Work and energy

WORK Introduction Consider the following day-to-day activities which we consider as work: Reading, speaking, singing, writing, thinking etc. We require energy to perform these activities, which we derive from the food we eat. But actually no work is involved in performing these activities.

Even if we push a wall with the maximum force that we can apply, the wall will not move. It will be interesting for us to note that even in this case, we are not doing any work at all! Work is not done in all the above activities because there is a basic difference between the term work and the term which we use for our daily activities.

Scientifically, work is defined as the work done by a force that causes a displacement in an object. If we push a book placed on a table with a force, then it will move to a certain distance. Scientifically, we will say that some work has been done on the book. In this case, work is done against frictional force, which exists between the book and the surface of the table.

If we lift the book to a certain height, then a force is exerted against gravity, which displaces the book to a certain height. Hence, we can say that work is done on the book against the force of gravity.

Work doneWhenever displacement is brought in the line of force applied we call it as work done. Mathematically work done is given a symbol W and it is defined as the product of force(F) and displacement(s).

There could be four different cases according to the force and displacement relationship. If:

+Force +Displacement = +Work -Force -Displacement = +Work -Force +Displacement = -Work+Force -Displacement = -Work These are the four cases through which we can define positive or negative work done.

Work Done By a Constant ForceA wooden block is kept on a table. When a force of magnitude F acts on the block, it gets displaced through a distance S in the direction of the applied force, as shown in the given figure.

The magnitude of work done is given by the product of force (F) and displacement (S). Let W be the work done on the block. ∴ Work = Force × Displacement W= F × SWork has magnitude only. It has no direction.

Unit of WorkTo obtain the unit of work, we substitute the SI units of force, i.e. N, and distance, i.e. m, in the equation of work. W = N × m = NmHence, the unit of work is Nm. In the honor of physicist James P. Joule, the SI unit of work is written as Joule (J).Hence, 1 J = 1 Nm1 Joule is defined as the amount of work done by a unit force such that it displaces an object by a distance of 1 m.

Work done against gravity

When force is applied on an object in order to lift it above the ground, it is said that work is done against the force of gravity.Assume that a constant force of magnitude F is applied on a block of mass m to lift it to a height h above the ground.

In this case, the work done by the force against gravity is given by the product of the weight of the block and the height through which it is lifted above the ground.Work done = Weight × HeightW = mg × hW= mghWhere, g is acceleration due to gravity.

Negative work  If the force acts opposite to the direction of displacement, then the WORK done will be negative i.e. W=F x (-s) or (-F x s). Here, the directions of displacement (S) and applied force (F) are exactly opposite to each other. Suppose, a soccer player moves backward while stopping a fast moving football. To move backward, he applies a force in the forward direction. Hence, we can say that the work done by the force is negative.

Zero WorkWhen a body moves through a distance at right angle to the direction of force, the work done by the force on the body is zero. A book kept on a table moves from point A to point B through a distance S. In this case, the work done on the book by gravitational force is zero because the force is acting at right angle to the displacement of the book.

Energy

The world requires a lot of energy. To satisfy this demand, we have natural energy sources such as the sun, wind, water at a height, tides, etc. We also have artificial energy sources such as petroleum, natural gas, etc.

Forms of energySome forms of energy are(i) Light(ii) Sound(iii) Heat(iv) Mechanical(v) Electrical(vi) Chemical(vii) Nuclear

Mechanical energyIt is the form of energy possessed by an object that has the potential to do work. It is caused by the motion or the position and configuration of the object. Mechanical energy is of two types.(i) Kinetic energy (caused by motion of the object)(ii) Potential energy (caused by position and configuration of the object)

Kinetic energyEnergy stored into an object due to its motion. A moving arrow can be embedded into an object. Hence, it is said that the arrow possesses kinetic energy. The elastic string of a catapult is stretched to throw a stone. The work done is stored in the stone and the string. After its release, the stone is said to possess kinetic energy.

A stone dropped from a height has the capability to create a depression in wet ground. Hence, the dropped stone has some amount of kinetic energy. A fired bullet is embedded in a wall or wooden block. Hence, it is said that a moving bullet possesses kinetic energy.

Formula for kinetic energyKinetic energy of a moving body is equal to the work required to change its velocity from u to v.Let a body of mass m be moving with a uniform velocity u. Let an external force be applied on it so that it displaces a distance s and its velocity becomes v.

