# Energy vs Momentum: Physics Examining the Difference

• aloshi
In summary, the conversation discusses the concept of energy and momentum and why physics defines work as force multiplied by distance instead of force multiplied by time. It also explores how the ant's speed and energy change over time as it is affected by a constant force.
aloshi
Energy? or momentum?

a dorm ant crawled on 1kg affected by krfaften 10N, so it may be an acceleration of
10m / s ^ 2, then the following 1s have speeds 10m / s, and a movement of 5 m has taken place. continuing the body that are affected by the same power in 1 s to, it will then have the speed 20m / s and a total of a movement of 20 m, 15 m further. According to the work as it is defined as force * distance, has been eating more energy during the second second. but power over the other secondary was the same as in the first second. How can they actually require more energy to maintain the same effect during the second second??

why physics has chosen to define the work force multiplied by distance and not as a force multiplied by time (that is to say, momentum)?

Last edited by a moderator:
aloshi said:
a dorm ant crawled on 1kg affected by krfaften 10N, so it may be an acceleration of
10m / s ^ 2, then the following 1s have speeds 10m / s, and a movement of 5 m has taken place. continuing the body that are affected by the same power in 1 s to, it will then have the speed 20m / s and a total of a movement of 20 m, 15 m further. According to the work as it is defined as force * distance, has been eating more energy during the second second. but power over the other secondary was the same as in the first second. How can they actually require more energy to maintain the same effect during the second second??

why physics has chosen to define the work force multiplied by distance and not as a force multiplied by time (that is to say, momentum)?

Hi aloshi!

Because work done = ∫F ds = ∫m dv/dt ds = (chain rule ) ∫m dv/ds ds/dt ds
= ∫mv dv/ds ds = ∫mv dv = 1/2 mv2 + constant = kinetic energy + constant.

(and ∫F dt = ∫m dv/dt dt = ∫m dv = momentum + constant)

So the ant's speed (and momentum) is proportional to time, but its energy is proportional to distance.

Both energy and momentum are important concepts in physics, but they are not interchangeable. Energy is a scalar quantity that describes the ability of a system to do work or cause a change. It is measured in joules (J) and can exist in different forms such as kinetic, potential, thermal, and chemical energy.

On the other hand, momentum is a vector quantity that describes the motion of an object. It is the product of an object's mass and velocity and is measured in kilogram-meters per second (kg*m/s). Momentum is conserved in a closed system, meaning that the total momentum before and after an interaction remains the same.

In the example given, the force acting on the 1kg object causes it to accelerate and gain momentum. However, the amount of energy required to maintain the same effect (acceleration) in the second second is greater because the object now has a higher velocity and therefore more kinetic energy. This is due to the relationship between force, mass, and acceleration (F=ma), which shows that as the mass remains constant, a higher force is required to produce a greater acceleration.

As for why physics defines work as force multiplied by distance and not force multiplied by time, this is because work is a measure of the energy transferred to or from a system. It is the change in energy that occurs as a result of a force acting over a certain distance, not over a certain amount of time. This definition allows us to calculate the amount of energy needed to move an object a certain distance, regardless of the time it takes to do so.

In contrast, momentum is defined as the product of force and time (F*t) in Newton's second law of motion (F=ma). This allows us to calculate the change in momentum of an object over a certain amount of time, which is useful in analyzing collisions and other interactions between objects.

In summary, energy and momentum are both important concepts in physics, but they serve different purposes and are defined differently. Energy is a measure of the ability to do work, while momentum is a measure of the motion of an object. Both are necessary for understanding and describing the behavior of physical systems.

## 1. What is the difference between energy and momentum?

Energy and momentum are two fundamental concepts in physics that describe the motion of objects. While they are both related to the motion of an object, they represent different aspects of it. Energy is a measure of an object's ability to do work, while momentum is a measure of an object's motion.

## 2. Can energy and momentum be converted into each other?

No, energy and momentum cannot be converted into each other. They are two separate and distinct quantities that cannot be interchanged. However, they are related through the principle of conservation of energy, where the total energy of a system remains constant.

## 3. How is energy related to velocity and mass?

Energy is related to velocity and mass through the equation E = 1/2mv^2, where E is the object's kinetic energy, m is its mass, and v is its velocity. This means that an object with a higher mass or a higher velocity will have a higher kinetic energy.

## 4. How is momentum related to velocity and mass?

Momentum is related to velocity and mass through the equation p = mv, where p is the object's momentum, m is its mass, and v is its velocity. This means that an object with a higher mass or a higher velocity will have a higher momentum.

## 5. Why is it important to understand the difference between energy and momentum?

Understanding the difference between energy and momentum is crucial in various fields of physics, such as mechanics, thermodynamics, and electromagnetism. It allows us to accurately describe and predict the behavior of objects in motion, and it also helps us understand important concepts like conservation of energy and momentum.

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