Mam kilka zadań z fizyki do rozwiązania 4,5,6,7,8,9,10

[latex]Zad 4.\ n=120\ t=0,5min=30s\ r=6m\\ a)T=?\\ T=frac{t}{n}=frac{30}{120}=0,25s\\ b)f=?\\ f=frac{n}{t}=frac{120}{30}=4Hz\\ c)omega=?\\ omega=2pi f=2*3,14*4=25,12 s^{-1}[/latex] [latex]d)v=?\\ v=omega r=25,12*6=150,72frac{m}{s}[/latex] [latex]Zad 5.\ 1)\ m=4000g=4kg\ r=60cm=0,6m\ f=20Hz\\ v=omega r=2pi fr\\ Ek=frac{mv^2}{2}=frac{m(2pi fr)^2}{2}\\ Ek=frac{4*(2*3,14*20*0,6)^2}{2}\\ Ek=2*75,36^2\\ Ek=2*5679,13\\ Ek=11358,26J[/latex] [latex]2)\ m=1t\ v=5frac{km}{h}=1,39frac{m}{s}\ r=200m\\ F=frac{mv^2}{r}=frac{1000*1,39^2}{200}=5*1,9321=9,6605N[/latex] [latex]Zad 6.\ m=2kg\ r=0,5m\ F=80N\\ F=momega^2rRightarrow omega=sqrt{frac{F}{mr}}\\ omega=sqrt{frac{80}{2*0,5}}\\ omega=sqrt{80}\\ omega=8,45 s^{-1}[/latex] [latex]Zad 7.\ F_1=600mN\ a)\ F_1=frac{m_1m_2}{r^2}\\ F_2=frac{4m_1frac{m_2}{2}}{r^2}\\ F_2=frac{4}{2}frac{m_1m_2}{r^2}\\ F_2=2frac{m_1m_2}{r^2}=2F_1=2*600=1200mN=1,2N[/latex] [latex]b)\ F_2=frac{m_1m_2}{(frac{r}{5})^2}\\ F_2=frac{m_1m_2}{frac{r^2}{5^2}}\\ F_2=frac{m_1m_2}{frac{r^2}{25}}\\ F_2=frac{frac{m_1m_2}{r^2}}{25}=frac{F_1}{25}=frac{600}{25}=24mN[/latex] [latex]Zad 8.\ d=500kmRightarrow r=250km=2,5*10^5m\ g=1frac{m}{s^2}\ \\ g=Gfrac{m}{r^2}Rightarrow m=frac{gr^2}{G}\\ V_I=sqrt{frac{Gm}{r}}\\ V_I=sqrt{frac{Gfrac{gr^2}{G}}{r}}\\ V_I=sqrt{frac{gr^2}{r}}\\ V_I=sqrt{gr}\\ V_I=sqrt{1*2,5*10^{5}}\\ V_I=5*10^2=500frac{m}{s}[/latex] [latex]Zad 9.\ M=0,33*10^{24}kg\ D=4879kmRightarrow R=2439,5km=24,395*10^5m\ G=6,67*10^{-11}frac{m^3}{kg*s^2}\\ g=frac{GM}{R^2}\\ g=frac{6,67*10^{-11}*0,33*10^{24}}{(24,395*10^5)^2}\\ g=frac{2,2*10^{13}}{595,12*10^{10}}\\ g=0,0037*10^3\\ g=3,7frac{m}{s^2}[/latex] [latex]Zad 10.\ M_W=0,8M_Z\ R_W=0,95R_Z\ V_{I_Z}=7,91frac{km}{s}\\ V_{I_Z}=sqrt{frac{GM_Z}{R_Z}}\\ V_{I_W}=sqrt{frac{G*0,8M_Z}{0,95R_Z}}\\ V_{I_W}=sqrt{frac{0,8*GM_Z}{0,95R_Z}}\\ V_{I_W}=sqrt{0,85frac{GM_Z}{R_Z}}\\ V_{I_W}=sqrt{0,85}sqrt{frac{GM_Z}{R_Z}}\\ V_{I_W}=0,92*V_{I_Z}=0,92*7,91=7,28frac{km}{s}[/latex] Pozdrawiam, Adam