/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 A horizontal force of \(10 \math... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 77

A horizontal force of \(10 \mathrm{~N}\) is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \(0.2\) (Fig. 7.349). The weight of the block is a. \(2 \mathrm{~N}\) b. \(20 \mathrm{~N}\) c. \(50 \mathrm{~N}\) d. \(100 \mathrm{~N}\)

Short Answer

Expert verified
The weight of the block is 2 N (Option a).

Step by step solution

01

Understand the problem

We need to find the weight of the block against a wall when a horizontal force is applied. The block remains stationary due to friction. Given: the force applied is \(10\, \text{N}\), and the coefficient of friction is \(0.2\).
02

Identify forces involved

The horizontal force exerted causes a frictional force that holds the block stationary. The weight of the block is balanced by this frictional force. We need to relate these forces using the coefficient of friction.
03

Express friction force

The maximum static frictional force \( f \) is given by \( f = \mu N \), where \( \mu \) is the coefficient of friction (0.2) and \( N \) is the normal force, equal to the horizontal force of \(10 \text{ N}\).
04

Calculate friction force

Calculate the maximum static friction: \[ f = 0.2 \times 10 \text{ N} = 2 \text{ N} \]. This friction force equals the weight of the block to keep it stationary.
05

Determine the weight of the block

Since the frictional force that holds the block is the same as its weight, the weight of the block is \(2 \text{ N}\).

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 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Static Friction
Static friction is the force that keeps an object at rest when placed against or on a surface. It works to prevent motion between two surfaces in contact.
In the scenario of the block against the wall, static friction provides the necessary resistance to hold the block stationary against gravity. When you apply a horizontal force on the block, the static friction acts upwards, counteracting the weight of the block and preventing it from slipping.
Static friction can vary up to a maximum value, depending on the nature of the surfaces in contact. The maximum value of static friction can be calculated using the formula:
  • \( f = \mu N \)
where \( \mu \) is the coefficient of static friction and \( N \) is the normal force. When the horizontal force applied equals the static friction, the block stays at rest.
Normal Force
The normal force is the support force exerted by a surface perpendicular to an object resting on it. It keeps the object from falling through the surface. In mechanics, it plays a crucial role in calculations involving friction.
For the block against the wall, the normal force is due to the horizontal push applied, which is \(10 \text{ N}\). This force acts parallel to the wall's surface, pushing the block slightly in. Since this force is perpendicular to the direction of gravity, it becomes the normal force in our calculations.
The normal force is essential for determining static friction, as static friction is proportional to the normal force. To prevent the block from sliding down due to gravity, we rely on the static friction created by the normal force.
Coefficient of Friction
The coefficient of friction \( (\mu) \) is a dimensionless value that describes the amount of friction between two surfaces. It's crucial when calculating both static and kinetic friction. This coefficient varies based on the materials in contact and their surface roughness.
In the problem, the coefficient of friction between the block and the wall is given as \(0.2\). This number helps determine how much frictional force can be generated when the block is pressed against the wall with a horizontal force.
A higher coefficient of friction suggests stronger frictional resistance, while a lower coefficient means less friction, making it easier for the block to slide. In our scenario, the coefficient of friction ensures that the static friction generated can exactly counteract the weight of the block, keeping it from moving.

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

Mark out the most appropriate statement. a. The normal force is the same thing as the weight. b. The normal force is different from the weight, but always has the same magnitude. c. The normal force is different from the weight, but the two form an action- reaction pair according to the Newton's third law. d. The normal force is different from the weight, but the two may have same magnitude in certain cases.

A body of mass \(m\) starting from rest slides down a frictionless inclined surface of gradient \(\tan \alpha\) fixed on the floor of a lift accelerating upward with acceleration \(a\). Taking width of inclined plane as \(W\), the time taken by body to slide from top to bottom of the plane is a. \(\left(\frac{2 W}{(g+a) \sin \alpha}\right)^{\frac{1}{2}}\) b. \(\left(\frac{4 W}{(g-a) \sin \alpha}\right)^{\frac{1}{2}}\) c. \(\left(\frac{4 W}{(g+a) \sin 2 \alpha}\right)^{\frac{1}{2}}\) d. \(\left(\frac{W}{(g+a) \sin 2 \alpha}\right)^{\frac{1}{2}}\)

An intersteller spacecraft far away from the influence of any star or planet is moving at high speed under the influence of fusion rockets (due to thrust exerted by fusion rockets, the spacecraft is accelerating). Suddenly the engine malfunctions and stops. The spacecraft will a. immediately stops, throwing all of the occupants to the front b. begins slowing down and eventually comes to rest c. keep moving at constant speed for a while, and then. begins to slow down d. keeps moving forever with constant speed

A block \(A\) of mass \(2 \mathrm{~kg}\) is placed over another block \(B\) of mass \(4 \mathrm{~kg}\) which is placed over a smooth horizontal ffoor. The coefficient of friction between \(A\) and \(B\) is \(0.4\). When a horizontal force of magnitude \(10 \mathrm{~N}\) is applied on \(A\), the acceleration of blocks \(A\) and \(B\) are a. \(1 \mathrm{~ms}^{-2}\) and \(2 \mathrm{~ms}^{-2}\), respectively. b. \(5 \mathrm{~ms}^{-2}\) and \(2.5 \mathrm{~ms}^{-2}\), respectively. c. Both the blocks will moves together with acceleration \(1 / 3 \mathrm{~ms}^{-2}\) d. Both the blocks will move together with acceleration \(5 / 3 \mathrm{~ms}^{-2}\)

A horizontal force of \(25 \mathrm{~N}\) is necessary to just hold a block stationary against a wall the coefficient of friction between the block and the wall is \(0.4\). The weight of the block is a. \(2.5 \mathrm{~N}\) b. \(20 \mathrm{~N}\) c. \(10 \mathrm{~N}\) d. \(5 \mathrm{~N}\)
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Classical Mechanics

Read Explanation

Force

Read Explanation

Radiation

Read Explanation

Waves Physics

Read Explanation

Engineering 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.