# Grade 12 work energy and power pdf

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- Work,Energy and Power
- 8th Grade Energy Unit
- Work Energy and Power Conservation of Energy Collisions Notes in

## Work,Energy and Power

When the point of application of force moves in the direction of the applied force under its effect then work is said to be done. Force and displacement both are vector quantities but their product, work is a scalar quantity, hence work must be scalar product or dot product of force and displacement vector. Force varying with displacement In this condition we consider the force to be constant for any elementary displacement and work done in that elementary displacement is evaluated.

Total work is obtained by integrating the elementary work from initial to final limits. In this condition we consider the force to be constant for any elementary displacement and work done in that elementary displacement is evaluated.

If elementary displacement from M to N is ds, then elementary work done from M to N is. Thus work done in any part of the graph is equal to area under that part. Hence total work done from s 1 to s 2 will be given by the area enclosed under the graph from s 1 to s 2. Capacity of doing work by a body is known as energy. Note - Energy possessed by the body by virtue of any cause is equal to the total work done by thebody when the cause responsible for energy becomes completely extinct.

There are many types of energies like mechanical energy, electrical, magnetic, nuclear, solar, chemical etc. Energy possessed by the body by virtue of which it performs some mechanical work is known as mechanical energy. It is of basically two types-. Energy possessed by body due to virtue of its motion is known as the kinetic energy of the body.

Kinetic energy possessed by moving body is equal to total work done by the body just before coming out to rest. Energy possessed by the body by virtue of its position or state is known as potential energy. Example:- gravitational potential energy, elastic potential energy, electrostatic potential energy etc.

Energy possessed by a body by virtue of its height above surface of earth is known as gravitational potential energy. It is equal to the work done by the body situated at some height in returning back slowly to the surface of earth.

Consider a body of mass m situated at height h above the surface of earth. Force applied by the body in vertically downward direction is. This work was stored in the body in the form of gravitational potential energy due to its position. Energy possessed by the spring by virtue of compression or expansion against elastic force in the spring is known as elastic potential energy.

On increasing applied force spring further expands in order to increase restoring force for balancing the applied force. Thus restoring force developed within the spring is directed proportional to the extension produced in the spring. Hence force constant of string may be defined as the restoring force developed within spring when its length is changed by unity. Hence force constant of string may also be defined as the force required to change its length by unity in equilibrium.

Elastic potential energy of stretched spring will be equal to total work done by the spring in regaining its original length. If in the process of regaining its natural length, at any instant extension in the spring was x then force applied by spring is. If spring normalizes its length by elementary distance dx opposite to x under this force then work done by spring is. Total work done by the spring in regaining its original length is obtained in integrating dW from x 0 to 0.

It states that total work done on the body is equal to the change in kinetic energy. Provided body is confined to move horizontally and no dissipating forces are operating. Consider a body of man m moving with initial velocity v 1. After travelling through displacement s its final velocity becomes v 2 under the effect of force F.

It states that energy can neither be creased neither be destroyed. It can only be converted from one form to another. Forces are said to be conservative in nature if work done against thforces gets conversed in the body in form of potential energy.

Work done against these forces is never dissipated by being converted into nonusable forms of energy like heat, light, sound etc. Non conservative forces are the forces, work done against which does not get conserved in the body in the form of potential energy. Work done against these forces does not get conserved in the body in the form of P.

Work done against these forces is always dissipated by being converted into non usable forms of energy like heat, light, sound etc. Work done against non-conservative force is a path function and not a state function. Power developed within the body at any particular instant of time is known as instantaneous power. Collision between the two bodies is defined as mutual interaction of the bodies for a short interval of time due to which the energy and the momentum of the interacting bodies change.

That is the collision between perfectly elastic bodies. In this type of collision, since only conservative forces are operating between the interacting bodies, both kinetic energy and momentum of the system remains constant. That is the collision between perfectly inelastic or plastic bodies. After collision bodies stick together and move with some common velocity.

In this type of collision only momentum is conserved. Kinetic energy is not conserved due to the presence of non-conservative forces between the interacting bodies. That is the collision between the partially elastic bodies. In this type of collision bodies do separate from each other after collision but due to the involvement of non-conservative inelastic forces kinetic energy of the system is not conserved and only momentum is conserved.

Consider two bodies of masses m 1 and m 2 with their center of masses moving along the same straight line in same direction with initial velocities u and u 2 with m 1 after m 2. Collision starts as soon as the bodies come in contact.

Due to its greater velocity and inertia m 1 continues to push m 2 in the forward direction whereas m due to its small velocity and inertia pushes m 1 in the backward direction. Due to this pushing force involved between the two colliding bodies they get deformed at the point of contact and a part of their kinetic energy gets consumed in the deformation of the bodies. Also m 1 being pushed opposite to the direction of the motion goes on decreasing its velocity and m being pushed in the direction of motion continues increasing its velocity.

This process continues until both the bodies acquire the same common velocity v. Up to this stage there is maximum deformation in the bodies maximum part of their kinetic energy gets consumed in their deformation. Elastic collision In case of elastic collision bodies are perfectly elastic. Hence after their maximum deformation they have tendency to regain their original shapes, due to which they start pushing each other. Since m 2 is being pushed in the direction of motion its velocity goes on increasing and m 1 being pushed opposite to the direction of motion its velocity goes on decreasing.

