A 660 N cat burglar is supported by cables in the figure below. Assume the angle è of the inclined cable is 36.0°.
Find vertical cable? Thank you so much for your help.
Vertical T = force of burgular
Find inclined tension using Ay = A*sin(theta)
Find horizontal tension using Pythag: A^2 = Ay^2 + Ax^2
Ax is the horizontal tension
To find the vertical component of the cable supporting the cat burglar, you can use trigonometry.
Given that the angle (θ) of the inclined cable is 36° and the weight of the cat burglar (W) is 660 N, we need to find the vertical component of the cable (Fv).
We can use the equation: Fv = W * sin(θ)
Plugging in the values, we have:
Fv = 660 N * sin(36°)
Using a calculator, we find:
Fv ≈ 660 N * 0.5878
So, the vertical component of the cable supporting the cat burglar is approximately 388 N.
To find the vertical component of the cable's tension, we need to resolve the tension into its horizontal and vertical components.
Given:
Weight of the cat burglar (force acting downward) = 660 N
Angle of the inclined cable (θ) = 36.0°
The weight of the cat burglar is balanced by the tension in the vertical cable and the horizontal component of tension in the inclined cable.
Let's start by finding the tension in the inclined cable. The horizontal component of the tension (T_h) can be calculated using trigonometry:
T_h = Tension * cos(θ)
Where Tension is the total tension in the inclined cable.
Using this formula, we can find the horizontal component of the tension in the inclined cable:
T_h = Tension * cos(36.0°)
Now, since the cat burglar is in equilibrium, the vertical component of tension in the inclined cable must balance the weight of the burglar:
T_v = Weight of the burglar = 660 N
Therefore, the vertical component of the cable's tension is equal to the weight of the burglar.
So, in this case, the vertical cable has a tension of 660 N.