K.E and P.E

Ok. I try to elaborate more on the ENERGY topic

1)
KE and PE is not a vector. In fact, all energies are not vectors. They are scalars.They only have magnitudes.

Example:
Object A (1kg) is moving to the RIGHT at 4m/s
Object B (1kg) is moving to the LEFT at 4m/s

KE of A = 0.5 x mass x speed^2 = 0.5 x 1 x 4^2 = 8J
KE of B = 0.5 x 1 x 4^2 = 8J

Although they are moving in different directions, they have the same value of KE. Hence we can see KE is a scalar, not a vector.

2)
There is a rule that you have to know:

In any mechanical systems,
Change in KE + Change in PE = Work done to this system.

Hence, if you want to increase KE and PE at the SAME time, you need to do work to the system. Actually you need to inject some energy to the system. If you do not inject energy to the system, then the energy can only transform itself from KE to PE or PE to KE.

Example:
Ignoring all the air resistance, a simple pendulum (單擺) swings back and forth. Its energy is converted from PE to KE and then PE to KE. This can be explained by the rule that i mentioned.

because there is no external energy injection or ejection, the workdone to the system is zero. Hence,

Change in KE + Change in PE = 0. Hence, any change of KE will result in change in PE

CONCLUSION:
Whenever external energy is injected to the system, KE and PE can be increased at the same time.

3) You have to remember that energy is always conserved. Energy cannot be created nor destroyed. This is the golden rule in classical physics.

But sometimes we just misunderstand some observations.

Example:
a ball is rolling on the table. Initially it has KE. But later it stops. Obviously there is no gain of PE on the flat surface. But it stops...so KE is zero. Where does the energy go? Energy is not conserved anymore?

Remember, energy is always conserved. sometimes we just look at the system too close. We move our eyes a bit away from the ball and see the system again. We will find that KE of the ball is used to overcome the friction. Energy is converted into workdone against friction.

If we move ourselves further away and try to consider the atmosphere around, we will find that the workdone against friction is converted to heat energy and dissipated in the atmosphere.

So, ENERGY is always conserved.

1 都不是vector
energy 不是 vector

2, because
ke + pe + wd =ke + pe + wd

所以對該物件作功 (work done)
ke and pe may increase at the same time

3, energy conserve
簡單來說是沒有energy loss
energy 任何時間也 conserve
只在乎你怎樣假設
像假設 no energy loss 在一個system 上
就會變成
ke + pe + wd =ke + pe