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An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that a person inside is stuck to the wall and does not slide down when the floor drops away.
The acceleration due to gravity is 9.8 m/s/s.
Given g = 9.8 m/s/s, the coefficient u=0.444 of static friction between a person and the wall, and the radius of the cylinder R = 3.7 m. For simplicity, neglect the person's depth and assume he or she is just a physical point on the wall. The person's speed is
v= (2 Pi r)/ T
where T is the rotation period of the cylinder
Find the maximum rotation period T of the cylinder which would prevent a 65 kg person from falling down. Answer in units of s.

2007-12-16 12:48:57 · 3 answers · asked by Anonymous in Science & Mathematics Physics

3 answers

V = 2πr /T
The centripetal acceleration is a = v^2 /r = 4r π^2/T^2
The frictional acceleration acting up = μ a.
Acceleration acting down = g
g = μ a = μ 4r π^2/T^2
T^2 = μ 4r π^2 /g = 0.444*4*3.7* π^2 /9.8
T = 2.57s
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2007-12-16 13:38:12 · answer #1 · answered by Pearlsawme 7 · 0 0

To avoid the falling of the person from the wall his weight should be balanced by the frictional force between the wall & person.
Here the force of the person towards the wall is his centrifugal force, (m*v²/r). So, the normal reaction 'R' offered by the wall also will be equal to "m*v²/r".
Frictional force "μ*R" should be more than or equal to the weight of the person.
μ x R >/= m x g
μ x (m x v²) / r >/= m x g
v² >/= (m x g) / μ x m x r
v² >/= g / μr
v >/= √(g/μr)
v >/= √{9.8 / (.444 x 3.7)}
v >/= 2.44 m/s
Hence, the time period 'T' should be 'T' T ============

2007-12-16 22:00:23 · answer #2 · answered by Joymash 6 · 0 0

We need the friction force to equal the person's weight:

mg = μN

so

N = mg / μ

That force is what's keeping the person of mass m moving in a circle of radius r at angular velocity ω

F = m r ω²

Set them equal...

mg / μ = m r ω²

The mass cancels as expected. Plug in g, μ, and r and solve for ω, the minimum angular velocity required to prevent people of any mass from falling down. Then you can convert that into the maximum period requested.

2007-12-16 21:12:46 · answer #3 · answered by jgoulden 7 · 1 0

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