# kinetic energy= potential energy.

#### avito009

Suppose an object is moving, so it has kinetic energy which is 10 joules. Now this object is at rest so does the potential energy equal 10 joules?

So does that mean kinetic energy = potential energy when the object is at rest? This has to be the case if law of conservation of energy is true. Since at rest kinetic energy is 0 and during motion potential energy is 0.

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#### studiot

Suppose an object is moving, so it has kinetic energy which is 10 joules. Now this object is at rest so does the potential energy equal 10 joules?

So does that mean kinetic energy = potential energy when the object is at rest? This has to be the case if law of conservation of energy is true. Since at rest kinetic energy is 0 and during motion potential energy is 0.
Careful here you need to consider both the circumstances of motion and the proper version of energy conservation.

The law of conservation of mechanical energy says that in an isolated system the sum of the potential energy and the kinetic energy is a constant.

This applies, for instance to a swinging pendulum since that can be considered isolated in the absence of friction.
Here the motion is a continual interchange between KE and PE.
When the pendulum is at the bottom of its swing the energy is all KE (PE is zero) and the velocity is a maximum.
When the motion is at the top of the swing it is the reverse. The energy is all PE (KE is zero) and the velocity is at a minimum (zero) - the pendulum is momentarily stationary.

However

Conservation of energy applies in a different way to a speeding bullet.

This is because the circumstances are different..
What stops the bullet?
Some external agency, eg impact with a block of wood.

The bullet does work in penetrating the block, loosing KE in the exchange.
PE does not enter into the analysis.

Does this help?

• 1 person

#### HallsofIvy

Suppose an object is moving, so it has kinetic energy which is 10 joules. Now this object is at rest so does the potential energy equal 10 joules?
If no energy has been added to or subtracted from the object, yes. That is "conservation of energy".

So does that mean kinetic energy = potential energy when the object is at rest? This has to be the case if law of conservation of energy is true. Since at rest kinetic energy is 0 and during motion potential energy is 0.
No, it means that "kinetic energy, when the object is at 0 potential energy" = "potential energy when the object is at rest". It is also not, in general, true that "during motion potential energy is 0". You seem to have the impression that an object must have either "kinetic energy 0" (motionless) or "potential energy 0" (in motion).

That is not correct. An object typically goes gradually from being motionless to having greater and greater speed- so goes gradually from 0 kinetic energy to greater and greater kinetic energy. As that happens, its potential energy decreases from the initial value to 0.

Consider an object sitting on the top of a hill. At the top of the hill, it potential energy (relative to the bottom of the hill) is its weight times the height of the hill. Now, it starts rolling down the hill. Its speed is initially 0 but as the object rolls down its potential energy (still its weight times it height) gradually decreases. The kinetic energy gradually increases so that the total energy remains the same.

#### Pmb

PHF Hall of Fame
Suppose an object is moving, so it has kinetic energy which is 10 joules. Now this object is at rest so does the potential energy equal 10 joules?

So does that mean kinetic energy = potential energy when the object is at rest? This has to be the case if law of conservation of energy is true. Since at rest kinetic energy is 0 and during motion potential energy is 0.
There are two instances when energy is conserved

1) When the system under consideration is closed
2) When all the forces are conservative.

The value of potential energy is arbitrary. I.e. you can set it to be anything that you'd like it to be at a given point in space. The only physical requirement of interest is that the total mechanical energy be constant.

A well known example of setting potential to zero at an arbitrary point in space is a charged particle in the field of an infinite line charge. See

Electric potential energy

Such objects don't exist in nature but its an interesting example. However there may be cosmic strings which are actually infinitely long. But that's a different ball game altogether.

#### Woody

Potential energy could be viewed as a book-keeping exercise

Let us look at a ball rolling along at some speed,
it starts to roll uphill, and as it rolls uphill its speed diminishes.
So it is loosing kinetic energy.
That kinetic energy is being used to move the ball to a different position in the gravitational field.
If you let the ball roll back down the hill the kinetic energy is restored.
The kinetic energy has been transferred to potential energy, where it is stored until the ball rolls back down the kill and the potential energy is transferred back to kinetic energy.

You could equally well have the ball rolling up against a spring,
as the spring compresses the kinetic energy of the ball is transferred to the potential energy of the tension within the spring, which can then be released to convert the energy stored in the spring back into kinetic energy.

#### Pmb

PHF Hall of Fame
Potential energy could be viewed as a book-keeping exercise
Nice! To extend that, the entire concept of energy itself is a bookkeeping system. I wrote about this in my website. See: What is Energy?