4. The end of a semi-circular water trough is closed by a massless rectangular gate, shown below. If the water level gets too high, the gate can rotate about a frictionless hinge and let some water out of the trough. When the water in the trough is 3-ft deep, as shown in the figure, the gate is just held shut by the spherical counterweight attached to the gate. If the distance between the hinge and the counterweight is l = 3.5 ft, determine a) The mass (m) of the counterweight, in slugs. b) The horizontal and vertical reaction forces, R., and Ry, respectively, at the hinge when the gate is just about to open. m | l- Hinge V 1 ft Water Gate X/1² Hinge 3 ft radius 6 ft- 4 ft

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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4. The end of a semi-circular water trough is closed by a massless rectangular gate, shown below. If the water level
gets too high, the gate can rotate about a frictionless hinge and let some water out of the trough. When the water
in the trough is 3-ft deep, as shown in the figure, the gate is just held shut by the spherical counterweight attached
to the gate. If the distance between the hinge and the counterweight is l = 3.5 ft, determine
a) The mass (m) of the counterweight, in slugs.
b) The horizontal and vertical reaction forces, R., and Ry, respectively, at the hinge when the gate is just about
to open.
m
| l-
Hinge
V
1 ft
Water
Gate
Hinge
3 ft
radius
-6 ft-
4 ft
Transcribed Image Text:4. The end of a semi-circular water trough is closed by a massless rectangular gate, shown below. If the water level gets too high, the gate can rotate about a frictionless hinge and let some water out of the trough. When the water in the trough is 3-ft deep, as shown in the figure, the gate is just held shut by the spherical counterweight attached to the gate. If the distance between the hinge and the counterweight is l = 3.5 ft, determine a) The mass (m) of the counterweight, in slugs. b) The horizontal and vertical reaction forces, R., and Ry, respectively, at the hinge when the gate is just about to open. m | l- Hinge V 1 ft Water Gate Hinge 3 ft radius -6 ft- 4 ft
Expert Solution
Step 1

Given data 

Water depth = 3ft 

L = 3.5 ft 

Find the mass of counterweight in slugs and reactions at the hinged support 

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