Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

A5.00kgstone is rubbed across the horizontal ceiling of a cave passageway (Fig. 6-48). If the coefficient of kinetic friction is0.65and the force applied to the stone is angled atθ=70.0°, what must the magnitude of the force be for the stone to move at constant velocity?

Short Answer

Expert verified

F=118 N

Step by step solution

01

Given data

  • Mass of stone,m=5.00 kg.
  • Coefficient of friction,μk=0.65.
  • The angle of force,θ=70.0o
02

To understand the concept

The problem deals with Newton’s second law of motion, which states that the acceleration of an object is dependent upon the net force acting upon the object and the mass of the object.

Draw the free body diagram of the stone. Then, applying Newton’s second law, the given problem can be solved.

03

Draw the free body diagram and write force equations

The free-body diagram for the stone is shown below, with Fbeing the force applied to the stone, FNthe normal downward force of the ceiling on the stone, mgthe force of gravity, and fthe force of friction. We take the +xdirection to be horizontal to the right and the +ydirection to be up.

The equations for thexand theycomponents of the force according to Newton's second law are:

role="math" localid="1661240446674" Fx=Fcosθf=ma

Fy=FsinθFNmg=0

04

Calculate the magnitude of the force for the stone to move at constant velocity 

Friction can be written as,

f=μkFN

f=μk(Fsinθmg)

This expression is substituted forfin the first equation to obtain as:

Fcosθμk(Fsinθmg)=ma.

For a=0, the force is,

F=μkmgcosθμksinθ

With μk=0.65,m=5.0 kg, and θ=70o, we can write the above expression as,

F=0.65×5.0 kg×9.8 m/s2cos70o0.65sin70oF=118 N

Thus, the magnitude of the force must be 118 N for the stone to move at constant velocity.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Figure 6-16 shows the overhead view of the path of an amusement-park ride that travels at constant speed through five circular arcs of radii,R0,2R0and3R0. Rank the arcs according to the magnitude of the centripetal force on a rider traveling in the arcs, greatest first.

A slide-loving pig slides down a certain35slide in twice the time it would take to slide down a frictionless35slide.What is the coefficient of kinetic friction between the pig and the slide?

A certain string can withstand a maximum tension of 40 Nwithout breaking. A child ties a 0.37 kgstone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 M, slowly increasing the speed until the string breaks. (a) Where is the stone on its path when the string breaks? (b) What is the speed of the stone as the string breaks?

The terminal speed of a sky diver is 160km/hin the spread-eagle position and310km/h in the nosedive position. Assuming that the diver’s drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in the faster position.

Continuation of Problem 8. Now assume that Eq. 6-14 gives the magnitude of the air drag force on the typical 20kgstone, which presents to the wind a vertical cross-sectional area of0.040m2and has a drag coefficient C of0.80. (a) In kilometers per hour, what wind speedValong the ground is needed to maintain the stone’s motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of10m. Assume wind speeds are2.00 times those along the ground. (b) For your answer to (a), what wind speed would be reported for the storm? (c) Is that value reasonable for a high-speed wind in a storm?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free