an electric sign weighing 200 newtons is supported by two slanting cables. each cable is attached to the same point of the sign and makes a 45 degree angle with the horizontal. what is the component of the force exerted by the sign along each of its cables?
if the cables are at the center of the sign, assume each one carries 100N due to symettry.
Sin45=100/Tension
solve for tension.
To determine the component of the force exerted by the sign along each of its cables, we need to use trigonometry to find the vertical and horizontal components of the force.
First, let's visualize the problem. We have an electric sign weighing 200 newtons, and two cables attached to the sign, slanting at a 45-degree angle with the horizontal.
Now, let's break down the forces. Since both cables attach to the same point on the sign, the total force exerted by the sign will be divided equally between the two cables. Let's call this splitting force 'F'.
To find the vertical and horizontal components of the force, we need to use the trigonometric ratios.
We know that the angle between the cable and the horizontal is 45 degrees, which means the angle between the cable and the vertical is also 45 degrees.
The vertical component of the force, Fv, can be determined as follows:
Fv = F * sin(45)
where sin(45) is the sine of 45 degrees.
Similarly, the horizontal component of the force, Fh, can be determined as follows:
Fh = F * cos(45)
where cos(45) is the cosine of 45 degrees.
Now, let's calculate these components:
Fv = F * sin(45)
Fv = 200 N * sin(45)
Fv = 200 N * 0.7071
Fv ≈ 141.42 N (rounded to two decimal places)
Fh = F * cos(45)
Fh = 200 N * cos(45)
Fh = 200 N * 0.7071
Fh ≈ 141.42 N (rounded to two decimal places)
Hence, the component of the force exerted by the sign along each of its cables is approximately 141.42 newtons.