An acrobat hangs by his hands from the mid-
dle of a tightly stretched horizontal wire so
that the angle between the wire and the hori-
zontal is 12.5◦.
If the acrobat’s mass is 88.8 kg, what is
the tension in the wire? The acceleration of
gravity is 9.8 m/s2.
Answer in units of N.
didn't I just answer this/
12
To find the tension in the wire, we can use the forces acting on the acrobat.
From the given information, we know the mass of the acrobat, which is 88.8 kg, and the angle between the wire and the horizontal, which is 12.5 degrees.
Let's consider the forces acting on the acrobat when hanging from the wire:
1. Weight (mg): This force acts vertically downwards and is given by the formula weight = mass * acceleration due to gravity.
2. Tension (T): This force acts horizontally on the wire and provides the necessary centripetal force for the acrobat to stay in circular motion (i.e., not fall down). This force is directed towards the center of the circular path.
To find the tension in the wire, we need to calculate the component of the weight parallel to the wire. This can be done using trigonometry.
The component of the weight parallel to the wire is given by the formula weight_parallel = weight * sin(angle).
Substituting the given values:
weight = mass * acceleration due to gravity = 88.8 kg * 9.8 m/s^2 = 868.32 N
angle = 12.5 degrees
weight_parallel = 868.32 N * sin(12.5 degrees)
Calculating the value of sin(12.5 degrees), we get:
sin(12.5 degrees) ≈ 0.2146
weight_parallel ≈ 868.32 N * 0.2146 ≈ 186.43 N
Therefore, the tension in the wire is approximately 186.43 N.