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Chapter 8: Q. 49 (page 201)

In an old-fashioned amusement park ride, passengers stand inside a 5.0-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?

Short Answer

Expert verified

The minimum angular speed for safe ride in rpm is 24.446 rpm

Step by step solution

01

Given Information

µ =0.60

r =2.5 m

02

Explanation

The frictional force is given by

f=μFn

Now equate force components

μmv2r=mg..........................(1)

So

v=rgμ…………….(2)

Substitute v=ωr , and solve for ω, we get

ω=gμr...............(3)

Substitute the given values in equation(3) we get

ω=9.8m/s2(0.6)(2.5m)=2.556rad/sec

Convert in rpm

ω=24.446 rpm

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Most popular questions from this chapter

A 1500kgcar takes a 50-m-radius unbanked curve at localid="1649866624550" 15m/s.What is the size of the friction force on the car?

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a. If the mission fails, how many hours is it until the asteroid impacts the earth?

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If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola described by the equationz=ω22gr2

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