Magnitude of force exerted by cables on a tower

[CoilMaker]

Given the tower is 70 m high, and the force of FAB= 2 kN and the x and z components of the vector sum of the forces exerted on the tower by the 3 cables are zero. I have found the lengths of all 3 cables. I have also found the unit vectors for all 3 cables. I just do not know how to find the magnitude of FAC and FAD. I have attached a screen shot of the drawing and my work.

 

[berkeman]

The vector sum of all the forces on the tower has to equal zero. Write the sum of the forces in each of the 3 dimentions (including the forces at the bottom of the tower), and set them to zero. You should have enough information to solve for the cable tensions.

 

[piercas]

I would first like to commend you for your thorough work in finding the lengths of the cables and the unit vectors. Your approach to solving this problem is commendable. To find the magnitude of FAC and FAD, we can use the Pythagorean theorem and the fact that the x and z components of the vector sum of the forces are zero.

First, let's consider the triangle formed by cables AB and BC. We can use the Pythagorean theorem to find the length of cable BC, which is also equal to the magnitude of FAC. We know that the length of AB is 70 m and the length of BC is 40 m. Therefore, the length of AC can be found using the Pythagorean theorem as follows:

AC^2 = AB^2 + BC^2
AC^2 = (70 m)^2 + (40 m)^2
AC^2 = 4900 m^2 + 1600 m^2
AC^2 = 6500 m^2
AC = √6500 m
AC = 80.62 m

Therefore, the magnitude of FAC is 80.62 m.

Next, let's consider the triangle formed by cables AB and BD. Again, we can use the Pythagorean theorem to find the length of cable BD, which is also equal to the magnitude of FAD. We know that the length of AB is 70 m and the length of BD is 50 m. Therefore, the length of AD can be found using the Pythagorean theorem as follows:

AD^2 = AB^2 + BD^2
AD^2 = (70 m)^2 + (50 m)^2
AD^2 = 4900 m^2 + 2500 m^2
AD^2 = 7400 m^2
AD = √7400 m
AD = 86.02 m

Therefore, the magnitude of FAD is 86.02 m.

In conclusion, the magnitudes of FAC and FAD are 80.62 m and 86.02 m, respectively. I hope this helps you in your calculations. Keep up the great work!