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PREMEDICAL COURSE – PHYSICS, DR. EMŐKE BÓDIS
WORK, ENERGY, CONSERVATION OF ENERGY, WORK-ENERGY THEOREM
Work
Mathematically, work can be expressed by the following equation:
W = F • d • cos Θ
where F is the force, d is the displacement, and Θ (theta) is defined as the angle between the
force and the displacement vector. The force doesn't cause the displacement but rather
hinders it.
The SI unit of work is the joule. [ J = Nm = kg m2/s2 ]
To gather an idea of it's meaning, consider the following scenarios:
1 The Meaning of Negative Work
Force acts in the direction opposite the objects motion in order to slow it down. The negative
of negative work refers to the numerical value that results when values of F, d and theta are
substituted into the work equation. Cosine Θ is negative between 90 and 270 degrees.
Energy
In physics, energy is a property of objects, transferable among them via fundamental
interactions, which can be converted in form but not created or destroyed.
1. Potential Energy
An object can store energy as the result of its position. This stored energy of position is
referred to as potential energy.
1.1. Gravitational Potential Energy
The energy is stored as the result of the gravitational attraction of the Earth for the object.
There is a direct relation between gravitational potential energy and the mass of an object.
Epot = m.g.h
To determine the gravitational potential
energy of an object, a zero height position
must first be arbitrarily assigned. Typically,
the ground is considered to be a position of
zero height.
The SI unit of energy is the joule. [ J = Nm = kg m2/s2 ]
1.2. Elastic Potential Energy
This energy is stored in elastic materials as the result of their stretching or compressing.
Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs,
an arrow drawn into a bow, etc.
A force is required to compress a spring:
Fspring = k.x (Hooke's Law)
Springs are a special instance of a device that can store
elastic potential energy due to either compression or
stretching.
Espring = ½ k.x2
where k = spring constant
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.
2 2. Kinetic Energy
Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or
horizontal motion - has kinetic energy.
Forms of kinetic energy:
vibrational (the energy due to vibrational motion)
rotational (the energy due to rotational motion)
translational (the energy due to motion from one location to another)
The amount of translational kinetic energy: Ekin = ½ m.v2
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.
The SI unit of energy is the joule. [ J = Nm = kg m2/s2 ]
Mechanical Energy
When the work is done upon the object, that object gains energy. Mechanical energy is the
energy that is possessed by an object due to its motion (kinetic energy = energy of motion) or
due to its position (potential energy = stored energy of position).
Mechanical Energy as the Ability to Do Work
An object that possesses mechanical energy is able to do work. In fact, mechanical energy is
often defined as the ability to do work.
The Total Mechanical Energy
The total amount of mechanical energy is merely the sum of the potential energy and the
kinetic energy:
Emech = Epot + Ekin
The Principle of Conservation of Mechanical Energy
If you know the kinetic and potential energies that act on an object, then you can calculate the
mechanical energy of the object.
Kinetic energy converted to potential energy and then back to kinetic energy.
If there’s no friction (or another non-conservative force), then ME1 = ME2, or
3 These equations represent the principle of
conservation of mechanical energy. The
principle says that if the net work done by
non-conservative forces is zero, the total
mechanical energy of an object is conserved;
that is, it doesn’t change. (If, on the other
hand, friction or another non-conservative
force is present, the difference between ME2
and ME1 is equal to the net work the nonconservative forces do: ME2 – ME1 = Wnc.)
Kinetic Energy and the Work-Energy Theorem
This is the complete Work-Energy theorem. It is powerfully simple, and gives us a direct
relation between net work and kinetic energy. Stated verbally, the equation says that net work
done by forces on a particle causes a change in the kinetic energy of the particle.
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