We have velocity-position relation asv2 = u2 + 2aswhere, a → acceleration of the body during the change of velocityOr ………… (1)

Hence, work done on the body by the force will be given by, W=F×sF = ma

If the body was initially at rest, i.e. u = 0, then Since kinetic energy is equal to the work done on the body to change its velocity from 0 to v, we obtain

Hence, kinetic energy of a body increases with its velocity. Its SI unit is Joule (J).

Kinetic energy of a body is directly proportional to:(i) Its mass (m)(ii) The square of its velocity (v2)It is the kinetic energy of the wind that is used in windmills to generate electricity.

Potential EnergyThere are mainly two types of potential energy:Potential energy possessed by a body by virtue of its configuration is known as elastic potential energy

Potential energy possessed by a body by virtue of its position with respect to the ground is known as gravitational potential energy.

A body possesses potential energy by virtue of its configuration or position.

Potential energy of an object at an height………

Any object located at a height with respect to a certain reference level is said to possess energy called gravitational potential energy. This energy depends on this reference level (sometimes also referred as ground level or zero level).

When a ball is taken to the top floor from the ground floor, it acquires some gravitational potential energy. When this ball is dropped from a height h1 on the top floor, the zero level is the top floor itself. When the ball is dropped from a height h2 on the ground, the zero level is the ground. Since the distance covered by the ball will be greater in the second case, i.e.h2 > h1, it rebounded to a greater height from the ground than that from the top floor.

Hence, we conclude from the above discussion that potential energy stored in a body is directly proportional to its height with respect to zero level.

Formula for gravitational potential energy

Consider an object of mass 'm', raised through a height 'h' above the earth's surface. The work done against gravity gets stored in the object as its Potential Energy (Gravitational Potential Energy). Therefore, Potential energy = work done in raising the object through a height ‘h’.

Consider an object of mass 'm', raised through a height 'h', then its Potential energy is given by:Potential energy = F × h .......................(1)where, F= force,h = height attained due to its displacement.But F = mg (Newton's second law of motion)Substituting for F in equation (1) we get,Potential energy, P.E = mgh or= mghThe above relation is called Potential Energy Equation.

Law Of Conservation Of Energy

Energy can neither be created nor destroyed. It can only be transformed from one form to another. In other words, the total amount of energy in a system always remains constant.For example, in a burning candle, chemical energy stored in the wax is transformed into light and heat energy. The total energy, before and after burning of the candle, remains constant.

Consider a simple example. Let an object of mass, m be made to fall freely from a height, h. At the start, the potential energy is mgh and kinetic energy is zero. Why is the kinetic energy zero? It is zero because its velocity is zero. The total energy of the object is thus mgh. As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, the kinetic energy would be .

As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h = 0 and v will be the highest. Therefore, the kinetic energy would be the largest and potential energy the least. However, the sum of the potential energy and kinetic energy of the object would be the same at all points. That is, potential energy + kinetic energy = constant or,

The sum of kinetic energy and potential energy of an object is its total mechanical energy. We find that during the free fall of the object, the decrease in potential energy, at any point in its path, appears as an equal amount of increase in kinetic energy. (Here the effect ofair resistance on the motion of the object hasbeen ignored.) There is thus a continualtransformation of gravitational potentialenergy into kinetic energy.

PowerPower is defined as the rate of work done. Power (P) is given by the ratio of work done (W) and time taken (t) to do that work i.e.Power = Or P= This relation shows that for a given work, power is inversely proportional to the time taken.

Whenever work is done, an equal amount of energy is consumed. Hence, we define power as

The SI unit of power is watt (W) in honor of physicist James Watt.

Commercial Unit Of EnergyJoule is a very small unit of energy. Therefore, we use bigger units of energy for commercial purposes. This commercial unit of energy is kilowatt-hour (kWh). We define kilowatt-hour as the amount of energy consumed when an electrical appliance of 1000 watt power rating is used for 1 hour.

The relation between joule and kilowatt-hour is given by1kWh = 3600000 Ws = 3.6 ×106 JThe amount of electrical energy consumed in our house is expressed in terms of ‘units’, where 1unit = 1kWh

Made by- Anushka Ninama

Class –