# Kinetic and gravitational potential energy

• pbonnie
In summary, friction may be a factor in why the skier's kinetic energy is not equal to the gravitational potential energy at the bottom of the hill.
pbonnie

## Homework Statement

Explain why the kinetic energy of the skier at the bottom of the hill is not equal to the gravitational potential energy of the skier at the top of the hill.

n/a

## The Attempt at a Solution

I think the answer is because the bottom of the hill is not at surface level, and therefore there is still gravitational potential energy. I just wanted to double check and make sure I'm not missing anything.
Thanks!

pbonnie said:

## Homework Statement

Explain why the kinetic energy of the skier at the bottom of the hill is not equal to the gravitational potential energy of the skier at the top of the hill.

n/a

## The Attempt at a Solution

I think the answer is because the bottom of the hill is not at surface level, and therefore there is still gravitational potential energy. I just wanted to double check and make sure I'm not missing anything.
Thanks!

I don't think that is the answer. If you define the GPE to be zero at the bottom of the hill and the skier starts from rest there, what else would keep the KE from being equal to all of the GPE when the skier reaches the bottom of the hill?

Potential energy is almost always a relative matter. I.e. it's the difference between two energy levels, rather than an absolute measure. (Sometimes the PE at infinity is considered zero, so the PE anywhere else is negative. This is commonly used in cosmological contexts.)
This makes the question a little unclear. You have interpreted it as taking zero PE to be at the centre of the Earth, right? Possibly, but I doubt that's what's intended. Why might the skier's KE not equal the difference in PE between top and bottom?

Oh okay. So does that mean that there is another kind of energy contributing to the total energy? So the kinetic energy is not equal because some of the energy was lost to thermal energy?

pbonnie said:
Oh okay. So does that mean that there is another kind of energy contributing to the total energy? So the kinetic energy is not equal because some of the energy was lost to thermal energy?

Yes. What caused that loss?

Friction?

pbonnie said:
Friction?

Bingo!

Great, thank you both very much!

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on an object's mass and velocity, and can be calculated using the equation KE = 1/2 mv², where m is the mass of the object and v is its velocity.

## 2. What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is dependent on an object's mass, height, and the strength of the gravitational field, and can be calculated using the equation GPE = mgh, where m is the mass of the object, g is the gravitational field strength, and h is the height of the object.

## 3. How are kinetic and gravitational potential energy related?

Kinetic and gravitational potential energy are related through the law of conservation of energy. This states that energy cannot be created or destroyed, only transferred between different forms. When an object falls, its gravitational potential energy decreases while its kinetic energy increases, and vice versa when an object is lifted.

## 4. Can an object have both kinetic and gravitational potential energy at the same time?

Yes, an object can possess both kinetic and gravitational potential energy at the same time. For example, a ball that is thrown up into the air will have both kinetic energy due to its motion and gravitational potential energy due to its height above the ground.

## 5. How can kinetic and gravitational potential energy be converted into each other?

Kinetic and gravitational potential energy can be converted into each other through the process of work. When an object is lifted, work is done on it, converting the energy from kinetic to gravitational potential. When an object falls, work is done by it, converting the energy from gravitational potential to kinetic.

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