A bicyclist travels in a circle of radius 26.4 m at a constant speed of 7.33 m/s. The bicycle-rider mass is 82.0 kg. Calculate the magnitudes of (a) the force of friction on the bicycle from the road and (b) the net force on the bicycle from the road.
Question
Answer:
(a) 166.89 N.
(b) 820.75 N
Explanation:
(a)
From the question, The horizontal component of force that act on the bicycle = Frictional Force.
Fr = mv²/r…………………… Equation 1
Where Fr = Frictional force, m = mass of bicycle-ride, v = velocity of the bicycle rider, r = radius of the circle.
Given: m = 82 kg, v = 7.33 m/s, r = 26.4 m
Substitute into equation 1
Fr = 82(7.33²)/26.4
Fr = 4405.7698/26.4
Fr = 166.89 N.
(b)
Net force on the bicycle = √(Fr²+Fv²)
F’ = √(Fr²+Fv²)………………….. Equation 2
Where F’ = Net force on the bicycle, Fv = Vertical force,
But,
Fv = mg………… Equation 3
Where g = acceleration due to gravity.
Given: m = 82 kg, g = 9.8 m/s²
Substitute into equation 3
Fv = 82(9.8)
Fv = 803.6 N
Substitute into equation 2
F’ = √(166.89²+803.6²)
F’ = √(673625.23)
F’ = 820.75 N