Find the tension in the two wires that support the 100 N light fixture. Assume θ is 39°.
left wire:
right wire:
Well, isn't that a bright question! Let's shed some light on this one, shall we?
To find the tension in the two wires, we're going to need to use a little trigonometry. Are you ready for some thrilling trigonometric calculations?
Assuming the left and right wires make an angle of 39° with the vertical, we can use the following formula:
Tension = Weight / (2 * sin(θ))
Since we know the weight of the light fixture is 100 N, we can substitute that in:
Tension = 100 N / (2 * sin(39°))
Now, let me just grab my calculator... *beep boop beep*
Ah-ha! The tension in each wire is about 82.029 N. So, the left wire and the right wire both have a tension of approximately 82.029 N.
Now, don't go hanging around too long with these calculations. Remember to always have a bright day! 🌞
To find the tension in the two wires, we can break down the force acting on the light fixture into its vertical and horizontal components.
Let's consider the horizontal components first. The horizontal component of the weight of the light fixture (100 N) would be equal to Tension_right * cos(θ), where θ is the angle between the right wire and the horizontal direction. Similarly, the horizontal component of the tension in the left wire would be Tension_left * cos(θ).
Now, let's consider the vertical components. The vertical component of the weight of the light fixture (100 N) would be equal to Tension_right * sin(θ), where θ is the angle between the right wire and the horizontal direction. Similarly, the vertical component of the tension in the left wire would be Tension_left * sin(θ).
Since the light fixture is in equilibrium (not accelerating), the sum of the vertical components of the tensions in the two wires should be equal to the weight of the fixture.
Therefore, we can set up the following equations:
Vertical components:
Tension_left * sin(θ) + Tension_right * sin(θ) = 100 N
Horizontal components:
Tension_left * cos(θ) = Tension_right * cos(θ)
Given that θ = 39°, we can solve these equations to find the values of Tension_left and Tension_right.
To find the tension in the two wires, we can use the concept of equilibrium. In this case, the light fixture is in equilibrium, meaning that the sum of the forces acting on it is equal to zero.
Let's consider the left wire first. We can break down the force of tension in the left wire into its vertical and horizontal components.
The vertical component of tension in the left wire will support the weight of the light fixture, which is 100 N, acting downwards. Since the light fixture is in equilibrium, the vertical component of tension must be equal in magnitude and opposite in direction to the weight. So, the vertical component of the tension in the left wire is 100 N in the upward direction.
The horizontal component of tension in the left wire will balance the horizontal components of forces acting on the light fixture. However, we don't have any horizontal forces acting on the light fixture, so the horizontal component of tension in the left wire is zero.
Now let's move on to the right wire. The right wire will share the weight of the light fixture with the left wire. Since the light fixture is in equilibrium, the vertical component of the tension in the right wire must be equal in magnitude and opposite in direction to the vertical component of the tension in the left wire. So, the vertical component of tension in the right wire is also 100 N in the upward direction.
Lastly, since there are no horizontal forces acting on the light fixture, the horizontal component of tension in the right wire is zero as well.
Therefore, the tension in the two wires that support the 100 N light fixture is as follows:
Left wire:
- Vertical component of tension: 100 N (upward)
- Horizontal component of tension: 0 N
Right wire:
- Vertical component of tension: 100 N (upward)
- Horizontal component of tension: 0 N