/*! 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 11 A bedroom bureau with a mass of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 11

A bedroom bureau with a mass of \(45 \mathrm{~kg}\). including drawers and clothing, rests on the floor. (a) If the coefficient of static friction between the bureau and the floor is \(0.45\), what is the magnitude of the minimum horizontal force that a person must apply to start the bureau moving? (b) If the drawers and clothing, with \(17 \mathrm{~kg}\) mass, are removed before the bureau is pushed, what is the new minimum magnitude?

Short Answer

Expert verified
Minimum force to move bureau with everything: 198.45 N. Minimum force to move bureau without drawers and clothing: 123.48 N.

Step by step solution

01

Identify Given Data

Mass of bureau (including drawers and clothing) is given as \(45 \, \mathrm{kg}\). The coefficient of static friction is \(0.45\). The mass of the drawers and clothing that can be removed is \(17 \, \mathrm{kg}\).
02

Calculate the Normal Force

The normal force \( F_N \) is equal to the gravitational force acting on the bureau. Gravitational force is given by \( F_N = m \cdot g \), where \( m \) is the mass and \( g = 9.8 \, \mathrm{m/s^2} \) is the acceleration due to gravity.For part (a): \[ F_N = 45 \, \mathrm{kg} \cdot 9.8 \, \mathrm{m/s^2} = 441 \, \mathrm{N} \]
03

Calculate the Force of Static Friction

The force of static friction \( F_s \) can be calculated using \( F_s = \, \mu_s \cdot F_N \), where \( \mu_s \) is the coefficient of static friction.For part (a): \[ F_s = 0.45 \cdot 441 \, \mathrm{N} = 198.45 \, \mathrm{N} \]This is the minimum horizontal force required to start the bureau moving.
04

Recalculate the Normal Force after Removing Drawers and Clothing

After removing the drawers and clothing, the mass of the bureau becomes \[ 45 \, \mathrm{kg} - 17 \, \mathrm{kg} = 28 \, \mathrm{kg} \].The new normal force \( F_N \) is:\[ F_N = 28 \, \mathrm{kg} \cdot 9.8 \, \mathrm{m/s^2} = 274.4 \, \mathrm{N} \]
05

Calculate the New Force of Static Friction

With the reduced mass, the minimum force required to overcome static friction is:\[ F_s = 0.45 \cdot 274.4 \, \mathrm{N} = 123.48 \, \mathrm{N} \]

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.

Normal Force
The normal force is fundamental in understanding various physical interactions. Simply put, it is the force exerted by a surface to support the weight of an object resting on it. This force acts perpendicular to the surface. In our exercise, when the bureau rests on the floor, the floor exerts an upward normal force that balances the downward gravitational force. This concept is crucial because the normal force determines the frictional force, which we delve into next.
The magnitude of the normal force ( F_N ) can be calculated using:$$ F_N = m \times g $$ where $$ m $$ is the mass (kg) and $$ g = 9.8 \frac{m}{s^2} $$ due to Earth's gravity.
Coefficient of Static Friction
The coefficient of static friction ( \( \regex_p \) ) quantifies how much friction force resists the initiation of motion between two surfaces. This coefficient varies depending on the materials in contact. For instance, our exercise reveals a static friction coefficient of 0.45 between the floor and the bureau. Knowing this value helps us compute the resistive force before motion starts
To calculate the static friction force ( \(F_s \)), use the formula:$$ F_s = \regex_p \times F_N $$Remember, $$F_s $$ is the force needed to overcome to make objects move initially.
Gravitational Force
Gravitational force pulls objects toward the center of the Earth. Its magnitude depends on an object's mass and the Earth's gravity ($$ g = 9.8 \frac{m}{s^2} $$). For instance, a 45 kg bureau will have a gravitational force of:$$ F_g = 45 \times 9.8 = 441 N $$This force directly affects the normal force, which then influences the static friction force required to move the object. Understanding gravitational force is vital for solving problems involving motion and stability.
Newton's Laws of Motion
Newton's Laws of Motion help explain the behavior of objects in our physical world. The first law, often referred to as the law of inertia, tells us that an object stays at rest unless acted upon by an unbalanced force. This law is foundational in understanding why static friction must be overcome to move the bureau. The second law, ($$ F = ma $$), relates the force applied on an object to its mass and acceleration. In our exercise, we calculate forces resulting from the mass of the bureau and the acceleration due to gravity. Lastly, the third law states that for every action, there is an equal and opposite reaction. This principle helps understand the interaction between the ground and the bureau, ensuring the bureau does not sink but stays on the floor with a normal force exerted upwards.

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

During an Olympic bobsled run, the Jamaican team makes a turn of radius \(7.6 \mathrm{~m}\) at a speed of \(96.6 \mathrm{~km} / \mathrm{h}\). What is their acceleration in \(g\) -units? \((1 g\) -unit \(=\) \(\left.9.8 \mathrm{~m} / \mathrm{s}^{2} .\right)\)

While two forces act on it, a particle is to move at the constant velocity \(\vec{v}=(3 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}-(4 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}} .\) One of the forces is \(\vec{F}_{A}=(2 \mathrm{~N}) \hat{\mathrm{i}}+(-6 \mathrm{~N}) \hat{\mathrm{j}}\). What is the other force?

A \(68 \mathrm{~kg}\) crate is dragged across a floor by pulling on a rope attached to the crate and inclined \(15^{\circ}\) 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 \(\mu^{\text {kin }}\) \(=0.35\), what is the magnitude of the initial acceleration of the crate?

An electron with a speed of \(1.2 \times 10^{7} \mathrm{~m} / \mathrm{s}\) moves horizontally into a region where a constant vertical force of \(4.5 \times 10^{-16} \mathrm{~N}\) acts on it. The mass of the electron is \(9.11 \times 10^{-31} \mathrm{~kg} .\) Determine the vertical distance the electron is deflected during the time it has moved \(30 \mathrm{~mm}\) horizontally.

A \(1400 \mathrm{~kg}\) jet engine is fastened to the fuselage of a passenger jet by just three bolts (this is the usual practice). Assume that each bolt supports one-third of the load. (a) Calculate the force on each bolt as the plane waits in line for clearance to take off. (b) During flight, the plane encounters turbulence, which suddenly imparts an upward vertical acceleration of \(2.6 \mathrm{~m} / \mathrm{s}^{2}\) to the plane. Calculate the force on each bolt now.
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Electricity

Read Explanation

Scientific Method Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Modern Physics

Read Explanation

Astrophysics

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.