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Dynamics  Normal and Tangential Motion 
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#1
Feb1113, 09:28 AM

P: 122

1. The problem statement, all variables and given/known data
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? 2. Relevant equations ƩF_{n} = ma_{n} 3. The attempt at a solution F_{f} = 1753 lb v = 75 ft/s ρ=560 ft w_{car} = 3150 lb a_{n} = [itex]\frac{v^2}{ρ}[/itex] = [itex]\frac{75^2}{560}[/itex] = 10.04 ft/s^{2} I believe that the acceleration would be the magnitude of the tangential and normal acceleration. ƩF_{n} = ma_{n} = [itex]\frac{3150}{32.2}[/itex]*10.04 = 982.2 lb 1753 = √F_{t}^{2} + 982.2^{2} Solving for F_{t} = 1452 lb; Now solving for a_{t} → 1452 = [itex]\frac{3150}{32.2}[/itex]*a_{t} a_{t} = 14.85 ft/s^{2} a = √a_{t}^{2} + a_{n}^{2} = √14.85^{2} + 10.04^{2} = 17.90 ft/s^{2} I'd appreciate it if someone could verify my work. 


#2
Feb1113, 10:26 AM

P: 1,195

I get the same answer as you. I think the question is asking for the maximum tangential acceleration which is 10.04 ft/sec^2.



#3
Feb1113, 12:10 PM

P: 122

And it makes sense too. Thanks. 


#4
Feb1113, 01:08 PM

P: 1,195

Dynamics  Normal and Tangential Motion



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