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The coordinates of a bird flying in the xy plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2

1 answer:

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In a classical carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast en

g100num [7]

Answer:

- the speed of a person "stuck" to the wall is 14.8 m/s

- the normal force of the wall on a rider of m=54kg is 1851 N

- the minimum coefficient of friction needed between the wall and the person is 0.29

Explanation:

Given information:

the radius of the cylindrical room, R = 6.4 m

the room spin with frequency, ω = 22.1 rev/minutes = 22.1 $\frac{2\pi }{60}$ = 2.31 rad/s

mass of rider, m = 54 kg

the speed of a person "stuck" to the wall

v = ω R

= 2.31 x 6.4

= 14.8 m/s

the normal force of the wall on a rider

F = m a

a = ω^2 R

= $\frac{v^{2} }{R^{2} }$ R

= $\frac{v^{2} }{R}$

F = $\frac{mv^{2} }{R}$

= $\frac{(54)(14.8)^{2} }{6.4}$

= 1851 N

the minimum coefficient of friction needed between the wall and the person

F(friction) = μ N

W = μ N

m g = μ $\frac{mv^{2} }{R}$

g = μ $\frac{v^{2} }{R}$

μ = $\frac{gR}{v^{2} }$

= $\frac{(9.8) (6.4)}{14.8^{2} }$

= 0.29

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