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A race car track has been constructed with the a bank angle of 32.2° so there is no friction force. The race car track has a curve radius of 360. m. What speeds, for the race cars, has the track been designed to accommodate? 15.1 m/s 47.1 m/s 2.22×103 m/s 54.6 m/s

Question

A race car track has been constructed with the a bank angle of 32.2° so there is no friction force. The race car track has a curve radius of 360. m. What speeds, for the race cars, has the track been designed to accommodate? 15.1 m/s 47.1 m/s 2.22×103 m/s 54.6 m/s

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Solution

The speed for which the race car track has been designed can be calculated using the formula for the speed of an object moving in a circular path under the effect of gravitational force and normal force only. This situation occurs when the banking angle of the track is such that no frictional force is required to keep the car in its circular path. The formula is:

v = sqrt(grtan(θ))

where: v is the speed, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), r is the radius of the circular path, and θ is the banking angle.

Substituting the given values:

v = sqrt(9.8 m/s² * 360 m * tan(32.2°))

Calculating the tangent of the angle and then the product:

v = sqrt(9.8 m/s² * 360 m * 0.625)

v = sqrt(2163 m²/s²)

v = 46.5 m/s

So, the closest speed to this result from the options given is 47.1 m/s.

This problem has been solved

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