- #1
aaronfue
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Homework Statement
The tires on a car are capable of exerting a maximum frictional force of 1753 lb. If the car is traveling at 75 ft.s and the curvature of the road is ρ=560 ft, what is the maximum acceleration that the car can have without sliding?
Homework Equations
ƩFn = man
The Attempt at a Solution
Ff = 1753 lb
v = 75 ft/s
ρ=560 ft
wcar = 3150 lb
an = [itex]\frac{v^2}{ρ}[/itex] = [itex]\frac{75^2}{560}[/itex] = 10.04 ft/s2
I believe that the acceleration would be the magnitude of the tangential and normal acceleration.
ƩFn = man = [itex]\frac{3150}{32.2}[/itex]*10.04 = 982.2 lb
1753 = √Ft2 + 982.22
Solving for Ft = 1452 lb;
Now solving for at → 1452 = [itex]\frac{3150}{32.2}[/itex]*at
at = 14.85 ft/s2
a = √at2 + an2 = √14.852 + 10.042 = 17.90 ft/s2
I'd appreciate it if someone could verify my work.