# Fundamentals of Physics Chapter 8 Solutions: Potential Energy and Conservation of Energy

Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions for ‘Potential Energy and Conservation of Energy’ are designed to help you prepare for JEE and CBSE Physics exams. The chapter of Resnick Halliday Walker discusses the distinction between conservative and nonconservative force, work done by conservative forces for the motion of a particle between two points, gravitational and potential energy, the elastic potential energy of a block spring system.

There are a total of 136 questions in Resnick Halliday and Walker Fundamentals of Physics Potential Energy and Conservation of Energy. The questions are put into 5 modules and are based on all the topics that are discussed in the chapter such as potential energy, conservation of mechanical energy, reading the potential energy curve, work done on a system by an external force, and conservation of energy. After solving these questions you will be able to understand the chapter to the core. It is very important if you are planning for competitive exams like IIT JEE or NEET. The practise questions will help you gain confidence for such exams.

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## Important Topics for Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions Chapter 8: Potential Energy and Conservation of Energy

Essential topics discussed in the chapter that are covered in Resnick Halliday & Walker Volume 1 Solutions for Chapter 8 are as follows:

**Potential Energy**

Potential energy is in relation to the configuration of the system in which a conservative force acts. When a conservative force does work on a particle within the system the change occurs in the potential energy of the system that is formulated as:

ΔU = -W

Where, ΔU = Change in potential energy, W = work done on a system of particle

**Gravitational Potential energy**

The potential energy combined with the system consisting of earth and a nearby particle is called gravitational potential energy.

**Elastic Potential Energy**

The energy combined with the state of compression or extension of an elastic object is known as elastic potential energy.

**Conservation of Mechanical Energy**

The sum total of Kinetic Energy (K) and Potential Energy (U) is referred to as Mechanical energy.

E_{mec} = K+U

The principle of conservation of mechanical energy, in case of conservative forces working on an isolated system, the formula is written as:

K_{2}+ U_{2} = K_{1} + U_{1}

**Potential Energy Curve**

Cases in which one-dimensional force acts upon a particle, in potential energy work for a system. The force can be calculated as

F(x) = – dU(x)/dx

At any value of x, if Ux is mentioned on the graph then the force is the negative of the slope of the curve there and the kinetic energy is given by

K(x) = E_{mec} – U(x)

**Work Done on a System by an External Force**

Work (w) is the energy transferred to or from a system from an external force acting on the system. In case of application of more than the force on a system, their network is the transferred energy. When there is no involvement of any friction then the work done on the system is equivalent to a change in the mechanical energy of the system.

W = ΔE_{mec} = ΔK +ΔU

When a kinetic frictional force is acted upon the system as an external force, thermal energy of the system changes. The work done is then

W = ΔE_{mec} + ΔE_{th}

**Conservation of Energy**

The overall systems energy i.e the sum of mechanical energy and its internal energies, including thermal energy, can change only with the help of energy that is transferred to and from the system. It is an experimental fact that is known as the law of conservation of energy.

### Exercise Wise discussion of Halliday Resnick & Walker Volume 1 Solutions Chapter 8: Potential Energy and Conservation of Energy

**Module 1: Potential Energy**

The Resnick Halliday module comprises 8 questions in all in which you are required to answer the work done in gravitational force or calculation of the gravitational force, causes of change in the potential energy in the system, and calculation of gravitational potential energy.

**Module 2: Conservation of Mechanical Energy**

The Resnick Halliday and Walker module has overall 40 questions in which you will have to answer questions like determining the speed of an object using mechanical energy, calculating the magnitudes of different components, determining total mechanical energy of the system, and calculation of heights based on weighted objects.

**Module 3: Reading a Potential Energy Curve**

There are a total of 4 questions in this module. The questions are based on the concepts of potential energy curves. You will have to answer questions by finding equilibrium separation in terms of different forces applied, determining the least and greatest value of x particle can reach, determining the maximum kinetic energy of the particle.

**Module 4: Work Done on a System by an External Force**

The module comprises 4 questions. In this module, you will be asked questions like determining the work done by a workers force and thermal energy of the block-floor system, variations in the kinetic energy of the block and coefficient of the kinetic energy of the block.

**Module 5: Conservation of Energy**

The module consists of 19 questions in all. In this module, questions will be asked like how much is the mechanical energy of the ball, maximum kinetic energy of the block, original compression distance of the object, calculation of the speed, determining the equilibrium position of the object in different situations, and answering problems when variations made in the kinetic energy of the block.

**Module6: Additional Questions**

The additional questions module comprises 70 questions in total. This Resnick Halliday & Walker Physics module contains a mixture of questions based on the concepts discussed in the chapter. You will answer questions related from all the above modules like calculation of gravitational force, gravitational potential energy, calculating magnitudes, heights, determining mechanical energy, equilibrium separations, calculation of thermal energy, kinetic energy, speed and so on.

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