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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)渭s=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=渭smg.

03

Calculate the speed of a point on that rim

(a)

The distance traveled in one revolution is

2蟺搁=2蟺4.6m=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鈥檚 second law

fs=mv2/R=m0.20

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

fs,max=渭smg.

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

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Most popular questions from this chapter

A car weighing 10.7kNand traveling at 13.4 m/swithout negative lift attempts to round an unbanked curve with a radius of 61.0 m. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires and the road is 0.350, is the attempt at taking the curve successful?

In Fig. 6-37, a slab of mass m1=40kgrests on a frictionless floor, and a block of mas m2=10kgrests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force of magnitude 100Nbegins to pull directly on the block, as shown. In unit-vector notation, what are the resulting accelerations of (a) the block and (b) the slab?

Assume Eq. 6-14 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at1300km/h. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Making a reasonable guess of the pilot鈥檚 mass and using the appropriatevtvalue from Table 6-1, estimate the magnitudes of (a) the drag force on the pilot seatand (b) their horizontal deceleration (in terms of g), both just after ejection. (The result of (a) should indicate an engineering requirement: The seat must include a protective barrier to deflect the initial wind blast away from the pilot鈥檚 head)

In Fig. 6-57, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 250 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?

Engineering a highway curve.If a car goes through a curve too fast, the car tends to slide out of the curve. For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction water would drain). Consider a circular curve of radius R 200 mand bank angle u, where the coefficient of static friction between tires and pavement is. A car (without negative lift) is driven around the curve as shown in Fig. 6-11. (a) Find an expression for the car speed Vmaxthat puts the car on the verge of sliding out.

(b) On the same graph, plot Vmaxversus angle u for the range 0掳to50掳, first for渭s=0.60(dry pavement) and then for渭s=0.050(wet or icy pavement). In kilometers per hour, evaluateVmaxfor a bank angle of胃=10掳and for

(c)渭s=0.60and

(d)渭s=0.050. (Now you can see why accidents occur in highway curves when icy conditions are not obvious to drivers, who tend to drive at normal speeds.)
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