Question

a 5900-pound vehicle is driven at a speed of 30 miles per hour on a circular interchange of radius 100 feet. to keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? (round your answer to one decimal place.)

Answer 1

To find the frictional force that prevents the vehicle from skidding, we convert its weight to mass, calculate the centripetal force using the formula Fc=mv^2/r, and equate it to the required frictional force.

Step-by-step explanation:

To determine the frictional force that must be exerted on the tires of a 5900-pound vehicle to prevent it from skidding on a circular interchange, we first need to convert the weight of the vehicle into mass and calculate the centripetal force required for circular motion at the given speed and radius.

The vehicle's weight must be converted from pounds to kilograms (1 pound = 0.453592 kg). Then, the centripetal force (Fc) can be calculated using the formula Fc = mv2/r, where m is the mass of the vehicle, v is the velocity in meters per second, and r is the radius of the curve in meters.

After calculating the centripetal force, we know that this force has to be provided by the friction between the tires and the road. Hence, the minimum frictional force must be equal to the centripetal force to keep the vehicle from skidding. We can round this result to one decimal place as requested.