A 195.0-N sign is suspended from a horizontal strut of negligible weight. The force exerted on the strut by the wall is horizontal. Draw an FBD to show the forces acting on the strut. (Do this on paper. Your instructor may ask you to turn in this work.)The angle is 30 degree
Find the tension T in the diagonal cable supporting the strut.
N
I tried 195sin(30)= 97.5 N, but its wrong. Please someone help me out. Thank you.
To find the tension in the diagonal cable supporting the strut, we need to consider the forces acting on the strut.
1. The weight of the sign, which acts vertically downwards, has a magnitude of 195 N.
2. The force exerted by the wall on the strut, which acts horizontally, can be represented as Fwall.
To resolve the forces, we can consider the vertical and horizontal components separately.
1. Vertical Component:
The weight of the sign can be resolved into two components: one perpendicular to the strut and one parallel to it. Since the angle between the strut and the vertical direction is 30 degrees, the vertical component of the weight is given by Wv = 195 * sin(30°).
2. Horizontal Component:
The force exerted by the wall on the strut is horizontal and has the same magnitude as the tension in the diagonal cable, T.
Now, we can analyze the forces acting on the strut:
1. The weight of the sign, acting vertically downwards, can be represented by Wv.
2. The force exerted by the wall on the strut, acting horizontally, can be represented by Fwall.
3. The tension in the diagonal cable, acting from the top of the strut, can be represented by T.
Based on the information given, the FBD (Free Body Diagram) for the strut would include the following forces:
- A vertical force Wv pointing downwards.
- A horizontal force Fwall pointing towards the right.
- An upward diagonal force T acting at an angle of 30 degrees with the horizontal.
To find the tension T in the diagonal cable, you will need to use the values of the other forces and calculate it using the principles of equilibrium.
To find the tension in the diagonal cable supporting the strut, you can make use of the forces acting on the strut. Let's analyze the problem step by step.
1. Draw a diagram to represent the situation. In this case, draw a horizontal strut with a sign suspended from it. Draw a vertical cable attached to the top of the strut and assume it makes an angle of 30 degrees with the horizontal.
2. Identify the forces acting on the strut. In this case, there are three forces acting on the strut:
a) The weight of the sign pulling vertically downward with a force of 195.0 N.
b) The tension in the diagonal cable pulling upward and to the right.
c) The horizontal force exerted by the wall.
3. Now, draw a free-body diagram (FBD) for the strut. To do this, isolate the strut and draw all the forces acting on it. The weight of the sign will be acting vertically downward from the center of the sign's mass. The diagonal tension force will be acting upward and to the right, inclined at an angle of 30 degrees relative to the horizontal. The horizontal force exerted by the wall will act horizontally.
4. Resolve the forces into their respective components. The weight of the sign can be split into two components: one acting vertically downward and the other acting horizontally. The diagonal tension force can also be split into two components: one acting vertically upward and the other acting horizontally. The horizontal force exerted by the wall remains horizontal and does not need to be split.
5. Now, apply trigonometry to find the magnitudes of the individual components. For the weight of the sign:
Vertical component = weight × sin(angle)
Horizontal component = weight × cos(angle)
For the diagonal tension force:
Vertical component = tension × sin(angle)
Horizontal component = tension × cos(angle)
6. Equate the vertical forces. The vertical component of the diagonal tension force should equal the vertical component of the weight of the sign:
Tension × sin(angle) = weight × sin(angle)
Since the angle and the sine of the angle are known, you can solve for the tension.
7. Reorganize the equation and solve for the tension:
Tension = weight / cos(angle)
Plug in the given values: weight = 195.0 N and angle = 30 degrees. Calculate the tension to find the final answer.
Following these steps, you should be able to find the correct value for the tension in the diagonal cable supporting the strut.