/*! 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 45 A particle moves along a curve o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 45

A particle moves along a curve of unknown shape but magnitude of force \(F\) is constant and always acts along tangent to the curve. Then : (a) \(\overrightarrow{\text { F }}\) may be conservative (b) \(\vec{F}\) must be conservative (c) \(\overrightarrow{\mathbf{F}}\) may be non-conservative (d) \(\overrightarrow{\mathbf{F}}\) must be non-conservative

Short Answer

Expert verified
(c) \(\overrightarrow{F}\) may be non-conservative.

Step by step solution

01

Understanding the Problem

We are asked to determine the conservative nature of the force \(\overrightarrow{F}\) when it acts constantly along the tangent to a curve the particle is moving on.
02

Definition of Conservative Force

A force is defined as conservative if the work done by the force on an object moving between two points is independent of the path taken. Another property is that a conservative force can be associated with a potential energy.
03

Implications of Force along Tangent

If \(\overrightarrow{F}\) always acts along the tangent to the curve, this implies that the work done by the force depends on the path since it directly impacts the distance covered even when the total displacement is zero.
04

Path Dependence and Non-Conservative Forces

Forces that depend on the actual path taken are considered non-conservative since the work done over a closed path is not zero. As \(\overrightarrow{F}\) is always along the tangent, work varies with different paths.
05

Conclusion Regarding the Force

Given that \(\overrightarrow{F}\) acts tangent to a curve and makes the work path-dependent, \(\overrightarrow{F}\) is not necessarily tied to a fixed potential energy. Therefore, \(\overrightarrow{F}\) may be non-conservative.

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.

Non-Conservative Force
In physics, forces can be categorized as either conservative or non-conservative. A non-conservative force is one where the work done by or against the force on a moving object depends on the path taken between the initial and final points. Some common examples of non-conservative forces include friction, air resistance, and tension. Unlike conservative forces, non-conservative forces dissipate energy, usually in the form of heat or sound, making it impossible to fully recover the total mechanical energy. This loss of energy means that the work done by a non-conservative force over a closed path is not zero.
  • Work done is path-dependent.
  • Examples include friction and air resistance.
  • They lead to dissipation of mechanical energy.
When a force like \(\overrightarrow{F}\)\ always acts tangent to a curve, the path becomes crucial, implying path dependence and suggesting the force might be non-conservative.
Potential Energy
Potential energy is the stored energy in a system resulting from the position or configuration of its components. Only conservative forces have an associated potential energy because the work done by these forces is path-independent, meaning it only depends on the initial and final positions of the object. Take gravity as an example: when an object is lifted to a certain height, it gains gravitational potential energy \(U = mgh\), with \(m\) being mass, \(g\) the acceleration due to gravity, and \(h\) the height.
  • Associated only with conservative forces.
  • Depends on position, not path.
  • Serves as a form of stored energy.
The \(\overrightarrow{F}\)\ in our case does not have a fixed potential energy since it鈥檚 path-dependent, indicating its non-conservative nature.
Path Dependence
Path dependence is a concept that denotes the reliance of the work done by a force on the specific route taken between two points. This is a key characteristic of non-conservative forces. In cases where path dependence is observed, the amount of work done varies even if the starting and ending positions of an object are the same. For example, the work done against friction will vary depending on how far and over what surfaces an object travels.
  • Work varies based on path taken.
  • Common in cases involving non-conservative forces.
  • Leads to variable energy retention and dissipation.
For the force \(\overrightarrow{F}\)\ in our exercise, acting along the tangent to the curve implies that the work is path-dependent, further supporting that it may not be conservative.

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

The momentum of a body of mass \(5 \mathrm{~kg}\) is \(10 \mathrm{~kg} \mathrm{~m} / \mathrm{s}\). A force of \(2 \mathrm{~N}\) acts on the body in the direction of motion for \(5 \mathrm{sec}\), the increase in the kinetic energy is: (a) \(15 \mathrm{~J}\) (b) \(50 \mathrm{~J}\) (c) \(30 \mathrm{~J}\) (d) none of these

Two identical cylindrical shape vessels are placed, \(A\) at ground and \(B\) at height \(h\). Each contains liquid of density \(\rho\) and the heights of liquid in \(A\) and \(B\) are \(h_{1}\) and \(h_{2}\) respectively. The area of either base is \(A\). The total potential energy of liquid system with respect to ground is: (a) \(\frac{A p g}{2}\left(h_{1}^{2}+h_{2}^{2}+2 h h_{2}\right)\) (b) \(\frac{A \rho g}{2}\left(h_{1}+h_{2}\right)^{2}+h_{2}^{2}\) (c) \(h \cdot A p g\left(h_{1}+h+h_{2}\right)\) (d) \(\frac{A p g}{2}\left(\frac{h_{1}+h}{2}\right)+h_{2}^{2}\)

The earth's radius is \(R\) and acceleration due to gravity at its surface is \(g\). If a body of mass \(m\) is sent to a height \(h=\frac{R}{5}\) from the earth's surface, the potential energy increases by : (a) \(m g h\) (b) \(\frac{4}{5} m g h\) (c) \(\frac{5}{6} m g h\) (d) \(\frac{6}{7} m g h\)

A bomb of mass \(M\) at rest explodes into two fragments of masses \(m_{1}\) and \(m_{2}\). The total energy released in the explosion is \(E\). If \(E_{1}\) and \(E_{2}\) represent the energies carried by masses \(m_{1}\) and \(m_{2}\) respectively, then which of the following is correct? (a) \(E_{1}=\frac{m_{2}}{M} E\) (b) \(E_{1}=\frac{m_{1}}{m_{2}} E\) (c) \(E_{1}=\frac{m_{1}}{M} E\) (d) \(E_{1}=\frac{m_{2}}{m_{1}} E\)

A constant force of \(5 \mathrm{~N}\) is applied on a block of mass 20 \(\mathrm{kg}\) for a distance of \(2.0 \mathrm{~m}\), the kinetic energy acquired by the block is: (a) \(20 \mathrm{~J}\) (b) \(15 \mathrm{~J}\) (c) \(10 \mathrm{~J}\) (d) \(5 \mathrm{~J}\)
See all solutions

Recommended explanations on Physics Textbooks

Dynamics

Read Explanation

Linear Momentum

Read Explanation

Electrostatics

Read Explanation

Fundamentals of Physics

Read Explanation

Space Physics

Read Explanation

Energy 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.