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

In Fig. 6-15, a horizontal force of 100Nis to be applied to a 10kg slab that is initially stationary on a frictionless floor, to accelerate the slab. A 10kg block lies on top of the slab; the coefficient of friction μbetween the block and the slab is not known, and the block might slip. In fact, the contact between the block and the slab might even be frictionless. (a) Considering that possibility, what is the possible range of values for the magnitude of the slab’s accelerationlocalid="1657173176346" aslab? (Hint:You don’t need written calculations; just consider extreme values for m.) (b) What is the possible range for the magnitudelocalid="1657173167508" ablockof the block’s acceleration?

Short Answer

Expert verified

a) The possible range of values for the magnitude of the slab’s acceleration is5m/s2-10m/s2 .

b) The possible range for the magnitude of the block’s acceleration is0m/s2-5m/s2 .

Step by step solution

01

The given data

a) Mass of the slab,M=10 kg

b) Mass of the block,m= 10 kg

c) Force on the slab,F=100 N

02

Understanding the concept of the friction

To find the acceleration of slab and block, we have to use Newton’s 2nd law of motion. For each given case of slipping and no slipping, we use the coefficient of friction accordingly to determine the minimum and the maximum possible values of the accelerations of the slab and the block.

Formula:

The force according to Newton’s second law,

F = ma (1)

03

a) Calculation of the possible range of slab’s acceleration

Case (1): No slipping

When no slipping occurs (μis at its maximum value.), then block and slab stick together.

By using equation (1) along the horizontal direction, we can get the acceleration of the slab as follows:

role="math" localid="1657172766626" F=M+maslabaslab=FM+m=100N10mg+10mg=5m/s2

Case (2): In case of slipping

When there is slipping between block and slab ( μ=0), then the slab and block will move separately.

By using equation (1) along the horizontal direction, we get the slab acceleration as follows:

role="math" localid="1657173053653" F=Maslabaslab=FM=100N10kg=10m/s2

Therefore the possible range of acceleration of the slab is5m/s2-10m/s2 .

04

b) Calculation of the possible range of the acceleration of the block

Case 1: When there is slipping

If the coefficient of friction is 0, i.e.μ=0, then the acceleration of the block is 0 as there is no force acting on the block.

ablock=0m/s2

Case 2: No slipping

If the value of the coefficient of friction is maximum, then block and slab are stick together, then the acceleration of the block is given using equation (1) as:

F=M+maslabaslab=FM_m=100N10kg+10kg=5m/s2

Therefore the possible range of acceleration of the block is0m/s2-5m/s2 .

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

In Fig. 6-34, blocks A and B have weights of 44Nand 22N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if μkbetween A and the table is 0.20. (b) Block C suddenly is lifted off A. What is the acceleration of block A if μkbetween A and the table is 0.15?

A person pushes horizontally with a force of220Non a55kgcrate to move it across a level floor. The coefficient of kinetic friction between the crate and the floor is0.35. What is the magnitude of (a) the frictional force and (b) the acceleration of the crate?

When the three blocks in Fig. 6-29 are released from rest, they accelerate with a magnitude of 0.500m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table?

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)

A 68kgcrate is dragged across a floor by pulling on a rope attached to the crate and inclined 15°above the horizontal. (a) If the coefficient of static friction is 0.50, what minimum force magnitude is required from the rope to start the crate moving? (b) If μk=0.35 , what is the magnitude of the initial acceleration of the crate?

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