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Chapter 6: Q41P (page 143)

A cat dozes on a stationary merry-go-round in an amusement park, at a radius of5.4mfrom the center of the ride. Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every6.0s.What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding (or the cat clinging with its claws)?

Short Answer

Expert verified

The least coefficient of static friction between the cat and the merry-go-round is0.60.

Step by step solution

01

Given

R=5.4mT=6.0s

02

Determining the concept

This problem is based on the concept of uniform circular motion. Uniform circular motion is a motion in which an object moves in a circular path with constant velocity.

Formula:

The velocity in uniform circular motion is given by,

v=2蟺RT

where, v is the velocity, R is the radius andTis the time period

03

Determining the least coefficient of static friction between the cat and the merry-go-round

As the cat moving in the circular motion, it has centripetal accelerati ac=v2R, and frictional force is also directed to the center of the circle.

By using the Newton鈥檚 2nd law along the horizontal direction,

-fs=-mv2R

渭smg=mv2R

渭s=v2gR=2蟺RT2gR=4蟺2RgT2=4脳蟺2脳5.49.81脳62=0.60

Hence, the least coefficient of static friction between the cat and the merry-go-round is 0.60.

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Most popular questions from this chapter

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?

A banked circular highway curve is designed for traffic moving at 60km/h. The radius of the curve is200m. Traffic is moving along the highway at40km/hon a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

A police officer in hot pursuit drives her car through a circular turn of radius 300mwith a constant speed of 80.0km/h. Her mass is55.0kg. What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider both horizontal and vertical forces)

The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction 0.25 ofwith the floor. If the train is initially moving at a speed of 48 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

A 12Nhorizontal force F鈬赌pushes a block weighing 5.0Nagainst a vertical wall (Fig. 6-26). The coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. Assume that the block is not moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?
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