A bicyclist travels in a circle of radius 31.0 m at a constant speed of 5.00 m/s. The bicycle-rider mass is 88.0 kg.
(a) Calculate the magnitude of the force of friction on the bicycle from the road.
N
(b) Calculate the magnitude of the net force on the bicycle from the road.
N
To calculate the magnitude of the force of friction on the bicycle from the road, we can use the formula for centripetal force:
F_centripetal = m * v^2 / r
where m is the mass of the bicycle-rider, v is the velocity, and r is the radius of the circle.
(a) Calculate the magnitude of the force of friction on the bicycle from the road:
F_friction = F_centripetal
F_friction = m * v^2 / r
F_friction = 88.0 kg * (5.00 m/s)^2 / 31.0 m
F_friction ≈ 71.29 N
Therefore, the magnitude of the force of friction on the bicycle from the road is approximately 71.29 N.
(b) The net force on the bicycle from the road is equal to the centripetal force. So, the magnitude of the net force is also 71.29 N.
To calculate the magnitude of the force of friction on the bicycle from the road, we need to use the centripetal force formula. The centripetal force is provided by the frictional force between the bicycle tires and the road.
The formula for centripetal force is:
F = (m * v^2) / r
where:
F is the centripetal force,
m is the mass of the object (the bicycle-rider) = 88.0 kg,
v is the velocity of the object = 5.00 m/s, and
r is the radius of the circle = 31.0 m.
(a) To calculate the magnitude of the force of friction on the bicycle from the road, we use the formula for centripetal force:
F = (m * v^2) / r
F = (88.0 kg * (5.00 m/s)^2) / 31.0 m
Calculating this expression, we find:
F = (88.0 * 25.0) / 31.0
F = 2200.0 / 31.0
F ≈ 70.97 N
Therefore, the magnitude of the force of friction on the bicycle from the road is approximately 70.97 N.
(b) The magnitude of the net force on the bicycle from the road can be calculated by subtracting the force of friction from the centripetal force:
Net force = Centripetal force - Force of friction
Net force = F - F_friction
Net force = F - 70.97 N
Since the centripetal force and the force of friction are in opposite directions, the net force on the bicycle from the road will be the difference between these two forces.
Therefore, the magnitude of the net force on the bicycle from the road is F - 70.97 N.