Final answer:
The tension in the rope supporting a stationary mass is equal to the weight of that mass, which can be calculated using the formula T = mg, where m is the mass and g is the gravitational acceleration.
Step-by-step explanation:
To determine the tension in the rope, we must consider Newton's second law, which states that the sum of the forces must equal the mass times the acceleration (Fnet = ma). In the case where we have a stationary mass or a mass moving with constant velocity (with no acceleration), the net force is zero. Therefore, if we have a 5.00-kg mass hanging from a rope, the forces acting on it are the weight of the mass due to gravity (which we can calculate by w = mg, where m is the mass and g is the acceleration due to gravity) and the tension in the rope (T). Since the two forces must balance out for a stationary mass or mass moving with constant velocity, the equation becomes T - w = 0, leading to T = w = mg.
For a mass of 5.00-kg, assuming g = 9.81 m/s2 (standard gravity), the tension would simply be T = 5.00 kg * 9.81 m/s2 = 49.05 N, neglecting the mass of the rope and assuming a frictionless pulley.