Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 41

A cubical block rests on an inclined board with two sides parallel to the incline. The coefficient of static friction between block and board is \(0.95 .\) If the inclination angle of the board is increased, will the block first slide or first tip over?

Short Answer

Expert verified
The block will start sliding before it tips over when the angle of inclination is increased.

Step by step solution

01

Find the angle at which sliding starts

The friction force must be equal to the component of the weight along the incline for the block to start sliding. Using \( \mu = \frac{F_f}{F_n} \), where \( F_f \) is the friction force, \( F_n \) is the normal force and \( \mu \) is the coefficient of friction, we can find the critical angle \( \theta_s \) for sliding using \( \mu = \tan \theta_s \). Therefore, \( \theta_s = \arctan(\mu) \). With \( \mu = 0.95 \), we find \( \theta_s = \arctan(0.95) \).
02

Find the angle at which tipping starts

Now, for tipping to occur the line of action of the gravitational force must pass through an edge rather than the center of the base. The block will start tipping over when the perpendicular distance from the center of mass to the edge of the base is equal to half the length of the diagonal of the square base. Using the geometric relation, we find the critical angle for tipping, \( \theta_t \), as \( \theta_t = \arctan(\sqrt{2}) \).
03

Compare the critical angles

The next step is to compare these two angles to see if the block will slide or tip over first. Since \( \arctan(\sqrt{2}) \) is greater than \( \arctan(0.95) \), the block will start sliding before it tips over.

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.

Start your free trial

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

A 160 -kg highway sign of uniform density is \(2.3 \mathrm{m}\) wide and \(1.4 \mathrm{m}\) high. At one side it's secured to a pole with a single bolt, mounted a distance \(d\) from the top of the sign. The only other place where the sign contacts the pole is at its bottom corner. If the bolt can sustain a horizontal tension of \(2.1 \mathrm{kN},\) what's the maximum permissible value for the distance \(d\) ?

A uniform 5.0 -kg ladder is leaning against a frictionless vertical wall, with which it makes a \(15^{\circ}\) angle. The coefficient of friction between ladder and ground is \(0.26 .\) Can a \(65-\mathrm{kg}\) person climb to the top of the ladder without it slipping? If not, how high can that person climb? If so, how massive a person would make the ladder slip?

A 4.2 -m-long beam is supported by a cable at its center. A \(65-\mathrm{kg}\) steelworker stands at one end of the beam. Where should a \(190-\mathrm{kg}\) bucket of concrete be suspended for the beam to be in static equilibrium?

A stilt walker is standing motionless on one stilt. What can you say about the location of the stilt walker's center of mass?

In addition to the wings, most airplanes have a smaller set of horizontal surfaces near the tail. Why? What does this suggest about the airplane's center of gravity?
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Radiation

Read Explanation

Force

Read Explanation

Electricity

Read Explanation

Electricity and Magnetism

Read Explanation

Nuclear Physics

Read Explanation
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