Circular and Satellite Motion - Mission CG5 Detailed Help

 Mac and Tosh are on a roller coaster ride and moving rapidly over the crest of a small hill. The hilltop has a curve which resembles a section of a circle with a radius of 27.3 meters. The speed of the 421-kg roller coaster car at the crest is 15.6 m/s. Determine the acceleration (in m/s/s), net force (in N) and the magnitudes of all individual forces when the car is at the crest. Finally, indicate the direction of the net force and acceleration ...

(Note: Your numbers are randomly selected and may differ from the numbers listed above.)

Detail #1: Many students quickly reach a standstill on the questions in this mission because they fail to click on the Direction button for acceleration and net force in order to toggle to the correct direction. Since this is central to the solution, you might do it first.
Detail #2: Minds on Physics calculates answers to the fourth decimal place. Your answers do not need to be that accurate. To be safe, enter at least four digits on each answer. If doing a sequence of consecutive calculations, do not round intermediate values; save all rounding until the final value has been determined.

Often times, success in physics demands that you have the proper approach - a good game plan. The following strategy should serve you well:
  1. Read the physical situation, analyze the diagram and determine the direction of the net force and acceleration. Click on the Dir'n button to set the direction to inward.
  2. Determine the acceleration of the car from the knowledge of v and R. If necessary, see Formula Frenzy section.
  3. Determine the net force on the car from the knowledge of m and a. If necessary, see Formula Frenzy section.
  4. Determine the gravity force from the mass. If necessary, see Formula Frenzy section.
  5. The gravity force is directed inward. The normal force is directed outward. Together, these two forces must add as vectors to equal the net force. Since the normal force points in the opposite direction as the gravity force, it can be said that Fgrav - Fnorm = Fnet. The normal force can be calculated from knowledge of the net force and the gravity force.

All blanks should now be filled in. Check your answer. If there is a mistake, recheck your calculations and try again. Be cautious of the rounding of answers.

The acceleration (a) of an object moving in a circle is dependent upon the speed (v) of the object and the radius (R) of the circle. The relationship is expressed by the equation:
a = v2 / R

The weight of an object or gravitational force (Fgrav) is dependent upon the object's mass (m) and the acceleration of gravity (g) - 9.8 m/s/s. The relationship is expressed by the equation:   

Fgrav = m • g

The net force (Fnet) acting on an object is dependent upon the object's mass (m) and its acceleration (a). The relationship is expressed by the equation: 

Fnet = m • a