A bicycle racing track is a level circular road of radius 10 m. Three cyclists P, Q and R with identical cycles are cycling on the track with speeds 2 m/s, 3 m/s and 5 m/s respectively. If the coefficient of friction between the tyres and the road is 0.1, then which cyclist will slip? (Take \(g = 10 \, m/s^2\))
R only
For a cyclist moving on a level circular track, friction alone supplies the necessary centripetal force. No slipping occurs as long as \(\frac{mv^2}{r} \le \mu mg\), which gives the maximum safe speed \(v_{max} = \sqrt{\mu g r}\). Substituting \(\mu = 0.1\), \(g = 10 \, m/s^2\) and \(r = 10 \, m\): \(v_{max} = \sqrt{0.1 \times 10 \times 10} = \sqrt{10} \approx 3.16 \, m/s\). Cyclist P (2 m/s) and cyclist Q (3 m/s) both cycle below this limit, so they do not slip. Cyclist R (5 m/s) exceeds \(\sqrt{10} \, m/s\), so only R slips.
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