2 questions, both about balancing force/torque

[achacttn]

First question

Homework Statement

A gate is hanging on a fencepost (attached by 2 hinges).
The gate has mass 5.2kg and is 1.7m wide (weight acts down centre of gravity).
Distance between the 2 hinges is 0.7m
Find horizontal component of the force applied to the gate by the bottom hinge.

Homework Equations

F=mg,
Torque = F x perpendicular distance

The Attempt at a Solution

The top hinge exerts a force to the left and the bottom hinge to the right. Since I want to find the force that the bottom one applies, I use the top one as a pivot and try to balance the torque. However, if the gate's weight turns it clockwise, wouldn't the bottom hinge have to exert a force to the left?
I tried an alternative method where I said the overall horizontal forces must be zero, and said the horizontal forces exerted by the hinges were in equal and opposite directions. I tried finding the force exerted by the top hinge (towards the left) by making the bottom one a pivot, so that
Force of top hinge x 0.7m = 5.2kg x g x (1.7/2)
Solving for top hinge force gives 61.88N (g is taken as 9.8). So the bottom hinge must also exert a force of 61.88 but apparently this is not the answer.



Second question

Homework Statement

9.4kg object hung from ceiling using 2 wires. Each wire can hold up to 10kg.
First wire hangs at an angle of 9.08 degrees to the ceiling, and second wire hangs at an angle of 17 degrees to the ceiling. What is force on 1st wire on hanging up object?

Homework Equations

F=mg
g = 9.8 ms^-2

The Attempt at a Solution

The total vertical force must sum to 0. So the sin of 9.08 x F1 (wire 1) + sin17 x F2 (wire 2) = 9.4 x 9.8.
Also, the horizontal forces must total to 0, so I took F1cos9.08 = F2cos17.
This gave F2 = -F1(cos9.08/cos17), and I substitute this into the F2 of the original equation. When solving for F1, the force is 639.3N, which I'm not sure is the correct answer or not because it seems very high.


Any comments/help are much appreciated.
Thanks in advance.

 

[PhanthomJay]

question 1 answer looks good, except it should be rounded to 2 sig figs, so F= 62 N. When you take moments about the top hinge instead, the moment due to the weight still produces a cw moment, so the bot hinge force must point right to produce a counteracting ccw moment.