Game Development Reference
In-Depth Information
multiplied by its velocity magnitude squared. Work is performed on the projectile as it travels
upwards. When the projectile reaches its highest point, its velocity is zero, meaning that all of
its kinetic energy has been converted to work. The height, h , that the projectile will reach can
be found by equating its original kinetic energy to the work performed on it.
1
2
2
mv
=
mgh
(3.20)
2
v
h
=
(3.21)
2
g
Potential Energy
Kinetic energy is the energy of an object due to its motion. Potential energy is the energy of an
object due to its location. We saw earlier in this chapter that work is required to change the
location of an object. The work that is performed can be stored in the object as potential energy.
Potential energy can take several forms. For example, it takes work to compress a spring. The
work is converted to potential energy that is stored in the compressed spring. The magnitude
of the potential energy, P E , is equal to one half the spring constant, k , multiplied by the square of
the distance, Dx , that the spring was compressed.
1
2
E
k
x
2
(3.22)
P
If the compressed spring is released, the potential energy stored in the spring is released as
well and will typically be converted into either kinetic energy or work.
Another important form of potential energy is gravitational potential energy . If a person
lifts a ball over his head, he is performing work on the ball. The ball has been given potential
energy because it has been moved to a location farther away from the center of the earth. If the
person then drops the ball, the potential energy is converted into kinetic energy as the ball falls
towards the earth. The amount of gravitational potential energy an object has is equal to the
weight of the object, mg , multiplied by the height of the object, h , above some reference height
location (typically the ground).
p E h
=
(3.23)
If you look back at the problem at the end of the “Kinetic Energy” section, the term mgh
appears in Equation (3.20) indicating that when the projectile reaches its maximum height its
initial kinetic energy has been completely converted to gravitational potential energy.
Other Forms of Energy
Kinetic and potential energy are known as mechanical energy because they are based on external
factors such as velocity and location. Energy can also be stored internally inside the molecules
and atoms that make up an object. One form of internal energy is thermal energy or heat. One
mechanism that can transfer thermal energy to an object is friction. Try rubbing your hands
together quickly, and the palms of your hands will heat up. Another energy type is chemical
energy, which is the energy stored in the chemical bonds of molecules. When chemical energy
is rapidly released, an explosion can occur, a subject that will be covered in Chapter 13.
 
Search WWH ::




Custom Search