Understanding Momentum: The Relationship Between Mass, Velocity, and Force

[rudransh verma]

“Momentum is clearly a vector quantity.
The following common experiences indicate the
importance of this quantity for considering the
effect of force on motion.
1. Suppose a light-weight vehicle (say a small
car) and a heavy weight vehicle (say a loaded
truck) are parked on a horizontal road. We all
know that a much greater force is needed to
push the truck than the car to bring them to
the same speed in same time.”
So it is basically explaining F=dp/dt. To bring the body to a certain same speed or to a certain momentum greater force needs to be applied for massive bodies. It is also saying to produce a required acceleration more massive body needs more force f=ma.

2. “Similarly, a greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed.”
So this one is telling if with initial velocity something is moving and it has to be brought to rest more massive both needs more force. Again F=dp/dt.

3.If two stones, one light and the other heavy,
are dropped from the top of a building, a
person on the ground will find it easier to catch
the light stone than the heavy stone.
“The mass of a body is thus an important
parameter that determines the effect of force on its motion.” I don’t understand this line!

4. Speed is another important parameter to
consider. A bullet fired by a gun can easily
pierce human tissue before it stops, resulting
in casualty. The same bullet fired with
moderate speed will not cause much damage.
Thus for a given mass, the greater the speed,
the greater is the opposing force needed to stop the body in a certain time.
Taken together, the product of mass and velocity, that is momentum, is evidently a relevant variable of motion. The greater the change in the momentum in a given time, the greater is the force that needs to be applied.

 

[phinds]

“The mass of a body is thus an important
parameter that determines the effect of force on its motion.” I don’t understand this line!

What's not to understand? Several of the statements in your post either say directly or clearly imply, that the heavier something is the larger the force needed to change it's state of motion.

 

[rudransh verma]

What's not to understand? Several of the statements in your post either say directly or clearly imply, that the heavier something is the larger the force needed to change it's state of motion.

Effect of force on its motion? Is it saying F/m needs to be more to create the required change in velocity?
If the value of mass m increases so has to force!

 

[Doc Al]

Effect of force on its motion? Is it saying F/m needs to be more to create the required change in velocity?
If the value of mass m increases so has to force!

Wouldn't you agree that the resulting change in motion of an object (its acceleration), given a certain net force F, depends upon the mass of the object?

 

[phinds]

Effect of force on its motion? Is it saying F/m needs to be more to create the required change in velocity?
If the value of mass m increases so has to force!

yes, that's what F/m implies.

 

[rudransh verma]

yes, that's what F/m implies.

and
“The following common experiences indicate the importance of this quantity for considering the effect of force on motion.”

Effect of force on body’s motion depends on mass and velocity?

 

[phinds]

You are beginning to sound like a troll. In how many different ways do we need to explain to you the equation F = ma ?

 

[rudransh verma]

You are beginning to sound like a troll. In how many different ways do we need to explain to you the equation F = ma ?

I want to attack the problem from every direction . Please explain above line.

 

[rudransh verma]

You are beginning to sound like a troll. In how many different ways do we need to explain to you the equation F = ma ?

By experiment $Fdt=dp$ for two bodies of mass M and m where M>m. Same force for same time produces same change in momentum.
So does it mean $Fdt=dp= Mv_1=mv_2$ (initially at rest)?
$v_1<v_2$

 

[Delta2]

By experiment $Fdt=dp$ for two bodies of mass M and m where M>m. Same force for same time produces same change in momentum.
So does it mean $Fdt=dp= Mv_1=mv_2$ (initially at rest)?
$v_1<v_2$

Yes this is correct, but one needs to be careful with the symbols, you write $dp$ and $dt$ but you actually mean $\Delta p$ and $\Delta t$. The first ones are differentials (of momentum and time) but the second ones are the differences.

 

[rudransh verma]

Yes this is correct, but one needs to be careful with the symbols, you write $dp$ and $dt$ but you actually mean $\Delta p$ and $\Delta t$. The first ones are differentials (of momentum and time) but the second ones are the differences.

