A bicyclist traveling with speed v=3.3 m/s on a flat road is making a turn with a radius r=8.6 m. The forces acting on the cyclist and cycle are the normal force (FN) and the friction force (Ffr) exerted by the road on the tires, and mg, the total weight of the cyclist and cycle. Calculate the tangent(theta) [called Static Stability Factor] for the values given.
I know that tangent(theta) must equal Ffr/FN, except I'm not sure how to calculate those forces. There are no specific values given for mass, so I'm assuming those must cancel. I'm not sure how to proceed, and how to come up with Ffr. Thank you for your help, please!
WEll, Ffr has to equal centipetal force, mv^2/r.
Solving for tangent(theta) using Ffr/Fn, where Ffr is equal to mv^2/(r), and Fn is equal to mg tells me it is an incorrect answer still. Do you have a different suggestion?
Thanks
To calculate the tangent of theta (also known as the Static Stability Factor), we need to determine the friction force (Ffr) and the normal force (FN) acting on the cyclist and cycle.
First, let's find the normal force (FN) which is the force exerted by the road on the tires, balancing the weight of the cyclist and cycle (mg).
FN = mg
Given that mass is not specified, let's assume an arbitrary mass of 1 kg for simplicity.
Now, let's calculate the friction force (Ffr) acting on the cyclist and cycle. The friction force is equal to the centripetal force required to keep the cyclist moving in a circle with radius r.
Ffr = mv²/r
Using the given values, v = 3.3 m/s and r = 8.6 m, and assuming a mass of 1 kg, we can calculate Ffr.
Ffr = (1 kg) * (3.3 m/s)² / 8.6 m
= 13.81 N
Now we can calculate the tangent of theta (Static Stability Factor) by dividing Ffr by FN.
tangent(theta) = Ffr / FN
tangent(theta) = 13.81 N / (1 kg * 9.8 m/s²)
= 1.41
Therefore, the tangent of theta (Static Stability Factor) for the given values is approximately 1.41.