# Category: Mechanics

## 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-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}} \\…