Gymnasts can do all sorts of ridiculous tricks on various equipment. In the rings event, the gymnast is supported by two rings attached by cords to the ceiling (see a picture here). If a gymnast weighs 75 kg and is motionless on the rings, what is the tension in each cord?
To find the tension in each cord supporting the gymnast on the rings, we need to consider the forces acting on the gymnast.
When the gymnast is motionless on the rings, the forces acting on the gymnast are the weight force (mg) and the tension forces in each cord (T).
To calculate the tension in each cord, we can use Newton's second law, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, since the gymnast is motionless, the acceleration is zero.
The force acting on the gymnast in the vertical direction is the combination of the weight force and the tension forces. Since the gymnast is motionless, this net force must be zero.
Therefore, we can write the following equation:
mg + T + T = 0
Simplifying the equation, we get:
2T + mg = 0
Now, we can substitute the given values:
m = 75 kg (mass of the gymnast)
g = 9.8 m/s² (acceleration due to gravity)
Plugging in these values, we can solve for T:
2T + (75 kg)(9.8 m/s²) = 0
2T + 735 N = 0
2T = -735 N
T = -735 N / 2
T ≈ -367.5 N
Since tension is a scalar quantity, it cannot be negative. Thus, we discard the negative sign.
Therefore, the tension in each cord supporting the gymnast on the rings is approximately 367.5 newtons (N).