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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 鈥渟tick鈥� 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 鈥淣o children under 30 kg allowed.鈥� 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

碌 =0.60

r =2.5 m

02

Explanation

The frictional force is given by

f=渭Fn

Now equate force components

渭mv2r=mg..........................(1)

So

v=rg渭鈥�鈥�鈥�鈥�鈥�.(2)

Substitute v=蝇r , and solve for 蝇, we get

蝇=g渭r...............(3)

Substitute the given values in equation(3) we get

蝇=9.8m/s2(0.6)(2.5m)=2.556rad/sec

Convert in rpm

蝇=24.446 rpm

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Most popular questions from this chapter

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