Category: 05 Work Energy Power

Worked Examples for PCOE

Ramp and Pulley
Application of PCOE, involving KE, GPE and heat (due to friction)

Maximum Compression
Application of PCOE, involving GPE, EPE and (no) KE.

Bungee Jump Energy graph.
Plotted against distance, GPE is straight, EPE is quadratic, and KE is “depends”.

Demonstrations of PCOE

It seems that any physics lecturer worth his/her salt must perform this demonstration

Walter Lewin did it.

Paul Hewitt did it

How can we not join in?

OMG, the biscuit tin is rolling upslope. Are you witnessing a PCOE violation?

explanation at xmdemo

OMG what black magic is this? Where are those balls drawing their energy from?

explanation at xmdemo

Principle of Conservation of Energy

The principle of conservation of energy is actually a very abstract concept. So it is amazing that we teach it to primary school kids. As a kid, I was taught that sound, light and electricity are all different forms of something called energy, which has this ability to morph from one form to another like a shape changer. It is also able to glide out of one body and slip into another, invisibly, like a ghost or spirit. I guess, as a kid, I didn’t have any problem accepting such a magical construct. Now that I am an adult, I realize that energy is a pretty bizarre idea. No one explains this better than Richard Feynman, in Section 4-1 What is Energy of the Feynman Lecture Series.


Spoiler: At the end of the analogy, Feynman dropped the profound punch line: “There are no blocks.” The idea that energy is never an actual thing really blew my mind.

509 Magnetic Cannon

The interesting part is when a magnetic ball collides into two stationary metallic NON-magnetic balls (@ 0:48).

Clearly, the outgoing ball had a much greater momentum and energy than the incoming ball. So is there a double violation of the conservation principles (of momentum and energy)? Gosh.

Nope. Nope.

First for momentum, notice two balls recoiled to the right after the collision. (The recoil was at quite a high speed, but friction brought them to rest quickly) So even though the outgoing ball had a large leftward momentum, after subtracting the rightward momentum of the recoil, the total momentum is still equal to the initial leftward momentum.

As for energy, note that the magnetic field must have an associated magnetic potential. Since the field is attractive, the balls must be losing magnetic potential energy as they come closer. So even though the outgoing ball had a large kinetic energy, after accounting for the loss in magnetic potential energy, the total energy is still equal to the initial total energy.

508 Anti-Gravity Wheel

We expect the biscuit tin to roll downslope. Why?


We assume that the biscuit tin has its center of mass (C.M.) at the center of the tin. If so, when the tin roll downward, the C.M. goes lower. So the tin loses GPE to gain KE. Everything makes sense.


The biscuit tin in the video however has a C.M. that is off centre (because of the mass of the magnets). If the C.M. is positioned on the uphill side, the tin rolls upward, but the C.M. actually goes lower. So again, the tin loses GPE to gain KE. There is nothing “anti-gravity” about the tin’s motion.

Picture3It is even possible for the tin to rest on the slope. This occurs when the C.M. of the tin is vertically above the contact point. The allows the contact force FC  to balances the weight of the tin, and yet does not exert any moment about the C.M. of the tin.