The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle of radius \left(\right. \frac{625}{8} \textrm{ }\textrm{ } cm \left.\right) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.8, and the angle θ in the drawing is 37°. How much time (in second) is required for your suitcase to go around once? (Assume limiting friction) (Take π2 = g)

Engineering

Physics

Variable Mass System

Question

The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle of radius $(\frac{625}{8} cm)$ as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.8, and the angle θ in the drawing is 37°. How much time (in second) is required for your suitcase to go around once? (Assume limiting friction) (Take π² = g)

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f cos θ – N sin θ = mω²r
f sin θ + N cos θ = mg
for limiting condtion f = μN
⇒ $\frac{ω^{2} r}{g}$ = $\frac{μcos θ - \sin θ}{\cos θ + μsin θ}$ = $\frac{0 .2}{6 .4}$
⇒ T = 10 s

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