Question

o bila cade de la inaltimea h=1m pe un resort , comprimarea maxima a acestuia fiind x=1 cm .cat va fi conclinarea maxima a resortului,daca bila va cadea de la inaltimea h=2m

Answer 1

[tex]Se~da:\\ \\ h_{1}=1m\\ \\ x_{1}=1cm=0,01m\\ \\ h_{2}=2m\\ \\ x_{2}=?m\\ \\ \\ Formule:\\ \\ 1)E_{p_{1}}=E_{pel_{1}}\\ \\ m\times g \times h_1=\frac {k\times x_{1}^2}2\\ \\ m=\frac{k\times x_1^2}{2\times g \times h_1}\\ \\ \\[/tex]


[tex]2)E_{p_2}=E_{pel_2}\\ \\ m\times g \times h_2=\frac{k\times x_2^2}2\\ \\ \frac{k\times x_1^2}{2\times g \times h_1}\times g \times h_2=\frac{k\times x_2^2}2\\ \\ \frac{x_1^2\times h_2}{h_1}=x_2^2\\ \\ x_2=\sqrt\frac{x_1^2\times h_2}{h_1}\\ \\ x_2=x_1\times\sqrt\frac{h_2}{h_1}\\ \\ \\ Calcule:\\ \\ x_2=0,1\times\sqrt\frac{2}{1}\approx 0,142m[/tex]