A 140 kg traffic light is suspended above the street by two cables. What is the tension in each cable?

a)Draw a Free Body Diagram and label all the forces on the suspension point for the light.

b) Find the angles the cables make with the horizontal.

c) Draw a vector sum diagram by lining up all the vectors from tip to tail. Remember that since this is a static problem the tip of the 3rd vector should touch the tail of the 1st vector. Be sure to label all the angles and forces/lengths that are known.

d) Decompose the tension vectors for the cable into horizontal and vertical components. You won’t be able to get exact numbers here, but you can symbolically solve for Tx and Ty for each cable.

ok

now what?
how far did you get?

a) Free Body Diagram for the suspension point of the traffic light:

____
| |
| |
| |
|____|
/ \
/ \

The forces acting on the suspension point are:

- Tension in Cable 1 (T1) pulling upwards
- Tension in Cable 2 (T2) pulling upwards

- Weight of the traffic light acting downwards (W)

b) The angles the cables make with the horizontal:
Since the angles are not specified, let's call the angle T1 makes with the horizontal as θ1 and the angle T2 makes with the horizontal as θ2.

c) Vector sum diagram:

θ1
T1 ------>
|
|
|
|
| W
|
|
|
|
T2 <------ θ2

d) Decomposing the tension vectors for the cables:

For Cable 1:
- The vertical component (Ty1) is equal to T1.
- The horizontal component (Tx1) is unknown.

For Cable 2:
- The vertical component (Ty2) is equal to T2.
- The horizontal component (Tx2) is unknown.

Note: Since the angles are not specified, we cannot determine the exact values of the horizontal and vertical components. It would require additional information to determine the precise values.

a) To draw a free body diagram, we need to show all the forces acting on the suspension point for the traffic light. In this case, there are two cables supporting the light. Let's call the tension in cable 1 as T1 and the tension in cable 2 as T2. We also have the weight of the traffic light acting vertically downward, which we can represent as mg, where m is the mass of the traffic light (140 kg) and g is the acceleration due to gravity (9.8 m/s²). The free body diagram for the suspension point will look like this:

```
T1

|
|
| Traffic light (140 kg)
|
|

T2

mg
```

b) To find the angles the cables make with the horizontal, let's assume the angle between the cable and the horizontal for cable 1 is θ1, and the angle for cable 2 is θ2. These angles can be different for each cable.

c) To create the vector sum diagram, we need to align all the vectors from tip to tail. The vector diagram will look like this:

```
-------- T2
/ /
/ /
/ /
/ /
/ /
/_______/ <-- T1
mg
```

In this diagram, T1 and T2 represent the tension in cable 1 and cable 2, respectively, and mg represents the weight of the traffic light. We label the angles at the intersection of the vectors as θ1 and θ2.

d) To decompose the tension vectors for the cables into horizontal and vertical components, we can use trigonometric relationships. Let's break down the tension vectors into Tx and Ty for each cable.

For cable 1:
Tx1 = T1 * cos(θ1)
Ty1 = T1 * sin(θ1)

For cable 2:
Tx2 = T2 * cos(θ2)
Ty2 = T2 * sin(θ2)

Please note that the exact values of Tx and Ty cannot be determined without additional information about the angles θ1 and θ2.

a) To draw a Free Body Diagram (FBD) for the suspension point of the traffic light, we need to consider all the forces acting on it. In this case, the two cables are supporting the light. So, there will be a tension force in each cable acting upwards. We can label these forces as T1 and T2. Additionally, there will be the weight of the traffic light acting downwards, which can be represented by the force of gravity (mg), where m is the mass of the light and g is the acceleration due to gravity.

b) To find the angles the cables make with the horizontal, we need to consider the geometry of the situation. Let's assume one cable makes an angle θ1 with the horizontal, and the other cable makes an angle θ2 with the horizontal. These angles can be calculated using trigonometric functions based on the geometry of the problem.

c) To draw a vector sum diagram, we need to consider the vector components of the forces involved. We can draw the force of gravity (mg) acting downwards, and the tensions T1 and T2 acting upwards. The vector sum diagram should show a closed triangle, where the third side is the resultant force. Label the angles between the forces and the angles between the forces and the horizontal (θ1 and θ2) on the diagram.

d) To decompose the tension vectors into horizontal and vertical components, we can use trigonometric functions. For the tension T1, the horizontal component would be T1x = T1 * cos(θ1) and the vertical component would be T1y = T1 * sin(θ1). Similarly, for the tension T2, the horizontal component would be T2x = T2 * cos(θ2) and the vertical component would be T2y = T2 * sin(θ2). Symbolically solve for these components using the values of T1, T2, θ1, and θ2. Note that the exact values are not given, so you will have symbolic expressions for the horizontal (Tx) and vertical (Ty) components of tension for each cable.