SORU $17$ A smooth $0\mathrm{.}10-$m$-$diameter cork ball $($ SG$=0\mathrm{.}21)$ is tied to an object on the bottom of a river as is shown in Figure $2.$ The flow speed U is $1\mathrm{.}12($m$)/($s$).$ Neglect the string drag. Deter$-$ mine $($a$)$ buoyancy force B $,($b$)$ weight W $,$ and $($c$)$ drag force on cork ball D$\_($f$)($Hint: D$\_($f$)=(1)/(2)\backslash$rho U$^(2)$AC$\_($D$)).($d$)$ Calculate angle $\backslash$theta $($Hint: Use $\backslash$Sigma F$\_($x$)=0$ and $\backslash$Sigma F$\_($y$)=0).(\backslash$rho $\_($water $)=998($kg$)/($m$^(3)),$v$\_($water $)=1\mathrm{.}12\backslash$times $10^(-6)($m$^(2))/($s$),$v$\_($sphere $)=(4)/(3)\backslash$pi R$^(3))$ Figure $2-($a$)$ Schematic and $($b$)$ free body diagram for crock ballSORU $17$

A smooth $0\mathrm{.}10-$m$-$diameter cork ball $(SG=0\mathrm{.}21)$ is tied

to an object on the bottom of a river as is shown in Figure $2.$

The flow speed $U$ is $1\mathrm{.}12\frac{m}{s}.$ Neglect the string drag. Deter$-$

mine $($a$)$ buoyancy force $B,($b$)$ weight $W,$ and $($c$)$ drag force on

cork ball $D_f($Hint: $D_f=\frac{1}{2}{U}^{2}A{C}_D).($d$)$ Calculate angle $($Hint:

Use $F_x=0$ and $F_y=0).$

$({}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=998\frac{kg}{m^3},v_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1\mathrm{.}12{10}^{-6}\frac{m^2}{s},{}_{\text{s}\text{p}\text{h}\text{e}\text{r}\text{e}}=\frac{4}{3}{R}^3)$