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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?

Verified Answer :

syed514

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

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