You are designing a drawbridge that crosses a major waterway. While there should be no

cars on a drawbridge when the bridge goes up, things happen. Your lawyers want to

know whether cars will slide down the drawbridge when it goes up, and would prefer if

you designed it so most cars will not.

The frictional force acting upon the car (shown in the free body diagram above) changes with

respect to angle. Each frictional forces array will depend on two equations. The first is the

equation for static frictional force. The second is the equation for kinetic frictional force. At some

point, the bridge will get to an angle that will cause your car to slide. Because of the nature of

how static coefficients of friction are calculated, we know that the static coefficient of friction

relates to the angle at which an object will slide on a surface by the following equation:

= tan

For angles less than and equal to , we use the equation for static frictional force, which is the

amount of frictional force that keeps our free body diagram in equilibrium. This amount of force

is given as:

= sin

Where m is the mass of the car (given as 1000 kg), g is the gravitational constant 9.81 m/s2 ,

and incline is the current angle of incline.

For angles greater than , we use the equation for kinetic frictional force. This amount of force

is given as:

=

Where FN is the normal force, given by:

= cos

Write a function that determines the force of friction for any car on your drawbridge, for a given

set of angles and a given set of friction coefficients. Once you have created your function, try it

out for the following materials:

Material Static coefficient Kinetic coefficient k

Concrete, dry 1.00 0.60

Concrete, wet 0.65 0.45

"Wonder material," dry 1.05 0.75

"Wonder material," wet 0.30 0.10

Calculate the frictional force for dry and wet concrete for a range of acute angles. Repeat for

"wonder material."