Question

A bicyclist is riding at a tangential speed of 13.6 m/s around a circular track with a radius of 42.1 m. If the magnitude of the force that maintains the bike’s circular motion is 361 N, what is the combined mass of the bicycle and rider?

A) 18.3 kg
B) 24.6 kg
C) 31.4 kg
D) 52.5 kg

Answer 1

To find the combined mass of the bicycle and the rider, the centripetal force formula is used, yielding a mass of 18.3 kg.

Step-by-step explanation:

To find the combined mass of the bicycle and the rider, we can use the centripetal force formula, which is F = mv2/r, where F is the centripetal force, m is the mass, v is the tangential speed, and r is the radius of the circular path. Given a tangential speed of 13.6 m/s, a centripetal force of 361 N, and a radius of 42.1 m, we can rearrange the formula to solve for m: m = Fr/v2. Plugging in the known values, we get:
m = (361 N * 42.1 m) / (13.6 m/s)2 which simplifies to m = 18.3 kg. Therefore, the combined mass of the bicycle and rider is 18.3 kg, which corresponds to option A.