Force and Momentum: Calculating Final Velocity

In summary, to find the final velocity of a 5kg ball dropped from a 2m distance, we can use the equation \vec{F}=\frac{d\vec{p}}{dt}. If we know the time taken, T, we can rewrite the equation as \int _0 ^T\vec{F}dt =\vec{p}_{fin}-\vec{p}_{in}. However, it may be more efficient to use the law of total energy conservation. It is not necessary to use this equation to prove Newton's second law, as it is a postulate and cannot be proved.
  • #1
UrbanXrisis
1,196
1
If I dropped a 5kg ball, from a 2m distance, the force acting upon it will be constant right? How would I get the final velocity of the ball before it hit the floor using this equation:
[tex]\vec{F}=\frac{d\vec{p}}{dt}[/tex]
 
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  • #2
If you can find time taken, T , then rewriting your equation

[tex]\int _0 ^T\vec{F}dt =\vec{p}_{fin}-\vec{p}_{in}[/tex]
 
  • #3
UrbanXrisis said:
If I dropped a 5kg ball, from a 2m distance, the force acting upon it will be constant right? How would I get the final velocity of the ball before it hit the floor using this equation:
[tex]\vec{F}=\frac{d\vec{p}}{dt}[/tex]

It is quite weird to chose this equation,which assumes many calculations which could be shortcutted by applying the law of total energy conservation.


Daniel.

PS.In physics problem,always try to chose the easiest path to reach at your results...It saves energy,paper and neurons...
 
  • #4
dextercioby said:
It is quite weird to chose this equation,which assumes many calculations which could be shortcutted by applying the law of total energy conservation.


Daniel.

PS.In physics problem,always try to chose the easiest path to reach at your results...It saves energy,paper and neurons...

It is needed that use that equation, I'm trying to prove Newton's second law in a momentum project.

Gokul43201 said:
If you can find time taken, T , then rewriting your equation

[tex]\int _0 ^T\vec{F}dt =\vec{p}_{fin}-\vec{p}_{in}[/tex]

The force is constant so time is not dependant right?
F=pf-pi
ma=mv-0
a=v?
 
  • #5
Why in the world would you think F= pf- pi?? That is NOT the equation that you quote. The equation you quote is
[tex]\int _0 ^T\vec{F}dt =\vec{p}_{fin}-\vec{p}_{in}[/tex]

The left side is [itex]\int_0^T\vec{F}dt[/itex], not F!
 
  • #6
UrbanXrisis said:
It is needed that use that equation, I'm trying to prove Newton's second law in a momentum project.

This is absurd.Newton's laws are postulated,axioms,they cannot be proved.It's like proving Schroedinger' equation,or the postulates of thermodynamics or the postulates of statistical mechanics (the axiomatical approach)...

Daniel.
 
  • #7
OKay, back to my example, I dropped a 5kg ball. The force is about 50N. This force is constant. Let's say it took 2 seconds to drop. Then change in time is 2s. How would I integrate that? 50x=mv?
 
  • #8
dextercioby said:
This is absurd.Newton's laws are postulated,axioms,they cannot be proved.It's like proving Schroedinger' equation,or the postulates of thermodynamics or the postulates of statistical mechanics (the axiomatical approach)...

Daniel.

Sorry, I mean verify
 
  • #9
UrbanXrisis said:
Sorry, I mean verify

Aha...That's something else.And it sounds right... :-p

UrbanXrisis said:
OKay, back to my example, I dropped a 5kg ball. The force is about 50N. This force is constant. Let's say it took 2 seconds to drop. Then change in time is 2s. How would I integrate that? 50x=mv?

It would be correct,if that "x" would be 2s.I guess it was a typo...

Daniel.
 

FAQ: Force and Momentum: Calculating Final Velocity

1. What is force and how does it relate to momentum?

Force is a physical quantity that describes the interaction between two objects, causing a change in motion. Momentum, on the other hand, is a measure of an object's motion, determined by its mass and velocity. In simple terms, force is what causes an object to accelerate, and momentum is the result of that acceleration.

2. How do you calculate final velocity using force and momentum?

The formula for calculating final velocity using force and momentum is Vf = Vi + (F/m)t, where Vf is the final velocity, Vi is the initial velocity, F is the force applied, m is the mass of the object, and t is the time duration of the force. This formula is derived from Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration.

3. What units are used to measure force and momentum?

Force is typically measured in Newtons (N), which is a derived unit of mass, length, and time. Momentum is measured in kilogram meters per second (kg*m/s), which is also a derived unit of mass and velocity.

4. How does the direction of force affect the final velocity of an object?

The direction of force is an important factor in calculating final velocity. If the force and initial velocity are in the same direction, the final velocity will be greater than the initial velocity. If the force and initial velocity are in opposite directions, the final velocity will be less than the initial velocity. If the force acts perpendicular to the initial velocity, it will cause a change in direction but not in magnitude of the final velocity.

5. Are there any other factors that can affect the final velocity of an object?

Yes, in addition to force and momentum, there are other factors that can affect the final velocity of an object. These include the mass of the object, the duration of the force, and external forces such as friction or air resistance. These factors must be taken into consideration when calculating final velocity in real-world situations.

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