Dynamics - Normal and Tangential Motion

[aaronfue]

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

ƩF_n = ma_n

The Attempt at a Solution

F_f = 1753 lb
v = 75 ft/s
ρ=560 ft
w_car = 3150 lb

a_n = \frac{v^2}{ρ} = \frac{75^2}{560} = 10.04 ft/s²

I believe that the acceleration would be the magnitude of the tangential and normal acceleration.

ƩF_n = ma_n = \frac{3150}{32.2}*10.04 = 982.2 lb

1753 = √F_t² + 982.2²

Solving for F_t = 1452 lb;

Now solving for a_t → 1452 = \frac{3150}{32.2}*a_t
a_t = 14.85 ft/s²

a = √a_t² + a_n² = √14.85² + 10.04² = 17.90 ft/s²

I'd appreciate it if someone could verify my work.

 

[LawrenceC]

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.

 

[aaronfue]

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.

Tangential was actually 14.85 ft/s^2.

And it makes sense too.

Thanks.

 

[LawrenceC]

Tangential was actually 14.85 ft/s^2.

And it makes sense too.

Thanks.

I typed the wrong number...should have typed 14.85 ft/s^2.