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Dynamics - Normal and Tangential Motion

by aaronfue
Tags: dynamics, motion, normal, tangential
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aaronfue
#1
Feb11-13, 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

ƩFn = man

3. 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.
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LawrenceC
#2
Feb11-13, 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.
aaronfue
#3
Feb11-13, 12:10 PM
P: 122
Quote Quote by LawrenceC View Post
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
#4
Feb11-13, 01:08 PM
P: 1,195
Dynamics - Normal and Tangential Motion

Quote Quote by aaronfue View Post
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.


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