Final answer:
The student's question focuses on using the equilibrium of forces under Newton's Laws to calculate the tension in swing ropes and the horizontal force maintaining the swing's position.
Step-by-step explanation:
The question presented involves the application of Newton's Laws, specifically when analyzing forces in equilibrium. In part (a), we are tasked with calculating the tension in each of the ropes supporting a swing, with the swing ropes making an angle with the vertical. The scenario is treated as one where the forces acting on the swing must be balanced, hence why the swing is at rest even though it is pushed to the side.
In part (b), we need to calculate the magnitude of the horizontal force (F) that holds the swing in place. This force is responsible for keeping the swing to one side. We apply the principles of equilibrium for the vertical forces (gravity and tension's vertical component) and horizontally (the applied force and tension's horizontal component).
By setting up the free-body diagram and equations based on Newton's second law (Σ F = 0 for a system in equilibrium), we can use trigonometry to solve for the unknowns. The tension in the ropes and the magnitude of F can be determined by applying principles of static equilibrium and vector decomposition of forces.