8.36 In an old-fashioned amusement park ride, passengers stand inside a 5.2-m -d

Question

8.36
In an old-fashioned amusement park ride, passengers stand inside a 5.2-m -diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed."
What is the minimum angular speed, in rpm , for which the ride is safe?
Express your answer using two significant figures.

Explanation / Answer

For minimum speed when the floor may be removed the friction is the limiting force which is equal to sN
so                     sN = mg
but normal force   N = mv2/r
so              s*mv2/r = mg
hence linear speed                                 v = rg/s                                    = 2.6*9.8/0.6                                    = 6.52 m/sec
Therefore angular speed                                 = v/r                                     = 6.52 m/s / 2.6 m                                    = 2.51rad/sec                                    = 0.4 rev/s                                    = 23.96 rpm

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.