Question

Question #4021a

Answer 1

They can be, but not necessarily.

Explanation:

If a roller coaster is moving fast along a horizontal track and it starts to rise up a slope, the wagon will slow down (lose KE) as it gains height (PE increases.) There will come a point where both are equal.

Similarly, as it falls from the top of a slope, PE is converted to KE so there will come a point where the two are equal.

In summary, it is not unusual - many systems do it.

Answer 2

They can be.

Explanation:

If all of one form of energy is converted from one form to the other without energy being lost to the environment, then in theory they will be equal. However this is unlikely as nearly all of the time energy is transferred to the environment, be it by heating, or sound. So while it is possible for them to be equal in theory, it is actually very unlikely.

Answer 3

Mathematical interpritation...

Explanation:

For this idea, we are going to try and understand mathematically what it is meant for `P.E = K.E`

For this:

`K . E = "Kinetic Energy "= 1/2 * m * v^2`

`P.E = "Gravatational potential energy" = m * g * h`

So for `P.E = K.E`:

`=> 1/2 * m * v^2 = m * g * h`

`=> v^2 = 2gh`

`=> v = sqrt(2gh)`

So this means that when the velocity of an object is equal to `sqrt(2gh)` where `h` is the vertical hight, and `g approx 9.81` The gravatational constant... Then the `P.E` will be equal to `K.E`

For example...

An object with hieght `h = 32/g approx 3.261978 " metres"`

And has velocity of `sqrt(2cancel(g) * 32/cancel(g) ) = 8 ms^(-1)`

Then `K.E = P.E`