Physics presentation: energy

Isn't there a better way to get up a steep hill with a bicycle? Well, other than walking your bike up the hill...

Oh wait, I guess there is. And only just a few kröner? This ride would be a bargain at any price. (Video link: "Bicycle Lift ‘Steep is nothing’ -Panasonic ecoideasnet.")

We'll introduce different forms of energy and one particular form of energy transfer, and apply the principle of conservation of energy to situations like this.

Starting off with three forms of mechanical energy--translational kinetic energy, gravitational potential energy, and elastic potential energy (with a few more to follow later on in this course.) And a form of adding or subtracting mechanical energy: work.

Translational kinetic energy is the energy of motion. (We'll deal with rotational motion later on.)

Translational kinetic energy depends quadratically on speed, and the resulting units of kg·m^2/s^2 are also expressed as joules. A stationary object has no translational kinetic energy, and the faster the object moves, the more translational kinetic energy it has.

Gravitational potential energy, as all potential energy forms, is a stored form of energy. Here an object that is at the top of its trajectory has a maximum amount of gravitational potential energy, which here will soon be converted to translational kinetic energy.

Gravitational potential energy (for objects near the surface of Earth) depends linearly on height, and the units are again, also expressed as joules. An object at ground level has no gravitational potential energy, and the higher an elevated object is, the more gravitational potential energy it has.

Elastic potential energy is another form of potential, or stored energy. An object that exerted on by a restoring force has elastic potential energy, which here will soon be converted to translational kinetic energy.

Elastic potential energy depends on the strength of the elastic material (e.g., the "strength" of the spring, or bungee cord), and quadratically on the displacement of the elastic material from its equilibrium (whether by compressing or stretching). The units of elastic potential energy are given in N·m, or yet again, joules.

To start off, or to end all these transfers between these three (so far) mechanical energy forms, "non-conservative" work needs to be done, which occurs when we add energy in, or remove energy from mechanical energy forms. In general, work is not a form of energy, but transfer to or from energy forms.

Work is accomplished by exerted a force on an object, but in such a way that the object moves through a displacement ∆r, and the angle between the tail-to-tail force and displacement vectors is anything besides 90°. The units of work are given in N·m, or yet again, joules, so keep in mind that work can be transferred into or out of any mechanical energy form or forms.

Let's put all these concepts together by applying the principle of energy conservation.


Limiting the scope of our discussion to mechanical energy forms, they can either change by increasing or decreasing (resulting mathematically in positive or negative delta signs), but all changes on the right-hand side of this equation, overall, must be balanced by a corresponding amount of non-conservative work on the left-hand side.

Consider this catapulted squirrel. Assuming that the trajectory of the squirrel is approximately horizontal (such that there is no change in gravitational potential energy), and neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "squirrelcatapult.gif.")

A kid sliding down an (ideally frictionless) slide. With no springs or bungee cords involved, and neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "Whoosh!")

Don't blink, or you'll miss Mrs. P-dog in action! Note that she starts from rest below the screen, and then reaches the highest point in her trajectory, momentarily stationary, such that there is no initial-to-final change in kinetic energy. Neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "110530-1230869-excerpt.")

Note as this car stops, the brakes glow from the heat generated! Since this is a horizontal track, and no springs or bungee cords are involved, then both gravitational potential energy and elastic potential energy forms do not change. So how does the remaining translational kinetic energy term in the energy conservation equation increase or decrease, along with the amount of non-conservative work done? (Video link: "McLaren SLR review - Top Gear - BBC.")

As a closing example, let's just watch and appreciate the perfect storm of energy conservation with an all-terrain vehicle performing non-conservative work on stretching a bungee cord (with elastic potential energy) attached to a raft and rider at the top of a ramp (with gravitational potential energy), all of which transfer to...translational kinetic energy. Whee! (Video link: "Human Slingshot Slip and Slide - Vooray.")