What is the smallest radius of an unbanked (flat) track around which a motorcyclist can travel if her speed is 25 km/h and the coefficient of static friction between the tires and road is 0.28?

To find the smallest radius of an unbanked (flat) track that a motorcyclist can travel, we can use the concept of centripetal force.

The centripetal force required to keep the motorcyclist moving in a circular path is provided by the friction force between the tires and the road.

The formula for centripetal force is given by:
Fc = m * v² / r

Where:
Fc is the centripetal force
m is the mass of the motorcyclist and the bike
v is the velocity of the motorcyclist
r is the radius of the circular path

In this case, we are given the speed of the motorcyclist, which is 25 km/h. However, we need to convert it to meters per second (m/s) in order to use the formula.

To convert km/h to m/s, we divide by 3.6 (since 1 km/h = 1000 m/3600 s = 1/3.6 m/s).

So, 25 km/h can be converted to (25/3.6) m/s ≈ 6.94 m/s.

Now, we can rearrange the formula to solve for the radius (r):

r = m * v² / (Fc)

We need to determine the value of the centripetal force (Fc). Since the friction force between the tires and the road provides the centripetal force, we use the formula:

Fc = μ * N

where:
μ is the coefficient of static friction between the tires and the road
N is the normal force exerted on the motorcycle, which is equal to the weight of the motorcyclist and the bike (N = m * g)

We are given the coefficient of static friction, which is 0.28.

Now, substituting the values into the formula:

Fc = μ * N

N = m * g

r = m * v² / (Fc)

we can calculate the radius (r) of the circular path. We will assume the mass (m) of the motorcyclist and the bike, as well as the acceleration due to gravity (g), to proceed with the calculations.