Final answer:
The tension in the rope when the gymnast hangs motionless can be found using the equation T = mg, which equals the gymnast's weight, where 'm' is the mass and 'g' is the gravitational acceleration. The tension equals 744.76 N for a 76.0 kg gymnast.
Step-by-step explanation:
To calculate the tension T in the rope when the gymnast hangs motionless, we make use of Newton's second law, which states that if there is no acceleration, the net force (Fnet) acting on the body must be zero. In the case of the motionless gymnast, the two forces acting on them are the tension in the rope and their weight. The gymnast's weight (W) can be calculated using the equation W = mg, where m is the mass of the gymnast, and g is the acceleration due to gravity (9.81 m/s2).
Therefore, since the gymnast is at rest and there is no acceleration:
- Fnet = T - W = 0
- T = W
- T = mg
Assuming the gymnast has a mass of 76.0 kg, the calculation would be:
T = 76.0 kg * 9.81 m/s2
T = 744.76 N
Therefore, the tension in the rope is 744.76 N.