# Integral of Momentum - Questions Answered

• Dominique
In summary, the conversation discusses various quantities related to force, linear momentum, energy, and power. The first question considers whether there is a defined quantity for mass times position or the derivative of force over time, while the second question asks about the derivative of energy over time and the integral of power over time. The expert concludes that while there may be ways to define certain quantities, their usefulness is what ultimately matters.
Dominique
Hi,

QUESTION 1
??=dF/dt
F =ma=dp/dt (force)
p =mv=d?/dt (linear momentum)
? =mx

A) Is there a quantity defined as the mass times the position or as the integral over time or the the linear momentum?
B) Is there a quantity defined as the derivative wr to time of the force?

QUESTION 2
?? = intergal over time of power
P =(mv^2)/2t (power)
K =(mv^2)/2 (kinetic energy)
? = dK/dt

A) Is there a quantity defined as the derivative over time of energy?
B) Is there a quantity defined as the integral over time or the power?

Thank you very much for your help!

You can define any quantity you want ... but is it useful?

For example (I am making this up) the quantity ##mx## could find use in athletic competition where strong athletes pull vehicles over a distance. Their rating of how strong they are could be cast in terms of the product ##mx## for comparative purposes. Not a very useful quantity to define.

Question 2 requires nothing to be made up artificially. The time-rate of change of energy is power and of course the integral of power over time is energy or mechanical work. Power is a very useful quantity and is used extensively as you know to characterize anything that has to do with the use of electricity, heat and mechanical work.

## 1. What is the definition of integral of momentum?

The integral of momentum is a mathematical concept that represents the total amount of momentum accumulated over a given time period. It is calculated by taking the integral (area under the curve) of the momentum function with respect to time.

## 2. Why is the integral of momentum important?

The integral of momentum is important because it helps us understand the overall motion of an object by taking into account its momentum over time. It also allows us to calculate the change in momentum, which is related to the net force acting on an object.

## 3. How is the integral of momentum related to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the net force acting on an object is equal to the rate of change of its momentum. The integral of momentum allows us to calculate the change in momentum over a given time period, which is directly related to the net force acting on the object.

## 4. Can the integral of momentum be negative?

Yes, the integral of momentum can be negative. This would occur if the momentum of an object decreases over time, indicating that there is a net force acting in the opposite direction of its initial momentum.

## 5. How is the integral of momentum calculated?

The integral of momentum is calculated by taking the integral of the momentum function with respect to time. This can be done using integration techniques such as the fundamental theorem of calculus or by using numerical methods such as Riemann sums.

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