What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 35 km/h and the μs between tires and track is 0.35?
friction force=centripetalforce
mu*mg=m* v^2/r
change km/h to m/s
To find the smallest radius of an unbanked track around which a bicyclist can travel, we can use the concept of centripetal force. The centripetal force required to keep an object moving in a circular path is given by the equation:
F = m * a
Where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration. In this case, the object is the bicyclist and the centripetal force is provided by the friction between the tires and the track.
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
Where v is the velocity of the bicyclist and r is the radius of the track.
Now, we can calculate the centripetal force:
F = m * (v^2 / r)
In this problem, the coefficient of static friction (μs) between the tires and the track is given as 0.35. The maximum static friction force (Fs) can be calculated as:
Fs = μs * N
Where N is the normal force acting on the tires, which is equal to the weight of the bicyclist (mg).
Now, we can equate the centripetal force to the maximum static friction force:
F = Fs
m * (v^2 / r) = μs * N
Since we're looking for the smallest radius, we want to find the minimum value of r. So, we need to calculate the maximum value of the normal force, which is when the bicyclist is on the verge of slipping:
N = mg
Finally, we can solve for the radius (r):
r = m * (v^2 / (μs * mg))
Let's calculate the value:
Given:
v = 35 km/h
μs = 0.35
First, we need to convert the velocity to meters per second:
v = 35 km/h = (35 * 1000) / (3600) m/s = 9.72 m/s
The mass of the bicyclist (m) and the acceleration due to gravity (g) are not given in the question. Without these values, we cannot calculate the exact radius.