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Category: Mechanics

Question-203794

Question Number 203794 by mr W last updated on 28/Jan/24 Commented by mr W last updated on 28/Jan/24 $${a}\:{triangual}\:{uniform}\:{thin}\:{rod}\:{frame}\: \\ $$$${with}\:{side}\:{lengthes}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:{and}\:{mass}\: \\ $$$$\boldsymbol{{M}}\:{is}\:{suspended}\:{through}\:{three}\:{thin} \\ $$$${strings}\:{with}\:{lengthes}\:\boldsymbol{{p}},\:\boldsymbol{{q}},\:\boldsymbol{{r}}\:{at}\:{its}…

Question-202816

Question Number 202816 by ajfour last updated on 03/Jan/24 Commented by ajfour last updated on 03/Jan/24 $${With}\:{what}\:{constant}\:{force}\:{should} \\ $$$${trolley}\:{be}\:{pushed}\:{towards}\:{left}\:{such} \\ $$$${that}\:{inclination}\:{of}\:{plank}\:{dont}\:{change} \\ $$$${and}\:{system}\:{moves}\:{at}\:{uniform}\:{speed}? \\ $$…

Question-200428

Question Number 200428 by Spillover last updated on 18/Nov/23 Answered by ajfour last updated on 18/Nov/23 $${F}={mg}−\frac{{kv}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\frac{{vdv}}{{dx}}={g}−\frac{{kv}^{\mathrm{2}} }{\mathrm{2}{m}}=−\frac{{k}}{\mathrm{2}{m}}\left({v}^{\mathrm{2}} −\frac{\mathrm{2}{mg}}{{k}}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:{v}}…

Question-200137

Question Number 200137 by ajfour last updated on 14/Nov/23 Commented by ajfour last updated on 14/Nov/23 $${Find}\:{range}\:{of}\:{M}\:\left({x}\:{coordinate}\:{of}\right. \\ $$$$\left.{point}\:{where}\:{it}\:{hits}\:{x}\:{axis}\right),\:{if}\:\mathrm{2}{M}\:{is} \\ $$$${dropped}\:{from}\:{height}\:{h}\:{and}\:{hits} \\ $$$${left}\:{gear}\:{elastically}. \\ $$…

Calculate-the-first-order-energy-correction-for-the-one-dimentional-non-degenerate-an-harmonic-oscillator-whose-harmiltonian-id-written-as-H-h-2-2m-d-2-dx-2-1-2-kx-2-1-5-x-3-1-

Question Number 199705 by jlewis last updated on 11/Nov/23 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{one}\:\mathrm{dimentional}\:\mathrm{non}-\mathrm{degenerate} \\ $$$$\mathrm{an}\:\mathrm{harmonic}\:\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian} \\ $$$$\mathrm{id}\:\mathrm{written}\:\mathrm{as}; \\ $$$$\hat {\mathrm{H}}=−\frac{\mathrm{h}^{\mathrm{2}} }{\mathrm{2}{m}}\:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }\:+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{kx}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{5}}\Upsilon\mathrm{x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{\mathrm{12}}\beta\mathrm{x}^{\mathrm{4}} \\…