# Dynamics - Normal and Tangential Motion

1. Feb 11, 2013

### aaronfue

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

ƩFn = man

3. The attempt at a solution

Ff = 1753 lb
v = 75 ft/s
ρ=560 ft
wcar = 3150 lb

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

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

ƩFn = man = $\frac{3150}{32.2}$*10.04 = 982.2 lb

1753 = √Ft2 + 982.22

Solving for Ft = 1452 lb;

Now solving for at → 1452 = $\frac{3150}{32.2}$*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.

2. Feb 11, 2013

### 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.

3. Feb 11, 2013

### aaronfue

Tangential was actually 14.85 ft/s^2.

And it makes sense too.

Thanks.

Last edited: Feb 11, 2013
4. Feb 11, 2013

### LawrenceC

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