Work, Energy and Power

When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.
Read the following five statements to understand the concept of work.
Statement
Answer with Explanation
A teacher applies a force No. to a wall and becomes exhausted.
No.
This is not an example of work. The wall is not displaced A force must cause a displacement in order for work to be done
A book falls off a table and free falls to the ground
Yes.
ground. ,This is an example of work. There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction (i.e., "fall").
A waiter carries a tray
full of meals above his head by one arm straight across the room at constant speed.
No.
This is not an example of work. There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.
A rocket accelerates through space.
Yes.
This is an example of work. There is a force (the expelled gases push on the rocket) which causes the rocket to be displaced through space.
Mathematically, work can be expressed by the following equation
where F is the force, d is the displacement, and the angle (theta) is defined as the angle between the force and the displacement vector.
The Meaning of Negative Work
On occasion, a force acts upon a moving object to hinder a displacement. Examples might include a car skidding to a stop on a roadway surface or a baseball runner sliding to a stop on the infield dirt. In such instances, the force acts in the direction opposite the objects motion in order to slow it down. The force doesn't cause the displacement but rather hinders it. These situations involve what is commonly called negative work. The negative of negative work refers to the numerical value which results when values of F, d and theta are substituted into the work equation.
Units of Work Whenever a new quantity is introduced in physics, the standard metric units associated with that quantity are discussed. In the case of work (and also energy), the standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of on~ meter. In other words,
The Joule is the unit of work.
1 Joule = 1 Newton * 1 meter
Potential Energy
Potential energy is the stored energy of position possessed by an object
Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the massive ball ofa demolition machine is dependent on two variables the mass of the ball and the height to which it is raised. 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 that an object is elevated, the greater the gravitational potential energy. These relationships are expressed by the equation:
PEgrav = mass * g * height
PEgrav = m * g * h
Elastic potential energy is the energy stored in elastic materials as the rusult of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, and arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy.
Springs are a special instance of a device which can store elastic potential energy due to either compression or stretching. A force is required to compress a spring; the more compression there is, the more force which is required to compress it further. For certain springs, the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k).
Fspring = k * x
Such springs are said to follow Hooke's Law. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no force applied to it. In terms of potential energy, the equilibrium position could be called the zero-potential energy position. There is a special equation for spr:ingswhich relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring constant. The equation is
PEspring = 1/2 * k * x2
where k = spring constant
x = amount of compression
(relative to equilibrium pos'n)
Kinetic energy is the energy of motion. An object which has motion whether it be vertical or horizontal motion - has kinetic energy. The following equation is used to represent the kinetic energy (KE) of an object.
KE = 1/2 * m * v2
where m = mass of object
v = speed of object
Kinetic energy is a scalar quantity; it does not have a direction.
1 Joule = 1 kg * m2/s2
The Total Mechanical Energy
The mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and /or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).
TME = PE + KE
Power
Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation.
Power = Work / time
The standard metric unit of power is the Watt.. Thus, a Watt is equivalent to a JouIe/second. For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. One horsepower is equivalent to approximately 750 Watts.