Force & Momentum: Understanding Newtons & Mass in Motion

In summary: And, as you know, the force is the impulse divided by the time of the collision.So the two forces are equal and opposite.
  • #1
Fuz
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Ive been studying basic mechanics lately and have been trying to understand what "force" really is. First off, here's my understanding of momentum: If you take the mass of a moving object and multiply it by its velocity (just a constant velocity) you get momentum. P=mv. I know that force is measured in Newtons. N=ma. Heres my problem... BTW, this is not a homework question so please don't badger me about that...

Scene 1: Let's say a car with a mass of 100 kg (being to scale isn't the point) is traveling east at a constant velocity of 20 m/s. After 100 meters it hits a wall.

Scene 2: The same modal car is accelerating at a rate of 10 m/s^2. After 100 meters it hits a wall.

Since the first car wasn't accelerating, does that mean it didn't exert any Newtons on the wall? It had momentum but no force so to my understanding the first car was "forceless" so to speak. Now why does the accelerating car exert force (Newtons) on the wall if it hits the wall just like the first car?

I hope my question made sense. Thanks in advance :)
 
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  • #2
In the first case though the car had a constant velocity of 20 m/s it is evident that the car must have started from 0 m/s ie at rest. from there it must have ACCELERATED to achieve this speed of 20m/s. So we cannot say that the Acceleration was ZERO.

In this case there is an initial acceleration equal to the difference in the initial velocity ie at rest = 0 m/s , and the final constant velocity 20 m/s which comes to be (20- 0)/t = 20/t m/s^2 where t is the time interval taken to reach 20m/s form rest.

So the car will be having this acceleration which shall be used for any calculation in the particular case where the velocity has remained constant for some time but it did have to rise from Zero to this value and this would not be possible without accelerating the car from rest.

So the car does have aceleration in the complete scenario as a whole. And so does have Force.

Hope its clear.
 
  • #3
But when the car hits the wall, the car is not accelerating. It has a constant velocity of 20 m/s. Are you saying that once something accelerates and then evens out to a constant speed, it keeps its force from when it started accelerating?
 
  • #4
Fuz said:
Since the first car wasn't accelerating, does that mean it didn't exert any Newtons on the wall? It had momentum but no force so to my understanding the first car was "forceless" so to speak. Now why does the accelerating car exert force (Newtons) on the wall if it hits the wall just like the first car?

The car will apply a force upon crashing into the wall no matter how it achieved it's speed. Force isn't a property of an object by the way. A force is an interaction between 2 objects; with 1 object, there is no force to speak of. Both cars will be decelerated to 0 from the velocity they have upon slamming into the wall. This change in velocity is due to the force of the wall resisting the impact which results in an acceleration and thus, a force.
 
  • #5
Welcome to PF!

Hi Fuz! Welcome to PF! :smile:
Fuz said:
Ive been studying basic mechanics lately and have been trying to understand what "force" really is.

Since the first car wasn't accelerating, does that mean it didn't exert any Newtons on the wall? It had momentum but no force so to my understanding the first car was "forceless" so to speak. Now why does the accelerating car exert force (Newtons) on the wall if it hits the wall just like the first car?

Force = rate of change of momentum.

Impulse = total change of momentum.

That's good ol' Newton's second law :-p … F = d(mv)/dt, I = ∆(mv).

(I know you usually see it written F = ma, but F = d(mv)/dt is the full version :wink:)

So the car's momentum is reduced by a total amount equal to the impulse on the wall. :smile:

(To put it another way: the car decelerates when it hits the wall)
 
  • #6
Thanks for the reply Tim. Impulse is new to me so I kinda got confused when you started talking about it.
 
  • #7
Hi Fuz! :wink:

Impulse is just a convenient name for the total force over a period of time (usually a very short period, as in a crash or a bat hitting a ball).

For some details, see http://en.wikipedia.org/wiki/Impulse :smile:
 
  • #8
I remember learning about force and momentum back in high school, and it was fun, imo!
 
  • #9
When the car hits the the wall then it is no longer traveling at a constant velocity, therefore it is decelerating and it exerts a force upon the wall;
 
  • #10
Oh so if any object hits another object, the first object will always hit the second object with force regardless of its speed? Does this apply to all physical things? Also, if the first object hits the second object with 10 Newtons, could you also say the second object exerted 10 Newtons on the moving object? Again, there is always force regardless of speed, correct?
 
  • #11
Fuz said:
Oh so if any object hits another object, the first object will always hit the second object with force regardless of its speed?

No, it's a lot more complicated than that.

Force (or rather, impulse) does depend on speed, or rather on change in speed … impulse = change of momentum.

Have you done "collisions" yet"?

Total momentum (ie, total of both bodies) is always conserved in a collision,

so the momentum transferred from one body is the same as that transferred to the other body …

and impulse is change in momentum,

so the two impulses are equal and opposite. :smile:
 

FAQ: Force & Momentum: Understanding Newtons & Mass in Motion

What is force and momentum?

Force is a push or pull on an object, while momentum is the measure of an object's motion. Both force and momentum are vector quantities, meaning they have both magnitude and direction.

Who was Sir Isaac Newton and why is he important in understanding force and momentum?

Sir Isaac Newton was an English physicist and mathematician who developed the laws of motion and the theory of gravity. His laws of motion, particularly the second law which relates force and momentum, are fundamental in understanding the behavior of objects in motion.

How are force and mass related?

According to Newton's second law of motion, force is directly proportional to an object's mass and acceleration. This means that the greater the mass of an object, the more force is needed to accelerate it.

What is the difference between mass and weight?

Mass is the amount of matter in an object, while weight is the force of gravity acting on an object. Mass is measured in kilograms, while weight is measured in newtons.

How does momentum affect the motion of an object?

Momentum is a measure of an object's motion and is directly related to its mass and velocity. The greater the mass and velocity of an object, the greater its momentum, making it more difficult to stop or change its direction of motion.

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