Ch 07: Newton's Third Law

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 07: Newton's Third Law

Problem 40b

Chapter 7, Problem 40b

The 1.0 kg physics book in FIGURE P7.40 is connected by a string to a 500 g coffee cup. The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficients of friction are μ_s = 0.50 and μ_k = 0.20. At the highest point, does the book stick to the slope, or does it slide back down?

Verified step by step guidance

Identify the forces acting on the book and the coffee cup. For the book, the forces include gravity (acting down the slope), the normal force (perpendicular to the slope), friction (opposing motion), and the tension in the string. For the coffee cup, the forces include gravity (acting downward) and the tension in the string (acting upward).

Determine the maximum static friction force that can act on the book. The formula for static friction is:

f

_max=μ_sN, where

μ

_s is the coefficient of static friction and

N

is the normal force. The normal force can be calculated as

N = m g cos θ

, where

m

is the mass of the book,

g

is the acceleration due to gravity, and

θ

is the angle of the slope.

Compare the forces acting on the book at the highest point. At this point, the book is momentarily at rest, so the static friction force must balance the component of gravity pulling the book down the slope and the tension in the string pulling it up. Write the force balance equation:

f

_static=m_bookgsinθ-T, where

T

is the tension in the string.

Calculate the tension in the string due to the coffee cup. The tension is equal to the weight of the coffee cup:

T = m

_cupg, where

m

_cup is the mass of the coffee cup.

Compare the static friction force required to keep the book stationary with the maximum static friction force. If the required static friction force exceeds the maximum static friction force, the book will slide back down the slope. Otherwise, it will stick to the slope.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Friction

Friction is the force that opposes the relative motion of two surfaces in contact. It is characterized by two coefficients: static friction (μₛ), which prevents motion, and kinetic friction (μₖ), which acts when surfaces are sliding against each other. In this scenario, the static friction will determine whether the book can remain at rest at the highest point after being pushed up the slope.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this problem, the kinetic energy of the book when it is pushed up the slope will convert into gravitational potential energy as it rises, and any energy lost to friction will affect whether it can reach the highest point without sliding back down.

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). This law is crucial for analyzing the forces acting on the book as it moves up the slope, including gravitational force, frictional force, and the tension in the string connected to the coffee cup.

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Intro to Forces & Newton's Second Law

Related Practice

Textbook Question

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Textbook Question

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Textbook Question

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