Question $1.(20$ marks$)$

A $3$ m wide rectangular gate of negligible weight is hinged at the bottom of the gate, and held against a frictionless stop at the waterline as shown in the figure below. The gate makes an angle of $\backslash (60^\{\backslash$circ$\}\backslash )$ with respect to a horizontal axis passing through the hinge at the bottom of the gate, and is held in position by a $70$ kN cylindrical block with a diameter of $1$ m $,$ that is connected to the gate by a cable passing over a frictionless pulley. If the bottom of the cylindrical block is $2$ m above the bottom of the channel, determine by calculation of all the forces involved whether the gate will open or remain closed. Assume water at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).($ANSWER: Force acting on gate due to the stop is $2\mathrm{.}92$ kN$,$ acting towards the gate so the gate will not open.$)$