What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 28 km/h and the μs between tires and track is 0.28? (Answer must be in meters)
To determine the smallest radius of an unbanked track that a bicyclist can travel around, we need to consider the forces acting on the bicycle. One of the key forces is the friction between the tires and the track, which provides the necessary centripetal force to keep the bicycle moving in a circular path.
The centripetal force can be calculated using the formula:
F = μs * m * g
Where:
F is the centripetal force
μs is the coefficient of static friction between the tires and the track
m is the mass of the bicyclist
g is the acceleration due to gravity (approximately 9.8 m/s²)
Since we are given the speed of the bicycle (28 km/h), we need to convert it to meters per second (m/s):
Speed = 28 km/h = (28 * 1000) m / (60 * 60) s = 7.78 m/s
Next, we need to calculate the mass of the bicyclist. Since the mass is not given, we'll assume a standard value of 70 kg.
Now, we can rearrange the formula for the centripetal force to solve for the radius of the track:
F = μs * m * g = (m * v²) / r
Where:
v is the velocity of the bicyclist
r is the radius of the track
Rearranging the formula to solve for r, we get:
r = (m * v²) / (μs * g)
Substituting the known values, we get:
r = (70 kg * (7.78 m/s)²) / (0.28 * 9.8 m/s²)
Calculating the value of r:
r ≈ 363.59 meters
Therefore, the smallest radius of an unbanked track that the bicyclist can travel around is approximately 363.59 meters.