Final answer:
No, the tension in the vine does not rely on Tarzan's mass when he is stationary or swinging at constant speed because the forces are in equilibrium, making the tension equal to his weight regardless of his mass.
Step-by-step explanation:
The tension in the vine when Tarzan swings or hangs motionless does not rely on his mass. When Tarzan is stationary or swinging at constant speed, the forces acting on him are in equilibrium, which particularly means the tension in the vine (T) is equal to his weight (w), which is the product of his mass (m) and the acceleration due to gravity (g).
As long as we are considering points where the net external force is zero and Tarzan's motion is either at rest or at a constant velocity, the mass of Tarzan does not affect the tension in the vine since his weight is the only downward force. However, if Tarzan was accelerating or decelerating, then his mass would indeed factor into calculations involving the net force and tension.