Question
A bicycle racer is riding at a speed of 13.2 m/s around a circular track with a radius of 40.0 m. If the magnitude of the centripetal force is 377 N, what is the combined mass of the bike and rider?
Answers
GPT 3.5
To find the combined mass of the bike and rider, we first need to calculate the centripetal force acting on the bicycle racer using the formula:
F_c = (m * v^2) / r
where:
F_c = centripetal force (377 N)
m = combined mass of the bike and rider (unknown)
v = speed of the bike racer (13.2 m/s)
r = radius of the circular track (40.0 m)
Plugging in the values we have:
377 = (m * (13.2)^2) / 40.0
Now we can solve for m:
377 = (m * 174.24) / 40.0
377 * 40.0 = m * 174.24
15080 = 174.24m
m = 15080 / 174.24
m ≈ 86.6 kg
Therefore, the combined mass of the bike and rider is approximately 86.6 kg.
F_c = (m * v^2) / r
where:
F_c = centripetal force (377 N)
m = combined mass of the bike and rider (unknown)
v = speed of the bike racer (13.2 m/s)
r = radius of the circular track (40.0 m)
Plugging in the values we have:
377 = (m * (13.2)^2) / 40.0
Now we can solve for m:
377 = (m * 174.24) / 40.0
377 * 40.0 = m * 174.24
15080 = 174.24m
m = 15080 / 174.24
m ≈ 86.6 kg
Therefore, the combined mass of the bike and rider is approximately 86.6 kg.