Force of a roller coaster track on a car

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SUMMARY

The discussion focuses on calculating the forces exerted by a roller coaster track on a car with a mass of 800 kg at different speeds. At point A, with a speed of 25.0 m/s, the correct force exerted by the track is determined by incorporating both the centripetal force and the normal force, leading to a solution that corrects the initial miscalculation of 50,000 N. At point B, with a speed of 10.0 m/s, the same principles apply, and the maximum speed at point B is derived using Newton's 2nd law, emphasizing the importance of net forces in the calculations.

PREREQUISITES
  • Understanding of Newton's 2nd Law of Motion
  • Familiarity with centripetal force calculations
  • Knowledge of normal force concepts in physics
  • Ability to apply kinematic equations in dynamics
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  • Study the derivation of centripetal force equations in circular motion
  • Learn how to calculate normal force in various scenarios
  • Explore advanced applications of Newton's laws in roller coaster dynamics
  • Investigate the effects of mass and speed on forces in circular motion
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Physics students, mechanical engineers, and anyone interested in the dynamics of roller coasters and forces acting on moving objects.

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Homework Statement


The roller coaster car shown below has a mass of 800 kg when fully loaded with passengers.
(a) If the car has a speed of 25.0 m/s at point A, what force does the track exert on the car at that
point. (b) If the car has a speed of 10.0 m/s at point B, what force does the track exert on the car.
(c) What is the maximum speed the car could have at B and still remain on the track?

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Homework Equations


F = mv²/r

The Attempt at a Solution


(a)
I thought I would just need to plug into the above formula but that didn't work. I did:
800kg * (25m/s)² / 10m and got the answer 50000N, but that is not the correct answer. I am not sure what else to
Edit: Figured out I had to add in the normal force and got the correct answer.
(b)
Edit: Figured out based on what I learned from part a.
(c)
Edit: Figured out based on what I learned from part a.
 
Last edited:
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Remember Newton's 2nd law...it's not f=ma, but F_net =ma, that is, the sum of all forces(that is, the net force) =ma =mv^2/r. Therb is another force acting on the car besides its weight..the contact force (the normal force) of the track on the car. Solve for it. What is the direction of the centripetal acceleration and the direction of the net force?
 
Thanks for the help! I realized I had to also add the normal force when it was at part a. I was able to figure out part b and c based on that information.
 

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