A 50.0 kg gymast hangs vertically from a pair of parallel rings. If the ropes are supported so that they make an angle of 45 degrees with the ceiling, what is the tension in each rope?
To find the tension in each rope, we need to consider the forces acting on the gymnast in equilibrium.
Let's break down the given information:
- The gymnast's weight is 50.0 kg.
- The ropes make an angle of 45 degrees with the ceiling.
First, let's resolve the weight of the gymnast into its components.
The component of the weight acting parallel to the ropes is equal to the tension in each rope (T).
The component of the weight perpendicular to the ropes is balanced by the normal force from the rings.
Now, let's calculate the weight component parallel to the ropes:
Weight component parallel to the ropes = Weight * sin(angle)
Weight component perpendicular to the ropes = Weight * cos(angle)
Substituting the given values into the equations:
Weight component parallel to the ropes = 50.0 kg * sin(45 degrees)
Weight component parallel to the ropes = 50.0 kg * 0.707
Weight component parallel to the ropes = 35.35 kg
Since the weight component parallel to the ropes is equal to the tension in each rope, the tension in each rope is 35.35 kg.
Therefore, the tension in each rope is 35.35 kg.