Thanks! I am not very good at describing eqns into words of physics. So that’s why I try to understand each sentence and how it converts into different eqns. Well the basic eqn is same F=dp/dt. But it can describe different things.

Like the 1. is saying to produce same $\frac{\Delta v}{\Delta t}$ in two bodies, greater force is required for more massive body. ie $\frac{\Delta v}{\Delta t}=\frac{F_1}{m_1}=\frac{F_2}{m_2}$ where $F_1>F_2$ and $m_1>m_2$

In 2. $\Delta v$ is proportional to $F_1/m_1$
Similarly $\Delta v$ is proportional to $F_2/m_2$

In 3. $F_1=m_1g$ and $F_2=m_2g$ where $m_1>m_2$ so $F_1>F_2$.

In 4. $F=m\frac{\Delta v}{\Delta t}$ . If m is constant like for a Bullet then greater acceleration requires greater force to stop the bullet.
Edit: please verify these also @Delta2

 

[jbriggs444]

and
“The following common experiences indicate the importance of this quantity for considering the effect of force on motion.”

Effect of force on body’s motion depends on mass and velocity?

Wrong, wrong, wrong, wrong, wrong.

The acceleration of a body depends on force and mass. $a=\frac{f}{m}$. Newton's second law.

The acceleration from a fixed force on a fixed mass is independent of current velocity.

 

[rudransh verma]

Wrong, wrong, wrong, wrong, wrong.

The acceleration of a body depends on force and mass. $a=\frac{f}{m}$. Newton's second law.

The acceleration from a fixed force on a fixed mass is independent of current velocity.

I wrote the amount of the force delivered or required during the motion or to alter the state of motion of the object depends on its mass and change in velocity. Like a bullet moving very fast delivers a large force on the target and a truck massive enough can deliver a large force on the person standing.
Something like that.

 

[jbriggs444]

I wrote the amount of the force delivered or required during the motion or to alter the state of motion of the object depends on its mass and change in velocity. Like a bullet moving very fast delivers a large force on the target and a truck massive enough can deliver a large force on the person standing.
Something like that.

No. That is not what you wrote. What you actually wrote and what I actually quoted you writing was:

Effect of force on body’s motion depends on mass and velocity?

No, the effect of force on a body's motion (i.e. the resulting acceleration) does not depend on that body's current velocity.

You do not get to change your mind about the meaning of what you write after having written it. It is called intellectual honesty.

 

[rudransh verma]

You do not get to change your mind about the meaning of what you write after having written it. It is called intellectual honesty.

Ok!

 

[rudransh verma]

No, the effect of force on a body's motion (i.e. the resulting acceleration) does not depend on that body's current velocity.

I found a way to demonstrate Newtons law with the help of headphones. Take the headphone and hold both the round ear pieces which go directly on top of ears in both hands. Both the pieces should be touching in the beginning. Now stretch both the parts and leave at the same time. Both will collide and stop. If there will be any difference in the time of launch then piece left first will gain more momentum and the ear pieces will move in other direction after collision. Pretty cool.

 

[rudransh verma]

@Delta2 But why does a heavy ball breaks a tile dropped from some height. Is it because upon impact both should apply forces on each other and divert each other but the force applied by the ball is so much than the bonding forces of the atoms of the tile that the tile before applying any reaction force breaks into pieces?
Like in action films two bullets fired at the same time upon impact breaks into pieces.
The atoms acts like they are attached via springs. If a considerable force is applied the spring will rebound but if too much force is applied the atoms will break apart and the spring like bonds couldn't hold the atoms together.

 

[jbriggs444]

the tile before applying any reaction force

No. No. No.

Newton's third law applies always, exactly and immediately. There is no delay before the reaction force builds up. The very instant that a force exists from A on B, there is a force from B on A. Forces come in pairs.

 

[rudransh verma]

No. No. No.

Newton's third law applies always, exactly and immediately. There is no delay before the reaction force builds up. The very instant that a force exists from A on B, there is a force from B on A. Forces come in pairs.

