The equation below gives the maximum velocity in miles per hour that a vehicle can safely travel around a curve of radius r feet when friction is f. If the velocity is greater than Vmax, the tires will slip. Engineers find that under snowy conditions, Vmax = 15 miles per hour for a freeway off-ramp that has a radius of 50 feet. To the nearest tenth, what is the coefficient of friction for the off-ramp in these conditions?

Question

Physics

Hurst

22 August, 02:58

The equation below gives the maximum velocity in miles per hour that a vehicle can safely travel around a curve of radius r feet when friction is f. If the velocity is greater than Vmax, the tires will slip. Engineers find that under snowy conditions, Vmax = 15 miles per hour for a freeway off-ramp that has a radius of 50 feet. To the nearest tenth, what is the coefficient of friction for the off-ramp in these conditions?

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Melissa Mccall · Answer 1

Vmax in this case is 15 mph.

The radius of the ramp is 50.

For simplicity, let's change Vmax to feet per second:

15 miles / hour * (1 hour / 3600 seconds) * (5280 feet / mile) = 22 feet per second

Using your formula:

22 fps = sqrt (14.88 * f * 50 feet)

484 (feet^2/second^2) = 744 feet * f

f = 1.54 ft/sec^2