Final answer:
The force diagram for the car at the top of the hill would show a downward arrow for the gravitational force and an upward arrow for the normal force. The gravitational force (Fg) is calculated to be 11760 N, and the normal force (FN), which equals the centripetal force, is found to be 900 N.
Step-by-step explanation:
The student's question is about the forces acting on a car at the top of the hill while moving at a constant speed. Specifically, it asks to identify the forces, construct a force diagram, and calculate the normal force (FN) and gravitational force (Fg) on the car given its speed, mass, and the radius of the curve.
Force Diagram Description
At the top of the hill, two forces act on the car: the gravitational force acting downwards and the normal force acting perpendicular to the surface of the road. If we assume a frictionless surface as stated in the provided information, the force diagram would show a downward arrow to represent the gravitational force (Fg) and an upward arrow to represent the normal force (FN), with these arrows being of different lengths depending on their magnitudes.
Calculation of FN & Fg
The gravitational force (Fg) can be calculated using the formula Fg = m * g, where m is the mass of the car and g is the acceleration due to gravity. For a mass of 1200 kg and assuming g = 9.8 m/s2, Fg = 1200 kg * 9.8 m/s2 = 11760 N. The normal force (FN) is what provides the centripetal force needed to keep the car moving in a circular path at the top of the hill. Using the formula for centripetal force (Fc = m * v2/r) and the given values, Fc = 1200 kg * (15 m/s)2 / 25 m = 900 N. Since there is no friction, this centripetal force is provided entirely by the normal force (FN).