Answer:
The smallest radius will be four (4) times the initial radius
Explanation:
The car maintains a constant angular speed. According to Newton's Second Law F = m a
1. [tex]F_{r}=m*A_{n}[/tex]
2. [tex]A_{n}=\frac{v^2}{R_{p}}[/tex]
Replacing 2 in 1
3. [tex]F_{r}=m*\frac{v^2}{R_{p}}[/tex]
Where:
Fr= Frictional force
Rp= Initial Radius
An= Centripetal Acceleration
M= Mass
V= Velocity
Also we have that:
4. [tex]F_{r}=\mu *W=\mu*m*g[/tex]
μ= Coefficient of friction between the car and the surface
M= Mass
W= Weight
G= Gravity
r is cleared from equation 3
5. [tex]R_{p}=m*\frac{v^2}{F_{r}}[/tex]
Replacing 4 in 5
6. [tex]R_{p}=m*\frac{v^2}{\mu*m*g}[/tex]
Simplifying
7. [tex]R_{p}=\frac{v^2}{\mu*g}[/tex]
Now we have a new velocity equal to twice the initial velocity, We replace it by 2v in equation 7
8. [tex]R_{n}=\frac{(2v)^2}{\mu*g}[/tex]
Computing
9. [tex]R_{n}=\frac{4v^2}{\mu*g}[/tex]
Replacing 5 in 9
[tex]R_{n}=4*R_{p}[/tex]
