In a farm yard, a 20.0-kg light is suspended from a light beam on the end of a tall pole. The beam is supported by an arm that attaches to the beam at the suspension point of the light, as shown in the diagram below. The arm makes an angle of 50.0 with the pole. Ignore the weight of the beam and of the arm.

(a) In which parts of the light suspension system is there tension and in which parts is there compression?
(b) Draw a free-body diagram to represent the forces exerted around the suspension point of the light.
(c) If the angle between the supporting arm and the pole were decreased, what would be the effect on each of the forces represented, and why would it have this effect?
(d) Calculate the forces exerted at the suspension point of the light.

(a) In the light suspension system, there will be tension in the supporting arm and the light beam. There will be compression in the pole.

(b) The free-body diagram of the forces exerted around the suspension point of the light can be represented as follows:

<pre> O (suspension point)
|
|
|
T_light
(y-axis) |
↓ |
T_arm
______|______ → (x-axis)

In this diagram, T_light represents the tension in the light beam, and T_arm represents the tension in the supporting arm.</pre>

(c) If the angle between the supporting arm and the pole were decreased, the tension in both T_light and T_arm would increase. This is because as the angle decreases, the vertical component of the tension in the arm increases, which results in a larger total tension force in both the arm and the light beam.

(d) To calculate the forces exerted at the suspension point of the light, we can use the following equations:

For the vertical direction (y-axis):
∑F_y = T_light + T_arm - W_light = 0,
where W_light represents the weight of the light.

For the horizontal direction (x-axis):
∑F_x = T_arm*cos(50°) = 0,
since there is no horizontal acceleration.

Rearranging the equations, we can solve for T_light and T_arm:

T_light = W_light - T_arm,
T_arm = -T_arm*cos(50°),

Substituting the given values:
W_light = m*g = 20.0 kg * 9.8 m/s^2 = 196 N,
cos(50°) ≈ 0.6428,

We can calculate T_arm and then find T_light:

T_arm = -196 N / 0.6428 ≈ -304.6 N,
T_light = 196 N - (-304.6 N) ≈ 500.6 N.

Therefore, the forces exerted at the suspension point of the light are approximately 500.6 N tension in the light beam (T_light) and approximately 304.6 N tension in the supporting arm (T_arm).

To answer these questions, we need to analyze the forces acting on the light suspension system. Let's go step by step:

(a) In which parts of the light suspension system is there tension and in which parts are there compression?
To determine this, we need to understand the forces involved. Tension occurs when a force is pulling on an object, creating a stretching effect. Compression, on the other hand, occurs when a force is pushing on an object, causing it to compress or compressive stress.

In the given scenario, the light is suspended from the beam, so there is tension in the suspension cord that holds the light. Additionally, since the arm supports the beam, there is tension in the arm. So, the tension is present in the suspension cord and the arm.

(b) To draw the free-body diagram representing the forces exerted around the suspension point of the light, we consider the forces acting on the light and the direction in which they act.

The weight of the light acts downward, and we can represent it as a force vector pointing downward. The tension in the suspension cord acts vertically upward, counteracting the weight of the light. The arm exerts a horizontal force on the beam, supporting its weight.

The free-body diagram would include:
- A downward force representing the weight of the light.
- An upward force representing the tension in the suspension cord.
- A horizontal force representing the force exerted by the arm.

(c) If the angle between the supporting arm and the pole were decreased, it would affect the forces in the system.

As the angle decreases, the horizontal force exerted by the arm would increase because it has a component that is perpendicular to the pole, which increases with a decrease in the angle.

The tension in the suspension cord would remain the same since it depends on the weight of the light and is directed vertically upwards.

(d) To calculate the forces exerted at the suspension point of the light, we need to consider the given information:
- The mass of the light is 20.0 kg.
- The angle between the arm and the pole is 50.0°.
- We'll assume the acceleration due to gravity is 9.8 m/s².

By using trigonometry, we can find the horizontal force exerted by the arm. The horizontal component of the force equals the tension in the suspension cord, which counteracts this horizontal force.

Using the equation: force = mass × acceleration, we can calculate the weight of the light. Then, by using trigonometric functions, we can find the vertical force component and the tension in the suspension cord.

Finally, with the values obtained, we can calculate the forces exerted at the suspension point of the light.

Note: Without specific dimensions or additional information about the system, we cannot provide the exact numerical values of the forces.