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 rider, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F = centripetal force
m = combined mass of the bicycle and rider
v = tangential speed of the bicyclist
r = radius of the circular track
Rearranging the formula to solve for the mass (m), we have:
m = (F * r) / v^2
Now, let's substitute the given values into the formula:
F = 378 N
r = 38.4 m
v = 13.9 m/s
m = (378 N * 38.4 m) / (13.9 m/s)^2
m = (14515.2 N*m) / 193.21 m^2/s^2
m = 75.092 kg
Therefore, the combined mass of the bicycle and rider is 75.092 kg.
To find the combined mass of the bicycle and rider, we can use centripetal force formula.
The centripetal force acting on an object moving in a circular path can be calculated using the formula:
F = (m * v^2) / r
Where:
F is the magnitude of the force
m is the mass of the object
v is the tangential speed
r is the radius
We can rearrange the formula to solve for the mass:
m = (F * r) / v^2
Substituting the given values:
F = 378 N
r = 38.4 m
v = 13.9 m/s
m = (378 N * 38.4 m) / (13.9 m/s)^2
Now, let's calculate the combined mass of the bicycle and rider using the formula.
m = (378 N * 38.4 m) / (13.9 m/s)^2
m ≈ 401.6 kg
Therefore, the combined mass of the bicycle and rider is approximately 401.6 kg.
F=ma=mv²/R
m=FR/ v²