Final answer:
A free-body diagram is necessary to visualize the forces acting on the cart, and to move at constant velocity, the nurse must exert a horizontal force equal to the force of friction, ignoring the effects of the angle.
Step-by-step explanation:
The question pertains to the principles of physics, specifically related to forces and motion. In the scenario provided, a nurse is exerting a force at a downward angle to push a cart, which involves concepts such as Newton's laws of motion, free-body diagrams, and friction.
To address part (a) of the question, a free-body diagram would show all the forces acting on the cart. These forces include the gravitational force acting downward, the normal force acting upward, the applied force by the nurse, and the force of friction opposing the motion.
For part (b), to move at constant velocity, the nurse must exert a force that equals the opposing force of friction, taking into account the angle of application. Based on Newton's first law, if the cart is moving at a constant velocity, the net force acting on it is zero. Therefore, the horizontal component of the applied force should be equal to the force of friction, which is 60.0 N.