If we were to approach this problem using kinematics equations (which we could), it would take about a
page of work to solve. Instead, observe how quickly it can be solved using conservation of energy.
We will define our zero of potential to be the height of the box after it has slid the 5 m down the plane. By
defining it this way, the PE term on the right side of the equation will cancel out. Furthermore, because the
box starts from rest, its initial KE also equals zero.
The initial height can be found using trigonometry: h (^) i = (5m) (sin 30°) = 2.5 m.
In general, the principle of energy conservation can be stated mathematically like this:
The term W in this equation stands for work done on an object. For example, if there had been friction
between the box and the plane in the previous example, the work done by friction would be the W term.
When it comes to the AP exam, you will include this W term only when there is friction (or some other
exteral force) involved. When friction is involved, W = F (^) f d , where F (^) f is the force of friction on the
object, and d is the distance the object travels.
Let’s say that there was friction between the box and the inclined plane.