Final answer:
In a scenario where a pole vaulter holds a massless pole in static equilibrium, the downward force F1 needed to prevent movement is zero Newtons, as there is no weight from the pole to counterbalance.
Step-by-step explanation:
The student is tasked with analyzing a physical system in static equilibrium involving a pole and forces applied by a pole vaulter. When the pole's center of gravity (cg) is at the midpoint between the vaulter's hands and the pole is massless, the forces exerted by the hands are equal and opposite, satisfying the first condition for equilibrium (net F = 0) and the second condition (net t = 0). If the pole has mass, as per the example where the pole's mass is 5.00 kg, the force exerted by each hand would be equal to half the weight of the pole.
The question describes a scenario where the pole is massless, however, referring to the provided examples where the pole has a mass of 5.00 kg, if the pole were considered massless for the actual question at hand, the downward force F1 applied by the pole vaulter would be zero Newtons, as there would be no weight from the pole itself to counterbalance. However, it is crucial to check if other forces might be at play (like the vaulter's own weight or air resistance), which could require applying a force to maintain equilibrium even if the pole is massless.