What is the force of the track on the car?

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SUMMARY

The discussion centers on calculating the force of the track on a roller-coaster car at the top of a hill with a radius of 15 m and a mass of 500 kg. The car's speed at the top is 8.0 m/s. The correct calculation of the normal force, which represents the force of the track on the car, is determined to be 2.8 kN upward, contrary to the initial incorrect calculation of 4.9 kN. The error stemmed from misapplying the centripetal acceleration and misunderstanding the forces acting on the car.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of centripetal acceleration and its application
  • Familiarity with free body diagrams (FBD)
  • Basic principles of forces acting on objects in circular motion
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  • Review the concept of centripetal force and its calculation in circular motion
  • Study the role of normal force in different scenarios, particularly in vertical circular motion
  • Learn how to correctly draw and interpret free body diagrams for dynamic systems
  • Explore the effects of friction in circular motion and how it influences normal force
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Physics students, educators, and anyone interested in understanding forces in circular motion, particularly in the context of roller-coaster dynamics.

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Homework Statement


A roller-coaster has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius 15 m. When at the top of the hill, the car has a speed of 8.0 m/s. WHat is the force of the track on the car at the top of the hill?


Homework Equations


F=ma


The Attempt at a Solution


I drew an FBD: wtih mg pointing down, N pointing up and static friction pointing to the left. ( I think this may be wrong, but I figured it may need static friction to stay on the track).
Then when broken into i and j components I got:
i= -MsN=-MV2/r ...(because the acceleration is centripical)
then for j:
I have N-mg=0
N=mg
and since it was asking for the force of the track on the car, I thought this was the normal force, so I just plugged in the values for m ang, and got 4.9 kN up. This is wrong, it is saying the correct answer is 2.8 kN up. Any suggestions on where I went wrong?
 
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The car is at the top of the hill; you seem to have your i and j mixed up. The centripetal accelertion is vertically down. Ignore friction.
 

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