Vectors tension force

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Homework Statement

a 25 kg restaurant sign hangs from a 1.25m horizontal pole with one end fastened at right angle to the brick wall of a restaurant and the other end fastened to a 2.5m cable . determine the force of compression actng on the pole and the tension in the cable.

Homework Equations

im totally clueless this is a past test question. i was thinking u could possible use the sin law

t1=t2sin(angle2)/sin(angle1) ?? this is where t is the tension. i would like help understanding how to calculate them.


Oh i drew the diagram so i know how it loks like

The Attempt at a Solution

 

[cristo]

Try looking at moments (torques).

 

[Architeuthis Dux]

I would approach this problem by first identifying the relevant equations and principles that can be applied. In this case, the two main concepts involved are tension force and equilibrium of forces.

To determine the tension in the cable, we can use the principle of equilibrium, which states that the sum of all forces acting on an object must be equal to zero. In this case, the forces acting on the sign are its weight (mg), the tension in the cable (T), and the compression force on the pole (F). Since the sign is not moving, we can set up the following equation:

mg + T + F = 0

We know the mass of the sign (25 kg) and the acceleration due to gravity (9.8 m/s^2), so we can solve for T:

T = -mg - F

Next, we can use trigonometry to find the value of F, the compression force on the pole. We can use the sine law to relate the angle between the pole and the wall (angle 1) to the angle between the pole and the cable (angle 2):

F/sin(angle1) = T/sin(angle2)

We know the values for T and angle 2, so we can rearrange the equation to solve for F:

F = T*sin(angle1)/sin(angle2)

Plugging in the values, we get:

F = (-mg - T)*sin(angle1)/sin(angle2)

Now, we can substitute the value of T from our first equation to get the final answer:

F = (-mg - (-mg - F))*sin(angle1)/sin(angle2)

Solving for F, we get:

F = (mg + mg*sin(angle1)/sin(angle2))/(1 + sin(angle1)/sin(angle2))

We can then plug in the known values to get the final answer for the compression force on the pole.

As for the tension in the cable, we can use the same equation for equilibrium to find its value, since we now know the value of F:

T = -mg - F

Again, we can substitute the known values to get the final answer for the tension in the cable.

Overall, the key concepts used to solve this problem were equilibrium of forces and trigonometry. By applying these principles, we can find the values for the tension force and compression force in this scenario.