Amusement Park Physics: Solving for Friction Force in a Spinning Cylinder

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AI Thread Summary
In the discussion about the physics of a person leaning against the inner wall of a spinning cylinder, it is established that when the angular speed is doubled, the normal force increases significantly, leading to a quadrupling of the frictional force. This raises concerns about whether the increased friction could cause the person to move upward, despite gravity remaining constant. Participants clarify that friction acts to prevent relative motion and adjusts based on the load, but only up to a limit defined by the static friction coefficient. The conversation emphasizes that while friction can increase with added weight, it cannot exceed the maximum static friction threshold. Ultimately, the frictional force's behavior is crucial in understanding the dynamics of the scenario.
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Homework Statement



In an amusement park, a person leans against the inner wall of a spinning cylinder. Suppose the minimum angular speed needed so that the person doesn’t slide is w min. At this minimum speed call the friction force, F1. Suppose the cylinder rotates twice as fast. What is the new frictional force?

Homework Equations



F1 = mg
Normal force = N = m * v * v /R
friction <= coefficient static friction * N

The Attempt at a Solution



If w is doubled, then v is doubled and therefore N quadruples.
Therefore friction quadruples.
Therefore there is a net upward force (as mg is constant but friction has increased).
Therefore the person moves upwards.
I don't believe this will happen.
Where did I go wrong?

Obviously friction must remain <= mg but that is inconsistent with the equation:
friction <= coefficient static friction * N
 
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Frictional force comes into picture only during the relative motion between the surfaces.
Therefore friction quadruples means even heavier person may stay without slipping.
 
"Therefore friction quadruples means even heavier person may stay without slipping." Agreed.

"Frictional force comes into picture only during the relative motion between the surfaces." Agreed for dynamic friction.

Sorry. I still don't see why friction would remain the same if Friction = μ static * N
 
The friction is a self adjusting force, which prevents the relative motion between two surfaces due to irregularities on the surfaces. By adding extra load, the irregularities on the surface will not change. If you add force gradually, the frictional force will also increase gradually up to a certain limit. After this limiting value the body starts moving
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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