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Question
During a stunt, a cyclist (considered to be a particle) is undertaking horizontal circles inside a cylindrical well of radius 6.05 m. If the necessary friction coefficient is 0.5, how much minimum speed should the stunt artist maintain? The mass of the artist is 50 kg. If she/he increases the speed by 20%, how much will the force of friction be?
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Solution
Given data:
cylindrical well of radius (r) = 6.05 m
Coefficient of friction is (μ) = 0.5
Mass of the artist is m = 50 kg
Find Vmin = ?
The minimum velocity to maintain motion is given by
`"V"_"min" = sqrt("rg"/mu)`
`"V"_"min" = sqrt((6.05xx10)/0.5)` ....[g = 10 m/s2]
`"V"_"min" = sqrt(60.5/0.5)`
`"V"_"min" = sqrt(605/5)`
`"V"_"min" = sqrt121`
Vmin = 11 m/s
M = 50 kg,
V = Vmin + 20% Vmin,
fs = ? ...[Given]
This is the required minimum speed. So long as the cyclist is not sliding, at every instant, the force of static friction is
∴ fs = N = Mg
fs = 50 × 10
fs = 500 N
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