Answer to Question #202696 in Mechanical Engineering for Lihle

Question

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.

Answer 1

m = 180kg

W = 180kg × 9.8m/s² = 1764N

Horizontal Force required = $1764\cos60° =882\ N$

Vertical Force required = $1764 \sin60° = 1528\ N$

$F_x \cos45° = 882\ N\\ F_x = 1247\ N$

$F_y \sin 45° =1528$

$F_y =2 161$

F = $\sqrt{1247² + 2161²}$ = 2495 N