Introduction
In everyday life, the term work is applied to any form of activity that requires the exertion physical or mental effort, someone may say ‘I go to work’, another may say ‘I work in the office of the director’, so it is used variously with different meaning as it appeals to the user.
In physics however, the term is used in a specific sense. Work is said to be done, whenever a force is applied to cause a body to move, when a car is pushed a certain distance, or a load is lifted from the floor on to the table, you are said to do work. When no movement takes place after you have applied a force to a body, no work is done. Read this and you will marvel, If at a point you lift a bowl full of oranges from the ground floor on to your head and you remain at that point for twenty years without moving an inch, you have done no work, except that you lifted the bowl of oranges from the ground to your head, which could only be regarded as though you have done work, in its scientific true sense no work has been done by you in carrying the load and failing to move away from that spot, again, since no distance was covered, you have only done nothing.
Work refers to an activity involving a force and movement in the direction of the force. A force of 20 newtons pushing an object 5 meters in the direction of the force does 100 joules of work.
Work is said to be done whenever a force moves its point of application a distance in the direction of the force.
Work is defined as the product of the force and the displacement in the direction of the force.
W = F x S
The unit of work is the joule when the force is measured in newtons and the displacement in metres. Thus the work done when a force of 10 newtons displaces an object through 5 metres is given by W = 10 x 5 = 50 joules.
Work done in a force field
We must note that the earth’s gravitational field was an example of a force field. In that gravitational field there is always a force pulling a body towards the earth’s centre. We define the weight of a body as the as the force of attraction on the body due to the earth’s gravity, this weight acts downward. To lift a load through a height h, a pulling a force must be applied to overcome the weight of the body. Therefore, when an object is lifted vertically upwards, work is done against the force of gravity or against the weight of the body. The magnitude of the work done is given by
Work = force x distance
= mg x h
= mgh
Where m = mass of the body, g = acceleration due to gravity and h = height. (g = 10 ms-2).
For instance if a boy of mass m, moves up a step of steps of total height h, the work done by the wok = his weight (mg) x the height h.
Hence to lift a body against a force field (e.g. gravity) an opposing force is needed. Work done against gravity is equal to the product of the weight of the body (mg) and the vertical upward displacement (h)
w = m g h.
If a body of mass 50 kg runs up a set of steps of total height 3.0 m, find the work done against gravity.
Solution: Work done = mgh = 50 x 10 x 3 = 1500 joules
Falling bodies
When a body falls freely in a force field, the force of the field does work on the body. Hence for a body falling freely under gravity, the earth’s gravitational force does work on the body. If a body of mass m, falls through a vertical height h, the work done by gravity on the body is given by w = mgh
Energy
Energy is defined as the capacity to do work. Anything that is capable of doing work has energy. A person pushing a car along a road is doing work on the car. The person is said to possess energy which he exercises by making the car move some distance. A student running down the school field has energy. He is capable of moving his weight some distance, a mango fruit falling from the top of the tree all possess energy.
Work and energy are measured in the same unit, the joule. There are many forms of energy. These include: mechanical energy, heat (thermal) energy, light energy, chemical energy, electrical energy, atomic energy and solar energy.
Under mechanical energy, there are two classifications i.e. Potential and Kinetic energy.
Potential Energy (P.E.) is simply ‘stored energy’ or the energy possessed by a body by virtue of its position or state.
Such stored is used to do work when the body is free to move. A heavy note on top of a table has potential energy. When allowed to fall on to a glass plate on the floor, it will shatter the plate. The potential energy of the plate due to its position above the floor is expended in shattering the plate.
A body may have a potential energy due to its position in a force field, if the force field is the gravitational field then the body is said to possess a gravitational potential energy. The stone resting on top of a table has gravitational potential energy due to its height above the ground level .If the body is of mass m and the height of the table is h, the gravitational potential energy is given by Egp = mgh, where g is the acceleration due to gravity, if m is in kg, g in ms-2 and h in metres, then Egp the potential energy is in joules.
