Question

Un resort orizontal are constanta elastica k = 50 N/m si este fixat la un capat,ca in figura 2. Un corp de masa m = 250 g este lansat pe orizontala cu o viteza initiala v0 =5 m/s catre resortul nedeformat. Stiind ca frecarile sunt neglijabile ,iar acceleratia gravitationala se poate considera g = 10 N/Kg ,determinati deformarea maxima a resortului.​

Answer 1

$m=250 g=0,25 kg\\\Delta E_c=L\\L=L_G+L_N+L_F_{el}\\L_G=0\\L_N=0\\v=0\\L_{el}=-\frac{kx^2}{2}\\ \Delta E_c=E_c-E_c_o=\frac{mv^2}{2}-\frac{mv_o^2}{2}=-\frac{mv_o^2}{2} \\ \Delta E_c=L_{el}<=>-\frac{mv_o^2}{2} =-\frac{kx^2}{2}|(-2)<=>mv_o^2=kx^2=>x=\sqrt{\frac{mv_o^2}{k} }=\sqrt{\frac{0,25*5^2}{50} }=\sqrt{\frac{6,25}{50} }=\sqrt{0,125}=0,35 m\\x=0,35 m$