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 centripetal force formula:
F = (mv^2) / r
Where:
F is the magnitude of the force,
m is the combined mass of the bicycle and rider,
v is the tangential speed,
and r is the radius of the circular track.
We can rearrange the formula to solve for m:
m = F * r / v^2
Substituting the given values into the formula:
m = 378 N * 38.4 m / (13.9 m/s)^2
Now, let's calculate the combined mass:
m = 147196.66 kg / (193.21 m^2/s^2)
m ≈ 762.04 kg
Therefore, the combined mass of the bicycle and the rider is approximately 762.04 kg.