Did I do this question correctly?

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SUMMARY

The discussion centers on calculating the force of static friction and the coefficient of static friction for a race-car driver navigating a banked turn at 225 km/h. The driver’s car has a mass of 1450 kg and the turn is banked at 15°. The formula for static friction, F(s) = mv² / r, is applicable, but the radius must be determined using V = √(g r tan 15°). The coefficient of static friction, µ(s), can be calculated using µ(s) = F(s) / F(N), where F(N) is the normal force.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with the concepts of static friction and normal force
  • Knowledge of trigonometric functions related to angles
  • Ability to manipulate equations involving gravitational force
NEXT STEPS
  • Calculate the radius of the turn using V = √(g r tan 15°)
  • Determine the magnitude of the force of static friction using F(s) = mv² / r
  • Compute the normal force to find F(N) for the coefficient of static friction
  • Explore the implications of varying the bank angle on static friction requirements
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the dynamics of vehicles on banked curves will benefit from this discussion.

lanvin
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A race-car driver is driving her car at a record-breaking speed of 225 km/h. The first turn on the course is banked at 15°, and the car's mass is 1450kg.

1. If the car maintains a circular track around the curve (does not move up or down the bank), what is the magnitude of the force of static friction?

Do I use this formula?:

F(s) = mv^2 / r

And do I find the radius, using the formula V = √(g r tan15°)

2. What is the coefficient of static friction necessary to ensure the safety of this turn?

for this I use the formula µ(s) = F(s) / F(N) ?
 
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Are you sure there is no radius given? Or that the curve was designed for a particular speed?

The V2 = gRTanθ is based on the down-incline force of gravity being balanced by the up incline centripetal acceleration without friction. If you knew the speed it was designed for then you could use this formula.
 
Last edited:

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