Posted by **mark** on Tuesday, October 5, 2010 at 8:10pm.

Let the radius of the circular segment be

108 m, the mass of the car 1861 kg, and

the coefficient of the static friction between

the road and the tire 0.9. The banking angle

is not given.

Find the magnitude of the normal force N which the road exerts on the car at the opti-mal speed (the speed at which the frictional

force is zero) of 72 km/h.

Answer in units of N.

- college physics -
**Sorab**, Wednesday, October 6, 2010 at 9:53pm
FBD: friction down angled road/ramp, normal force perpendicular to ramp, gravity down, impending motion up ramp.

Fnet = ma

In r direction,

Friction_r+N_r=mv^2/r

(f_s)(cosX)+NsinX=mv^2/r

uNcosX+NsinX=mv^2/r

N=(mv^2)/(ucosX+sinX) (1)

In z direction, NcosX-uNsinX-W=0

N=mg/(cosX-usinX) (2)

Set equations 1 and 2 equal, solve for X, substitute back into either 1 or 2, yielding N

- college physics -
**Sorab**, Wednesday, October 6, 2010 at 9:55pm
lol, Equation 1 is actually

N=(mv^2)/(r)(ucosX+sinX)

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