Calculating the Radius of Curvature for a Car on a Hill

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Homework Help Overview

The discussion revolves around calculating the radius of curvature for a car traveling over the crest of a hill, specifically focusing on the forces acting on a package in the car. The subject area includes concepts from dynamics and circular motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between speed, gravitational force, and centripetal acceleration. Questions arise regarding the necessity of knowing the mass of the package to solve for the radius of curvature.

Discussion Status

Participants are actively engaging with the problem, with some providing corrections and clarifications on the initial calculations. There is an ongoing exploration of the relationship between forces and acceleration, and how to approach the problem without knowing the mass of the package.

Contextual Notes

There is a mention of the assumption that the only force acting on the package is gravity, which raises questions about the implications of this assumption on the calculations. Additionally, there are errors noted in the unit conversion for speed that may affect the problem setup.

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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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