{connected} \\ $$$${by}\:{a}\:{light}\:{string}\:{passing}\:{over}\:{a} \\ $$$${smooth}\:{pulley}\:{at}\:{the}\:{top}\:{of}\:{the} \\ $$$${wedge}.{The}\:{coefficient}\:{of}\:{friction}\: \\ $$$$\mu,\:{between}\:{each}\:{masses}\:{and}\:{the} \\ $$$${surface}\:{of}\:{the}\:{wedge}\:{is}\:\mathrm{0}.\mathrm{2}.{Find} \\ $$$${the}\:{acceleration}\:{of}\:{the}\:{masses} \\ $$$${when}\:{they}\:{are}\:{released}. \\ $$
Answered by ajfour last updated on 23/Oct/17
a=(((M−m)gsin 30°−μgcos 30°(M+m))/(M+m))  =((15−7(√3))/7) m/s^2   ⇒ a≈(2.143−1.732)m/s^2            ≈0.4 m/s^2
$${a}=\frac{\left({M}−{m}\right){g}\mathrm{sin}\:\mathrm{30}°−\mu{g}\mathrm{cos}\:\mathrm{30}°\left({M}+{m}\right)}{{M}+{m}} \\ $$$$=\frac{\mathrm{15}−\mathrm{7}\sqrt{\mathrm{3}}}{\mathrm{7}}\:{m}/{s}^{\mathrm{2}} \\ $$$$\Rightarrow\:\boldsymbol{{a}}\approx\left(\mathrm{2}.\mathrm{143}−\mathrm{1}.\mathrm{732}\right){m}/{s}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\approx\mathrm{0}.\mathrm{4}\:{m}/{s}^{\mathrm{2}} \: \\ $$
Commented by NECx last updated on 23/Oct/17
thankz sir..... please can it be  explained with a diagram.I′ll  appreciate that.Thanks in advance.
$${thankz}\:{sir}…..\:{please}\:{can}\:{it}\:{be} \\ $$$${explained}\:{with}\:{a}\:{diagram}.{I}'{ll} \\ $$$${appreciate}\:{that}.\boldsymbol{{T}}{hanks}\:{in}\:{advance}. \\ $$
Commented by NECx last updated on 23/Oct/17
thanks sir
$${thanks}\:{sir} \\ $$
Commented by ajfour last updated on 23/Oct/17

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