# Momentum-Determining External Forces

• Arman777
In summary, the conversation discusses the concept of momentum and external forces in a system. The total momentum of a system changes only when there is an external force acting on it. In the absence of external forces, the center of mass of the system remains stationary. The determination of external forces in a given system can be done by considering the free body diagram and using equations such as ##F=mg##. In a collision, the change in total momentum is zero, but the center of mass can still have a non-zero velocity.
Arman777
Gold Member
I am studying momentum and I just want to check that I understand the idea correctly.

Think there's a system.In this system there's two masses ##m_1## and ##m_2## moving with some velocity ##\vec v_1## and ##\vec v_2## and they exert a forces each other.Lets call the total force acting on ##m_1## is ##\vec F_1## and for ##m_2## is ##\vec F_2##.

So If ##\vec F_1=\vec F^{ext}+\vec F_{21}##
##\vec F_2=\vec F^{ext}+\vec F_{12} ##

Then the change in the total momentum;
##Δ\vec P=\vec {(F_{tot})^{ext}} Δt##

If there's no exteral force then, ##Δ\vec P=0## .So If there's no external force then the change in momentum should be zero .If there's external force and its constant then the change in momentum will be constant but non-zero.##Δ\vec P≠0##

If the change in momentum is zero(No external force) the center of mass of the system will be not moving.If there's external force it will accelerate by ##\frac {\vec {(F_{tot})^{ext}} } {M}=a_{com}## (##M## here total mass of the system)

Just I am confused with the idea of external force...Think there's two object making projectile motion.and colliding in the air.Is the external force in here is gravity ? (No air drag)

How can we determine the external forces in a given system ?

Most collions happens in a small amount of time (##Δt## nearly ##0##), in this case can we say ##Δ\vec P=0## ? and If we can why ? (There will be external force)

Last edited:
Arman777 said:
If the change in momentum is zero(No external force) the center of mass of the system will be not moving
Think again: its momentum doesn't change. But it can well be nonzero.

Arman777 said:
Think there's two objects making projectile motion and colliding in the air. Is the external force in here is gravity ? (No air drag)
Correct. The reverse process: fireworks ! A rocket shoots off and explodes into a bunch of fireballs. Without air drag the center of mass simply continues the parabola the original rocket was following.

Arman777 said:
How can we determine the external forces in a given system ?
For instance by using ##F = mg## when gravity is the only external force acting !

BvU said:
For instance by using F=mgF=mgF = mg when gravity is the only external force acting !

So in any system The free body diagram will be showing us the external forces ?

If we collide two objects in space.There would be no external force so the ##Δ\vec P=0## Even if there's external forces in small ##Δt## (the collusion time) from the equation of ##Δ\vec P=\vec {(F_{tot})^{ext}} Δt##

##Δ\vec P## should be zero

BvU said:
Think again: its momentum doesn't change. But it can well be nonzero.

##Δ\vec V_{com}=0⇔Δ\vec P=0## ##Δ\vec V_{com}## can have any value bot the change must be zero
Is this true ?

Arman777 said:
##Δ\vec V_{com}=0⇔Δ\vec P=0##
##Δ\vec V_{com}## can have any value but the change must be zero
Is this true ?
Yes, that's about it. We restrict our considerations to constant mass cases, so ## {d\over dt} \left ( m\vec v \right ) = m {dv\over dt}##.

Arman777

## 1. What are momentum-determining external forces?

Momentum-determining external forces are forces that act on an object and cause it to change its momentum. These forces can either increase or decrease the object's momentum, depending on their direction and magnitude.

## 2. How do momentum-determining external forces affect an object's motion?

Momentum-determining external forces can change an object's velocity, direction, or both. They can also cause the object to accelerate or decelerate, depending on the direction and magnitude of the force.

## 3. What are some examples of momentum-determining external forces?

Examples of momentum-determining external forces include friction, air resistance, gravity, and applied forces such as pushing, pulling, or kicking an object.

## 4. How can momentum-determining external forces be calculated?

Momentum-determining external forces can be calculated using the formula F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration caused by the force.

## 5. How can momentum-determining external forces be manipulated to change an object's momentum?

Momentum-determining external forces can be manipulated by changing the direction or magnitude of the force applied to an object. Increasing the force in the direction of motion will increase the object's momentum, while decreasing the force will decrease the object's momentum.

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