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.

 

[rezeew]

Your work looks correct. The maximum acceleration that the car can have without sliding is 17.90 ft/s^2. This means that the car can accelerate up to 17.90 ft/s^2 without losing traction and sliding off the road. It is important for car manufacturers to consider this maximum acceleration when designing tires and other components of the vehicle to ensure safe and efficient driving.