A cyclist attempts to travel around a vertical circular track of radius 3.0m. Calculate the minimum speed he must have on entry in order to remain in contact with the sphere when he is upside down.
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Answer:
We need to consider force calculations
When you go in circular motion, there's a centripetal acceleration of mv²/r required. When cyclist is at the very top, the only forces providing this acceleration is his weight and any reaction force from the track.
To just remain in contact, reaction force = 0
Hence, mv²/r = mg
and v = √(gr) at the top
Supposed he did not add more power when he is on that circular track, we need to take into account KE loss due to increase in PE
so loss in KE = 1/2mV² - 1/2mv² = mg(6), V = entry speed
V² = v² + 12g = 15g
V = √(15g) m/s
V = 12.13 m/s
