What is the safe speed limit for a car on a curved highway?

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Homework Help Overview

The problem involves determining a safe speed limit for a car navigating a curved highway with a specified radius and maximum static friction force. The subject area includes concepts from physics related to forces, motion, and circular dynamics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of the equation for centripetal force and attempt to isolate the variable for speed. There are differing calculations and results presented, with some participants questioning their own math and seeking clarification on where errors may have occurred.

Discussion Status

The discussion is active, with multiple participants providing different calculations and results. Some express uncertainty about their answers and seek validation or correction from others. There is no explicit consensus on the correct speed limit, as various interpretations and calculations are being explored.

Contextual Notes

Participants note discrepancies between their calculated speeds and the provided answer choices, indicating potential misunderstandings or errors in their approaches. The original poster is particularly concerned about the validity of their calculations in relation to the answer choices given in their practice exam.

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Homework Statement


On a highway curve with radius 55m, the maximum force of static friction that can act on a 795kg car going around the curve is 8740N. What speed limit should be posted for the curve so that cars can negotiate is safely?


Homework Equations


ƩF=ma, a=v^2/r


The Attempt at a Solution



8740N=795kg(v^2/55m)

8740N= 4375m*kg(v^2)

0.200m/s= v^2

v=0.144m/s

it looks like I performed my math correctly, but I need a second opinion. The solution that I solved does not appear in the answer choices of my practice exam.
 
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the answer choices are
A) 241.23m/s
B)10.99m/s
C)7798.95m/s
D)604.65m/s
E)24.59m/s
 
It is D)

m v2 / r = F

v = √(98740.55/795) = 604.65408805031446540880503144654 :wink:
 
thanks, but where did I go wrong with my math? everytime I isolate v I get letter E
 
Mentz114 said:
It is D)

m v2 / r = F

v = √(98740.55/795) = 604.65408805031446540880503144654 :wink:

Thanks, but I believe the velocity that you gave did not work, :( 11.14 would be the velocity.

Here's what I did, 8740N*55/795 = v^2

v = 24.59m/s
 

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