Final answer:
The tension in a rope used with a pulley matches the applied force due to Newton's third law, which states that forces between two objects are equal and opposite. Additionally, if the lifter is stationary, Newton's second law indicates that the net force is zero, hence the tension must equal the weight (mg) of the lifter for them to remain at rest.
Step-by-step explanation:
The tension in a rope is equal to the applied force when someone is using a pulley to lift themselves because of Newton's laws of motion, particularly the third law which states that for every action there is an equal and opposite reaction. When a person applies a force to lift themselves using a pulley, the rope transmits this force. The rope, being a perfectly flexible connector, exerts equal forces on both the person's hand and the mass being lifted (the person's own body in this case).
Newton's second law also plays a part in this scenario, especially if the person lifting themselves is at rest, meaning there is no acceleration. In this case, the net force (Fnet) acting on the person is zero, as the only external forces are the tension (T) and the person's weight (W), where W is the product of the mass (m) and the acceleration due to gravity (g).
In conclusion, when lifting oneself with a pulley, the tension in the rope must match the weight of the supported mass, which equates to T = mg, ensuring that the lifter is in equilibrium with the force they exert balanced by the tension in the rope.