AP Physics Chapter 5-8 Key Equations and Ideas
Forces


Fnet  ma
F
a  net
mtot
W = mg
Ff = FN
(pulleys)
Equilibrium: Fx net = 0 Fy net = 0 Fz net = 0
Fg incline plane = F|| = mg sin 
Fspring = -kx
Normal Force
FN = F = mg (horizontal surface)
FN = F = mg cos  (incline plane)
Work, Energy and Power
W
W = F  d  Fd cos  (constant force)
P=
dW d (Fx)
dx

F
 Fv
dt
dt
dt
Work-Energy Theorem:
Ki + Ui = Kf + Uf
 F(x) dx
USpring = ½kx2
Ug = mgh
Kf =Ki + W (no friction)
(area under a F versus x curve)
K = ½mv2
Q = Ffd = FNd
Kf =Ki + W - Q (with friction)
(Conservation of mechanical energy - no friction)
Ki + Ui = Kf + Uf + Q (Conservation of mechanical energy - with friction)

U = -W  U   F(x) dx
 F  
dU
dx
(F is  to equipotential energy lines & visa versa)
Key Ideas:

If no net force acts on a body, the body’s velocity will remain the same (i.e. no
acceleration). Conversely, if a body’s velocity is constant, the acceleration and net force
on the body must be zero.

Changes in vx, vy and vz (i.e. ax, ay and az) are independent of one another. Only the net
force parallel to the axis will result in a change in the velocity along the axis. Forces
perpendicular to the axis will not affect the velocity along the axis.

Be careful when adding vectors. Only the components along an axis can be added when
determining the force parallel to the axis.

Draw a rough sketch when solving a problem. Choose your axes wisely to make the problem
easier. A free body diagram is very useful. In a free body diagram, a single dot
represents the object and the tail of each vector is placed on the dot.

In equilibrium, Fx, Net = 0, Fy, Net = 0 and Fz, Net = 0.

The weight of a body is not “g”. Weight is a force.

When a body presses against a surface, the surface (even a seemingly rigid surface)
deforms and pushes on the body with a normal force, FN, that is perpendicular to the
surface.

When dealing with pulley problems, straighten out the pulley.

The frictional force, Ff, is always parallel to the surface and in the opposite direction of
motion.

In circular motion, the centripetal force and centripetal acceleration is always directed
towards the center and perpendicular to the velocity.

When a falling object has reached terminal velocity, the downward gravitational force is
equal to the upward air resistance force.

Work is energy transferred to or from an object by means of a force acting on the object.
Energy transferred to the object is positive work and energy transferred from the object
is negative work.

Only the force component along an object’s displacement is used to calculate the work
done on an object.

A force does positive work when it has a vector component in the same direction as the
displacement, and it does negative work when it has a vector component in the opposite
direction. The force does zero work when it is perpendicular to the displacement.

Work (energy) done on an object will change its kinetic energy (i.e. its energy of motion).

For a block on a spring, the work is positive if the block ends up closer to the relaxed
position (x = 0) than it was initially. It is negative if the block ends up farther away from
x = 0. It is zero if the block ends up in the same initial position.

If the force on an object varies with position (such as when it is attached to a spring), you
must integrate the force with respect to position to find the work.

The net work done by a conservative force (e.g. gravitational and electric forces) on a
particle moving around every closed path is zero.

The work (i.e. change in potential energy) done by a conservative force on a particle moving
between two points does not depend on the path taken by the particle.

The gravitational potential energy associated with a particle depends only on the vertical
position y (or height) of the particle relative to the reference position, y = 0, not on the
horizontal position.

Energy (e.g. kinetic + potential + heat + …) is conserved in a closed and isolated system.

Neutral equilibrium (e.g. marble on a flat surface), unstable equilibrium (e.g. marble at the
top of a hill) and stable equilibrium (e.g. marble at the bottom of a valley).

Work is energy transferred to or from a system by means of an external force acting on
the system. Work can be determined by the energy change within a system.

The total energy E of a system can change only by amounts of energy that are transferred
to or from the system.