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Chapter 6: Q96P (page 148)

A child places a picnic basket on the outer rim of a merry-go-round that has a radius of 4.6 mand revolves once every 30s. (a) What is the speed of a point on that rim? (b)What is the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to stay on the ride?

Short Answer

Expert verified

a) Speed of a point on rim is 0.96m/s

b)μs=0.021

Step by step solution

01

Given

Merry-go-round that has a radius of 4.6 m and revolves once every 30 s

02

Understanding the concept

The problem is based on the centrifugal force. Centrifugal force is the apparent outward force on a mass when it is rotated. It also deals with the static friction.

Formula:

Centrifugal force is given by

F=mv2R

and the maximum value of static friction is given by

fs,max=μsmg.

03

Calculate the speed of a point on that rim

(a)

The distance traveled in one revolution is

2πR=2π4.6m=29m.

The speed is

v=29m/30s=0.96m/s

04

Calculate the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to stay on the ride 

(b)

According to Newton’s second law

fs=mv2/R=m0.20

As N = mg in this situation, the maximum possible static friction is,

fs,max=μsmg.

Equating this withlocalid="1660973301753" fs=m0.20μs=0.20/9.8=0.021

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Most popular questions from this chapter

The mysterious sliding stones.Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if the stones had been migrating (Fig. 6-18). For years, curiosity mounted about why the stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playground is about.What horizontal force must act on astone (a typical mass) to maintain the stone’s motion once a gust has started it moving? (Story continues with Problem 37)

In Fig. 6-54, the coefficient of kinetic friction between the block and inclined plane is 0.20, and angle θis 60°. What are the

(a) magnitude aand

(b) direction (up or down the plane) of the block’s acceleration if the block is sliding down the plane?

What are (c) aand (d) the direction if the block is sent sliding up the plane?

The coefficient of static friction between Teflon and scrambled eggs is about 0.04.What is the smallest angle from the horizontalthat will cause the eggs to slide across the bottom of a Teflon-coated skillet?

What is the terminal speed of a 6.00 kgspherical ball that has a radius of 30 cmand a drag coefficient of 1.60? The density of the air through which the ball falls is1.20kg/m3.

You testify as an expert witness in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill (Fig. 6-25). You find that the slope of the hill is θ=12.00, that the cars were separated by distance d=24.0mv0=18.0m/swhen the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was v0=18.0m/s.With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.60(dry road surface) and (b) 0.10(road surface covered with wet leaves)?
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