Potential Energy
Potential energy comes in many forms: there’s gravitational potential energy, spring potential energy,
electrical potential energy, and so on. For starters, we’ll concern ourselves with gravitational potential
energy.
Gravitational PE is described by the following equation:
U = mghIn this equation, m is the mass of an object, g is the gravitational field of 10 N/kg on Earth, and h is the
height of an object above a certain point (called “the zero of potential”).^1 That point can be wherever you
want it to be, depending on the problem. For example, let’s say a pencil is sitting on a table. If you define
the zero of potential to be the table, then the pencil has no gravitational PE. If you define the floor to be
the zero of potential, then the pencil has PE equal to mgh , where h is the height of the pencil above the
floor. Your choice of the zero of potential in a problem should be made by determining how the problem
can most easily be solved.
REMINDER: h in the potential energy equation stands for vertical height above the zero of potential.
Conservation of Energy: Problem-Solving Approach
Solving energy-conservation problems is relatively simple, as long as you approach them methodically.
The general approach is this: write out all the terms for the initial energy of the system, and set the sum of
those terms equal to the sum of all the terms for the final energy of the system. Let’s practice.
A block of mass m is placed on a frictionless plane inclined at a 30° angle above the horizontal. It is
released from rest and allowed to slide 5 m down the plane. What is its final velocity?