A display sign is supported by a guy making an angle of 37o with the horizontal and by a bracket at the upper end near the vertical wall. The sign weighs 150N. Find
A. The tension in wire
B. The force exerted by the bracket on the sign.
To find the tension in the wire and the force exerted by the bracket on the sign, we can use the concepts of equilibrium and trigonometry. Let's go step by step:
A. Tension in the wire:
1. Draw a free-body diagram of the sign. Label the angles and forces involved.
Tension (T) |
|
-------------------------------------- <-- Sign
|
Weight (W) |
2. We have the weight (W) acting vertically downward. Decompose this force into its horizontal and vertical components.
Vertical component of weight (Wv) = W * sin(37°)
Horizontal component of weight (Wh) = W * cos(37°)
3. Since the sign is in equilibrium, the vertical forces must balance out. We have the equation:
T - Wv = 0
Rearranging the equation, we get:
T = Wv
Substituting the value of Wv, we get:
T = W * sin(37°)
Calculate the value of T using this equation, where W is the weight of the sign (150N).
B. Force exerted by the bracket on the sign:
1. Again, draw a free-body diagram of the sign, focusing on the forces involved at the bracket.
Force by bracket (F) |
|
---------------------------
|
|
|
|
|
|
|
|
---- <- Wall
2. We have the force by the bracket (F) exerted along the horizontal direction. Since the sign is in equilibrium, the horizontal forces must balance out. We have the equation:
F - Wh = 0
Rearranging the equation, we get:
F = Wh
Substituting the value of Wh, we get:
F = W * cos(37°)
Calculate the value of F using this equation, where W is the weight of the sign (150N).
By following these steps, you can calculate the tension in the wire (T) and the force exerted by the bracket on the sign (F).