But its possible that the ball breaks the tile and just pass through. That means no to minimal force from the tile.

 

[jbriggs444]

But its possible that the ball breaks the tile and just pass through. That means no to minimal force from the tile.

The ball breaks the tile without exerting any force on the tile? Nope. Not going to happen.

Yes, there is no minimum. But the force will be non-zero in every case in which the tile breaks. [Zero is the greatest lower bound but there is no minimum]

 

[Delta2]

if you real question is that since the forces come in pairs, why does the tile break but the ball doesn't break, well I guess there might be cases that both could break (if they are from the same material from example)

 

[Vanadium 50]

he ball breaks the tile without exerting any force on the tile? Nope.

Only in Verma-land.

@rudransh verma , when you make up physics, it annoys us and doesn't help you. Ask questions, fine, Arguing for your own unconventional physics? Unhelpful.

 

[Delta2]

I don't think it is his intention to make up physics, but yes he always somehow ends up doing so...

 

[Nugatory]

But its possible that the ball breaks the tile and just pass through. That means no to minimal force from the tile.

It is possible.
In that case the ball exerts a force on the tile sufficient to beak the tile, and the tile exerts an equal and opposite force on the ball until the tile breaks. After the tile breaks it is no longer in the way of the ball so there is zero force between the ball and tile.

 

[Vanadium 50]

Think in terms of energy, It takes a certain energy E to break a plate. This comes from the kinetic energy of the ball, p²/2m. When the ball gives up some energy, its momentum decreases - it has to. A change in momentum requires a force.

If you are arguing after they separate there is no longer any force, I believe you. But I don't think that's what we were discussing.

 

[rudransh verma]

In that case the ball exerts a force on the tile sufficient to beak the tile, and the tile exerts an equal and opposite force on the ball until the tile breaks.

So it’s like take a pen and put it on paper and start applying force with the pointy end. As we increase the force the paper also exerts the same amount of force until the paper couldn’t withstand the applied force of pen and it breaks.
I have a question. A ball placed on a table exerts force on the table due to its weight and the table exerts a normal force up on ball. Does this count as Newton’s third law? Does it not matter if it’s gravity or a push from someone?

 

[Doc Al]

I have a question. A ball placed on a table exerts force on the table due to its weight and the table exerts a normal force up on ball. Does this count as Newton’s third law? Does it not matter if it’s gravity or a push from someone?

There are several 3rd law pairs working here. There's a force between the table and the ball: So the upward normal force on the ball (table on ball) is equal and opposite to the downward force of the ball on the table. Those are 3rd law pairs.

Another force involved is gravity, which is a force exerted by the Earth on the ball. The Earth exerts a downward gravitational force on the ball and the ball exerts an equal and opposite gravitational force upward on the earth. Those are 3rd law pairs.

As far as the ball pushing on the table, it doesn't matter if someone is pushing it down or it's just sitting there. The ball and table will always push on each other with equal and opposite contact force.

 

[Nugatory]

A ball placed on a table exerts force on the table due to its weight and the table exerts a normal force up on ball. Does this count as Newton’s third law?

Yes, this is example of Newton’s third law.

Does it not matter if it’s gravity or a push from someone?

It does not matter.

But do pay attention to which forces are being applied to what. The force of the ball on the table and the force of the table on the ball form a third-law pair, and neither of these forces are whatever (gravity or a push from someone) is pushing the ball down against the table.

 

[rudransh verma]

Is it true that Newtons second law always act in the presence of Newtons third law?
Like if we push something , something pushes on us but at the same time it will accelerate forward ?

 

[Doc Al]

Is it true that Newtons second law always act in the presence of Newtons third law?

Not quite sure what you're thinking: All of Newton's laws apply all the time.

Like if we push something , something pushes on us but at the same time it will accelerate forward ?

If you push something, that something pushes back on you. Whether that something accelerates depends on the net force acting on it: That's Newton's 2nd law. (If you're the only thing pushing it, then it will accelerate in the direction of your push.)