Calculating the Radius of Curvature for a Car on a Hill

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SUMMARY

The discussion centers on calculating the radius of curvature for a car traveling over a hill at a speed of 85.7 km/h (2.38 m/s). The key formula used is the centripetal acceleration equation, a = v²/r, where the only force acting on the package is gravity. The mass of the package cancels out in the equation, allowing for the calculation of the radius of curvature (r) using the relationship F = ma and the gravitational force (mg). The final formula derived is r = v²/g, leading to a definitive method for solving the problem without needing the mass of the package.

PREREQUISITES
  • Understanding of centripetal acceleration
  • Familiarity with Newton's second law (F = ma)
  • Basic knowledge of gravitational force (g = 9.81 m/s²)
  • Ability to convert units (e.g., km/h to m/s)
NEXT STEPS
  • Learn how to derive centripetal acceleration formulas
  • Study the effects of gravitational force on objects in motion
  • Explore unit conversion techniques for speed and acceleration
  • Investigate real-world applications of radius of curvature in automotive engineering
USEFUL FOR

Physics students, automotive engineers, and anyone interested in dynamics and motion analysis will benefit from this discussion.

waldvocm
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An automobile moves at a constant speed over the crest of a hill traveling at a speed of 85.7km.h. At the top of the hill a package on a seat in the rear of the car barely remains in contact with the seat. What is the radius of curvature (m) of the hill?

85.7km/h=2.38m.s v=2.38m/s ac=v^2/r r=v^2/a

I know that the only force acting on the package is gravity. Does this mean that the mass of the package is 9.80? mg=m*ac

I am not sure where to go from here
 
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Error in "85.7km/h=2.38m.s"
In 85.7 km/h you must replace the km with 1000 m and the h with 3600 s.

You are so close when you say "only force acting on the package is gravity"!
Put this into F = ma and realize that the acceleration is centripetal so put that formula in for a. Solve for R.
 
So...
F=m*v^2/r

9.80=m*23.8^2/r

How do I solve for r if I don't know the mass of the package?
 
F = ma
mg = m*v^2/r
and the m's cancel.
 

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