Question

Problem 3 A gate, in the shape of a quarter-cylinder with a radius of 2.7 m, is hinged at A and scaled at B, as shown in the figure. The gate is 8 m wide. The bottom of the gate is 5 m below the water surface. Assume the water temperature is 20°C (a) Determine the magnitude and direction of the resultant force on the gate. (b) If the gate is made of a material with a density of 6400 kg/m, determine the required horizontal force at B to keep the gate closed. A H R B 77 777 Problem 3

Answer 1

A H R 2.1m H=5 m FHFV Swrfoce we all know that prenune aut norme to thu all parses trough centre forces must pas clue o all presune Hence Net force through centre for Horizmtal force H-R = A B. F9h(Apjetel

A1 200 C [fo wnten] pune 8 = Projet eal A read = A 21-6 m n-(936-2) 3 915-2* 7 7 2 0 28.2 4 33 N for vertical force caincka an KR shadeal ugon R x H Area 7 - (7-1x (27) 2 Areao 62.19557 m° Shaded rein=7-774YAS) Vvaum 998.2 x 62.18557 x9.8| = 6096103815 N -

a) Fret FV Fret 2023.743)t Gog00 3015) (7720 98 334 0.1 216 N 0 tan 38.269 Faut 83.310 k N counten clockwiše from - ve x div echiom 38. 269 FHB 38.263 YR

maleirl G4O0 Volum quanler - yinder 1R (7a)2 2 5.801 1 2 Man cylinden (m) 6400x 45.80442 29 3148. 2937 Momen abcut A O (R) m YR Frui Ws 38.26 I 37 -) F. 293148.2937 X 9.81 x 1 98 3310.1216 Cos38.269 t 3×ス g9 25 9.203 N clos ed to Keep tn Hen ce, m hovi 3 dnt af force cu G 99 2.519 kN F.