Thus condition necessary for separation i. In such collision the part of kinetic energy of the bodies which has been consumed in the deformation of the bodies is again returned back to the system when the bodies regain their original shapes. Hence in such collision energy conservation can also be applied along with the momentum conservation. Applying energy conservation. Hence in perfectly elastic collision between two bodies of same mass, the velocities interchange. If a moving body elastically collides with a similar body at rest.

Then the moving body comes at rest and the body at rest starts moving with the velocity of the moving body.

Hence if a huge body elastically collides with a small body then there is almost no change in the velocity of the huge body but if the small body is initially at rest it gets thrown away with twice the velocity of the huge moving body.

Hence if a small body elastically collides with a huge body at rest then there is almost no change in the velocity of the huge body but if the huge body is initially at rest small body rebounds back with the same speed. In case of inelastic collision bodies are perfectly inelastic. Hence after their maximum deformation they have no tendency to regain their original shapes, due to which they continue moving with the same common velocity.

In such collision the part of kinetic energy of the bodies which has been consumed in the deformation of the bodies is permanently consumed in the deformation of the bodies against non-conservative inelastic forces. Hence in such collision energy conservation can-not be applied and only momentum conservation is applied. In this case bodies are partially elastic.

Hence after their maximum deformation they have tendency to regain their original shapes but not as much as perfectly elastic bodies.

Hence they do separate but their velocity of separation is not as much as in the case of perfectly elastic bodies i. In such collision the part of kinetic energy of the bodies which has been consumed in the deformation of the bodies is only slightly returned back to the system.

When the centers of mass of two bodies are not along the same straight line, the collision is said to be oblique. In such condition after collision bodies are deflected at some angle with the initial direction.

In this type of collision momentum conservation is applied separately along x-axis and y-axis. If the collision is perfectly elastic energy conservation is also applied. Case-1 For perfectly elastic collision, velocity of separation is equal to velocity of approach, therefore. Case-3 For partially elastic or partially inelastic collision, velocity of separation is less than velocity of approach, therefore.

Please send your queries to ncerthelp gmail. Link of our facebook page is given in sidebar. Copyright ncerthelp. Force varying with time In this condition we consider the force to be constant for any elementary displacement and work done in that elementary displacement is evaluated.

Therefore G. But in equilibrium, restoring force balances applied force. Work done against conservative forces is zero in a complete cycle. Work done against non-conservative force in a complete cycle is not zero. Average Power It is defined as the ratio of total work done by the body to total time taken Instantaneous Power Power developed within the body at any particular instant of time is known as instantaneous power.

Or It is defined as the ratio of energy output to energy input. Or I It is defined as the ratio of work output to work input. Types of Collision There are basically three types of collisions- i Elastic Collision — That is the collision between perfectly elastic bodies. Case 3- If a small body elastically collides with a huge body, Hence if a small body elastically collides with a huge body at rest then there is almost no change in the velocity of the huge body but if the huge body is initially at rest small body rebounds back with the same speed.

## 8th Grade Energy Unit

Any force which conserves mechanical energy, as opposed to a nonconservative force. See statement of conservation of mechanical energy. Property of conservative forces which states that the work done on any path between two given points is the same. The energy of configuration of a conservative system. For formulae, see Definition of potential energy, gravitational potential energy, and Definition of potential energy given a position-dependent force. The sum of the kinetic and potential energy of a conservative system. See definition of total mechanical energy.

When the point of application of force moves in the direction of the applied force under its effect then work is said to be done. Force and displacement both are vector quantities but their product, work is a scalar quantity, hence work must be scalar product or dot product of force and displacement vector. Force varying with displacement In this condition we consider the force to be constant for any elementary displacement and work done in that elementary displacement is evaluated. Total work is obtained by integrating the elementary work from initial to final limits. In this condition we consider the force to be constant for any elementary displacement and work done in that elementary displacement is evaluated.

In Grade 10, you saw that mechanical energy was conserved in the absence of non-conservative forces. It is important to know whether a force is an conservative force or an non-conservative force in the system, because this is related to whether the force can change an object's total mechanical energy when it does work on an object. For example, as an object falls in a gravitational field from a high elevation to a lower elevation, some of the object's potential energy is changed into kinetic energy. However, the sum of the kinetic and potential energies remain constant. We can investigate the effect of non-conservative forces on an object's total mechanical energy by rolling a ball along the floor from point A to point B.

## Work Energy and Power Conservation of Energy Collisions Notes in

Register Now. Hey there! We receieved your request. This signifies, when the force and displacement are in same direction, work done is positive.

#### Worked example 6: Work-energy theorem

Unit 5-Fresh and Salt Water Systems. Grade 8 English Textbook, created for the Fijian national syllabus Class 6. How it works: Identify the chapter in your Prentice Hall Physical Science textbook with which you need help. Resources for Grade 8 Physical Science — Mrs. Carol Ann One reading resource we use is the textbook "Physical Science," put out by Glencoe in Physical Sciences.

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