# Explain Total Energy Problem: Kinetic & Gravitational Potential Energy

• apchemstudent
Summary: In summary, when the orbital speed decreases, the total energy increases due to a decrease in kinetic energy and a decrease in gravitational potential energy. This can be explained by the fact that gravitational potential energy is negative and when r increases, it becomes less negative.
apchemstudent
The answer to the problem is a), the orbital speed will decrease but the total energy will become larger. How is this? It's kinetic energy has decreased and the gravitational potential energy should also have decreased from this equation

GM(earth)m(object)/r where r has been increased, thus smaller Gravitational potential energy. Can some one explain this? Thanks

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Gravitational Potential energy is negative, so when r gets bigger you potential energy gets less negative, or bigger.

apchemstudent said:
The answer to the problem is a), the orbital speed will decrease but the total energy will become larger. How is this? It's kinetic energy has decreased and the gravitational potential energy should also have decreased from this equation

GM(earth)m(object)/r where r has been increased, thus smaller Gravitational potential energy. Can some one explain this? Thanks
The change in potential is positive.

$$U(r) = \int_{R{_0}}^\infty \frac{GMm}{r^2}\hat r \cdot d\vec{s} = \int_{R{_0}}^\infty \frac{GMm}{r^2}dr \hat r$$

$$U(r) = 0 -\frac{GMm}{R_0}$$

So as r increases, U(r) becomes less negative.

AM

## 1. What is total energy problem in physics?

The total energy problem in physics refers to the concept of energy conservation, which states that the total energy of a system remains constant over time. This means that energy cannot be created or destroyed, only transferred from one form to another.

## 2. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is dependent on the mass and velocity of the object, and is calculated using the equation KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## 3. What is gravitational potential energy?

Gravitational potential energy is the energy that an object has by virtue of its position in a gravitational field. It is dependent on the height and mass of the object, and is calculated using the equation GPE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

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

Kinetic and gravitational potential energy are related through the law of conservation of energy. When an object falls, its gravitational potential energy decreases while its kinetic energy increases. This means that the total energy of the object remains constant, as the decrease in potential energy is equal to the increase in kinetic energy.

## 5. How can the total energy problem be applied in real-life situations?

The total energy problem can be applied in various real-life situations, such as in the design of roller coasters or in understanding the movement of objects in space. It is also used in renewable energy systems, where the conversion of energy from one form to another is crucial for its efficiency.

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