You’re driving your pickup car around a curve that has a radius of 40 m with a 20 degree bank to it. How fast can you drive around this curve with rubber tires on a concrete road without sliding off the road? (hint: look up the kinetic coefficient of friction)

21.7 m/s

Explanation:

To solve this problem, we have to write the equations of motion along the two directions: horizontal and vertical.

Horizontal direction:

Vertical direction:

where:

N is the normal reaction on the car

is the banking angle of the road

is the coefficient of friction of concrete

m is the mass of the car

v is the speed of the car

r = 40 m is the radius of the curve

is the acceleration due to gravity

Combining the two equations together, we can find the maximum speed allowed for the car:

And substituting the data we have, we find:

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