Other examples of potential energy are:
A magnet at rest in a magnetic field (magnetic potential energy), an electric charge at rest in an electric field (electrical potential energy), a coiled spring when stretched or compressed possesses elastic potential energy also chemical potential energy is released when petrol, wood and other fuel sources burn.
An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.
There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher an object is elevated, the greater the gravitational potential energy.
Kinetic Energy
Kinetic Energy is the energy of motion. An object that has motion – whether it is vertical or horizontal motion – has kinetic energy. There are many forms of kinetic energy – vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.
K.E = ½ MV2
where m = mass of object
v = speed of object
This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine. And for a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon the square of the speed. As it is often said, an equation is not merely a recipe for algebraic problem solving, but also a guide to thinking about the relationship between quantities.
Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone. Like work and potential energy, the standard metric unit of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg x (m/s)2.
1 joule = 1kg x m2/S2
Find the potential energy of a boy of mass 10 kg standing on a building floor of 10 metres above the ground level.
Solution
P.E. = mgh
= 10 x 10 x 10 = 1000 joules.
Power
Power is defined as the time rate of doing work
If two boys of the same weight climb a flight of steps of the same height, the boy that gets to the top first is said to have the greater power. This is because he has done the work of moving that height at a shorter time. If the work W joules is done in time t seconds, then the power = work/time.
Power = work done or energy expended/time
Power is measured in watt, while 1 watt = 1 joule per second.
Other commonly used units of power are the kilowatt (kW), the megawatt (MW) and the horse power (h.p.).
1kW = 1000 W = 103 W, 1 MW = 1,000,000 W = 106 W, 1 h.p. = 746 W (Where h.p. means Horsepower).
Transformation and Conservation of Mechanical Energy
In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change from one form to another, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite.
By an isolated or closed system, we mean a group of object that neither receives energy from nor gives energy to objects outside the system.
If we consider mechanical energy, the law shows that the sum of the potential energy and the kinetic energy is always constant for a given body, but the energy may change from potential energy to kinetic energy or from kinetic to potential.
A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist. That is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings.
Potential and Kinetic Energy of a simple pendulum
The motion of a pendulum is a classic example of mechanical energy conservation. A pendulum consists of a mass (known as a bob) attached by a string to a pivot point. As the pendulum moves, it sweeps out a circular arc, moving back and forth in a periodic fashion. Neglecting air resistance, there are only two forces acting upon the pendulum bob. One force is gravity. The force of gravity acts in a downward direction and does work upon the pendulum bob. However, gravity is an internal force (or conservative force) and thus, does not serve to change the total amount of mechanical energy of the bob. The other force acting upon the bob is the force of tension. Tension is an external force and if it did do work upon the pendulum bob it would indeed serve to change the total mechanical energy of the bob. However, the force of tension does not do work since it always acts in a direction perpendicular to the motion of the bob. At all points in the trajectory of the pendulum bob, the angle between the force of tension and its direction of motion is 90 degrees. Thus, the force of tension does not do work upon the bob.
Since there are no external forces doing work, the total mechanical energy of the pendulum bob is conserved.
It is interesting to observe that the falling motion of the bob is accompanied by an increase in speed. As the bob loses height and PE, it gains speed and KE; yet the total of the two forms of mechanical energy is conserved.
EXERCISES
Lets see how much you’ve learnt, attach the following answers to the comment below
- Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. A. 105600 J B. 104635 J C. 160000 J D. 124980 J
- When a tightly pivoted pendulum is falling the speed ………………… and it gains ……………….. A. decreases, PE B. Increases, KE C. Increases, PE D. Decreases, KE
- A car is moving at a constant speed of 20 ms-1. The force retarding its motion is 500 N. Calculate the engine power of the car required to maintain the motion. A. 11.5 kW B. 12 kW C.16kW D.10 kW
- A man of mass 50 kg ascends a flight of stairs 5 m high in 5 seconds. If acceleration due to gravity is 10 ms-1, the power expended is A. 100 W B 200 W C. 250 W D. 500 W
- What is the value of 1 h.p. in watts? A. 467 W B 580 W C. 746 W D. 980 W
