Energy is the capacity to do work.
SI Unit: J
Types of energy
Kinetic Energy v.s Gravitational Potential Energy
Principle of Conservation of Energy
It states that energy can neither be created nor destroyed in any process. It can only be converted from one form to another but the total amount remains constant.
Some real-life examples:
1. connecting lamp to battery
chemical potential energy in battery -> electrical energy -> heat and light energy of lamp
2. diver on a spring board jumps on spring board, then dives
chemical potential energy in body -> elastic potential energy of bent board -> kinetic energy of diver
Note that when mentioning the energy conversion, have to be more specific by stating the subject.
Ideal Pendulum (no air resistance)
At A, when the pendulum bob is displaced to one side, it gains GPE, i.e max GPE and 0 KE.
When it is released, GPE is converted to KE as it swings down.
At B, it has both GPE and KE.
At C, when it returns to its original position, all GPE is converted to KE so it has max KE and 0 GPE.
As it swings to the opposite side, KE is converted to GPE.
At D, all KE is converted to GPE so it has max GPE and 0 KE.
Ideally, the pendulum will swing to and fro forever. GPE is continuously converted into KE and vice verse. The total energy of the pendulum remains constant throughout.
Note that ideally, the maximum height reached at D is same as the initial height displaced at A.
To help you understand this better, you can play with the applet below.
Part (a): The principle of Conservation of Energy without friction
From the principle of conservation of energy,
KE = GPE as there is no friction in this case
1⁄2 mv2 = mgh
v = √ 2gh
From this formula, you should be able to conclude that speed only depends on height and gravitational field strength, g when there is no friction or air resistance (in some cases).
Non-Ideal Pendulum (with air resistance)
Due to air resistance, some energy is lost as heat which is dissipated to the surroundings. As a result, the height reached at D is lower than the initial height at A. Subsequently, it will reaches a lower and lower height and eventually come to rest at C.
Although the pendulum comes to rest at the end, principle of conversation of energy still applies as all GPE gained at A is converted to heat (thermal energy) which is dissipated to surrounding.
To help you understand this better, you can again play with the same applet (can be found above) as before.
Energy input = useful energy output + waste energy output
The Figure below shows part of the route of a roller-coaster in which the passenger car pulled up to point A and released.
During one run, a car and passengers of total mass 800 kg are released from rest at point A, a height of 30 m above the terminal platform. The car travels a distance of 120 m along the track to reach the highest point B of the vertical loop which is 20 m above the terminal platform. A constant frictional force of 250N acts between the car and the track as the car moves from A to B.
(a) In moving from A to B, calculate
(i) the loss in potential energy of the car,
(ii) the work done against friction by the car,
(iii) the gain in kinetic energy of the car,
(iv) the speed of the car at B.
(b) In the design of the roller coaster, do you think the summit C can be higher than point B? Explain briefly.
(a)(i) Loss in GPE = mgh = 800*10*(30 – 20) = 80000 J
(ii) WD against friction = 250 x 120 = 30000 J
(iii) Gain in KE at B = 80000 – 30000 = 50000 J
(iv) KE = 1/2 m v^(2)
50000 = 1/2 * 800 v^(2)
v = 11.2 m/s
(b) By conservation of energy, no energy can be created or destroyed, it can only be converted from one form to another. If the KE at B is more than the sum of work done against friction from B to C and the gain in gravitational potential energy from B to C, then C can be at a higher point than B.