A bicyclist is riding at a tangential speed of 13.9 m/s around a circular track with a radius of 38.4 m.
If the magnitude of the force that maintains the bike’s circular motion is 378 N, what is the combined mass of the bicycle and rider?
Answer in units of kg
To find the combined mass of the bicycle and the rider, we can use the concept of centripetal force.
The centripetal force is given by the formula:
Fc = (m * v^2) / r
Where Fc is the centripetal force, m is the mass of the object, v is the tangential speed, and r is the radius of the circular track.
In this case, we're given that the tangential speed (v) is 13.9 m/s, the radius (r) is 38.4 m, and the magnitude of the force (Fc) is 378 N.
We can rearrange the formula to solve for mass (m):
m = (Fc * r) / v^2
Substituting the given values into the formula:
m = (378 N * 38.4 m) / (13.9 m/s)^2
Calculating the equation:
m = 14785.28 N * m / 192.1 m^2/s^2
m ≈ 76.92 kg
Therefore, the combined mass of the bicycle and rider is approximately 76.92 kg.