Answer to Question #202696 in Mechanical Engineering for Lihle

Question #202696

A 1 m^3 opening in a water reservoir is sealed with a plate having sides of 1 m. The plate hinges around its topside, which is 4m vertically below the surface. The plate is at an angle of 60 degrees to the surface. The plate is opened with a chain, which is attached to the centre of the bottom side and at an angle of 45 degrees to the plate. The plate has a mass of 180 kg. Calculate the force required in the chain to open the plate.

Expert's answer

m = 180kg

W = 180kg × 9.8m/s² = 1764N

Horizontal Force required = " 1764\\cos60\u00b0 =882\\ N"

Vertical Force required = "1764 \\sin60\u00b0 = 1528\\ N"

"F_x \\cos45\u00b0 = 882\\ N\\\\\nF_x = 1247\\ N"

"F_y \\sin 45\u00b0 =1528"

"F_y =2 161"

F = "\\sqrt{1247\u00b2 + 2161\u00b2}" = 2495 N

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