During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 148 N on the wire. The left section of the wire makes an angle of 12° relative to the horizontal and sustains a tension of 447 N. Find the magnitude and direction of the tension that the right section of the wire sustains.

Question

During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 148 N on the wire. The left section of the wire makes an angle of 12° relative to the horizontal and sustains a tension of 447 N. Find the magnitude and direction of the tension that the right section of the wire sustains.

Answer 1

To find the magnitude and direction of the tension in the right section of the wire, we can start by analyzing the forces acting on it.

Let's denote the tension in the right section as T (unknown value) and the angle the right section makes with the horizontal as θ (also unknown).

Since the left section of the wire sustains a tension of 447 N, we can use this information to find the vertical component of the tension in the left section. Given that it makes an angle of 12° with the horizontal, we can use trigonometry to calculate this vertical component:

Vertical component of the tension in the left section = T_left * sin(12°)
= 447 N * sin(12°)

Next, let's consider the forces acting on the tree limb. We know that it exerts a downward force of 148 N on the wire. This force can be decomposed into its vertical and horizontal components:

Vertical component of the downward force on the wire = 148 N
Horizontal component of the downward force on the wire = 0 N (since the limb falls directly downwards)

Now, let's balance the vertical forces acting on the right section of the wire:

Vertical component of the tension in the right section - Vertical component of the downward force = Vertical component of the tension in the left section

T * sin(θ) - 148 N = 447 N * sin(12°)

Now we have an equation with one unknown, θ. Solving this equation will give us the value of θ, which represents the angle the right section of the wire makes with the horizontal.

Once we solve for θ, we can substitute its value back into the equation above to find the magnitude of the tension in the right section of the wire, T.

With the given values, you can now solve the equation using basic algebraic techniques to find the magnitude and direction of the tension in the right section of the wire.