throw a baseball in the air: The ball does not move in one, continuous, straight direc-
tion because the Earth’s gravity pulls it downward toward the surface.
Newton’s Second Law (Law of Constant Acceleration)states that if a force acts on
an object, the object accelerates in the direction of the force; the force creates an
acceleration proportional to the force (and inversely proportional to the mass). This is
written in the following notation: Fma, in which Fis the force, mis the mass, and
ais the acceleration. Newton actually expressed this in terms of the calculus—a form
of mathematics he created to explain these physical laws (for more about the calculus
and Newton, see “History of Mathematics” and “Mathematical Analysis”). He wrote the
equation as follows:in which mis mass, vis the change in velocity, and tis the change in time.
This is because instantaneous acceleration is equal to the instantaneous change in
velocity in an instance in time (or change in time).
Newton’s Third Law (or Law of Conservation of Momentum)states that forces on
an object are always mutual. To put it another way, if a force is exerted on an object, the
object reacts with an equal and opposite force on the phenomenon that initially exerted
the force. Simply stated, objects exert equal but opposite forces on each other. This is
often phrased, “For every action, there is an equal and opposite reaction.” The mathe-
matical equations for these forces are complex and beyond the scope of this text.What is Newton’s Law of Universal Gravitation?
As hard as it is to comprehend, (almost) everything in the universe is attracted to
everything else. This physical law is not only one of the most well-known but also one
of the most important. Newton’s law states that the gravitational force between two
masses, mand M, is proportional to the product of the masses and inversely propor-
tional to the square of the distance (r) between them. In formula form, this is written
as follows (note: in some texts, the masses of the two objects are written as m 1 and m 2 ):Fm= OOvt278
Is mathematics used in physics to describe work and energy?
Y
es, mathematical equations can be used to describe work and energy. Energy
comes in many forms, but its basic definition is in terms of work. Work is
done when a force moves a body a certain distance. It is expressed in the simple
equation: WFd, in which Wis work, Fis the force, and dis the distance. In
this definition, only force in the direction of the object’s motion counts.