Question

cable
In figure the uniform gate weighs 300 N and is 3 m wide and 2 m high. It is
In 3m
3 m
supported by a hinge at the bottom left corner and a horizontal cable at the top left
corner, as shown. Find:
2m
(A) The tension in the cable
(B) The force that the hinge exerts on the gate (magnitude and direction).
(Ans.: (A) 225 N, (B) Fx = 225 N, F, = 300 N)
hinge​

Answer 1

Answer:

T = 225N, F hinge = 375 N

Explanation:

In order to undertand the question completely, first see the figure explaining the scenario.

Total torque about the point O is zero

T x2 = mg x 3/2

T = 300 x ¾

T = 225N

Hence the tension in string is 225N

Total Force is also zero;

F hinge + T + mg = 0

F hinge = Mag ( T + mg)

F hinge = √(〖225〗^2+〖300〗^2 )

F hinge = 375 N