# Something else besides force?

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Why does some accelerating body stop when an opposite force is equal to it and some others will continue at constant velocity?. For example, say a book at some height above the ground is against a wall is released from rest. The book will always slide down even if the friction between the wall and the book is equal to the weight, right? But let's now say we rub glue on the wall between the book and ground. This time if the glue is strong enough, it brings the book to a stop, making it hang on the wall.

Another example could also be a falling inflated balloon in air. The balloon keeps falling even when drag force equal gravity. While say the balloon were charged(rubbed with fur), and an electric field equal equal to gravity is introduced it hangs on the air.

Why is this happening? Is there something else that determines this outcomes?

stockzahn
Homework Helper
Gold Member
You have to sum up all the forces acting on a body and the resulting force (which is modelled as a vector) yields what happens with it. If the the resulting vector is zero, then the body will remain in its current status of movement.

A ball is dropped from a skyscraper. Since in the beginning the velocity is zero, there is no drag force acting on it, but the gravity does. The sum of these two forces yields a vector unequal zero, therefore the ball accelerates towards the ground. With increasing speed the drag force increases pointing into the opposite direction of gravity, therefore the sum of the forces decreases, but as long as the gravity is stronger than the drag force the velocity of the ball will increase. At a certein point gravity and drag are identical in magnitude and pointing in opposite directions. The sum of the forces is zero and the ball proceeds at constant speed. When it finally hits the ground a very strong force (much higher than gravity) acts on the ball and it is decelerated, since the sum of the vectors of these two forces points upwards. Finally the ball will rest at the ground: The gravity and the force acting on the ball from the ground are identical, but again are pointing in different directions, therefore the sum of the vectors is zero again, i.e. no change of the movement state.

Zaya Bell and russ_watters
CWatters
Homework Helper
Gold Member
Why does some accelerating body stop when an opposite force is equal to it and some others will continue at constant velocity?. For example, say a book at some height above the ground is against a wall is released from rest. The book will always slide down even if the friction between the wall and the book is equal to the weight, right?

Actually no. If the book is "released at rest" and friction = weight the net force acting vertically is zero. So the acceleration is zero, the velocity won't change so the book will stay at rest.

Another example could also be a falling inflated balloon in air. The balloon keeps falling even when drag force equal gravity.

Again the net vertical force is zero. So the acceleration or deceleration is zero and the velocity stays constant.

While say the balloon were charged(rubbed with fur), and an electric field equal equal to gravity is introduced it hangs on the air.

You are thinking of the situation where static electricity attracts a balloon to a wall or ceiling making it stick. In the case of a wall friction between the balloon and the wall is equal to gravity. In the case of the ceiling electrostatic force is equal to (or greater than) gravity. In both cases the net vertical force is zero so the acceleration is zero and the balloon stays where it is placed at rest.

In the case where the balloon is placed on the ceiling the electrostatic force can be greater than the weight of the balloon. In this case there are three forces acting on the balloon...

Gravity acting downwards.
The upward electrostatic force.
A normal force from the ceiling on the balloon acting downwards.

These three sum to zero

In summary, the net force determines the acceleration. The velocity is determined by the starting conditions and the acceleration.

In the equation f = ma the f stands for the net force.

The book will always slide down even if the friction between the wall and the book is equal to the weight, right?

No, not right. If there were some force, say friction, acting upwards and equal to the weight, the book would not slide down. The book slides down specifically because the friction is not equal to the weight. The friction is not equal to the weight because there is no force pushing the book into the wall. The friction force is zero.

The balloon keeps falling even when drag force equal gravity.

Balanced forces cause no acceleration. A body with no net force acting on it will remain in its current state of motion. If it isn’t moving, it will remain stationary. If it is moving it will continue in a straight line at a constant velocity.

Drag is zero until the balloon starts moving through the air. Drag is proportional to the speed (or speed squared) of the balloon through the air. From rest gravity accelerates the balloon downward. The speed increases and the drag increases until the drag is equal to the force of gravity. At that speed there is no net force, and so no acceleration, so the balloon continues falling at that speed.

While say the balloon were charged(rubbed with fur), and an electric field equal equal to gravity is introduced it hangs on the air.

First, just charging up the balloon doesn’t produce a new force. The charge has to have some other charge to attract or repel it for the charge to have any effect on the motion. Although some ionized air with gather around the charged ballon, I don’t believe there will be any significant net effect falling through air.

However, supposing there were a nearby surface with a charge that attracts the balloon. Why would it surprise you that introducing another force changes the motion?

Dale
Mentor
2020 Award
The book will always slide down even if the friction between the wall and the book is equal to the weight, right?
No, if friction were equal to the weight then it would not accelerate and it would remain at rest. The fact that you don’t see this indicates that the friction is less than the weight.

You can increase the friction force by pushing horizontally. The horizontal force will not change the vertical acceleration directly, but it can increase the vertical friction force to the point the friction and gravity forces are balanced and the book does not accelerate.

The balloon keeps falling even when drag force equal gravity.
This is a better example. At terminal velocity the drag force is equal to gravity. The balloon no longer accelerates. It continues to move at a constant velocity.

Why is this happening? Is there something else that determines this outcomes?
Yes. The something else is the initial velocity. When forces are balanced there is no acceleration. If it is moving already (balloon at terminal velocity) then it will continue with the same velocity. If it is initially stationary (book pushed on wall) then it will remain stationary.

At that speed there is no net force, and so no acceleration, so the balloon continues falling at that speed.
How about the case of the glue. The book was brought to a stop. If we say the force acted by the glue was greater, that would imply the book is supposed to accelerate upwards. Why did an equal force brought the book to a rest?

Yes. The something else is the initial velocity. When forces are balanced there is no acceleration. If it is moving already (balloon at terminal velocity) then it will continue with the same velocity. If it is initially stationary (book pushed on wall) then it will remain stationary.
Alright, but let me clear my confusions. Say I have a toy ship. If I were to hold the ship on the surface of water(no fraction of ship underwater, zero velocity), then left it to sink. Instantaneously, the force of gravity accelerates the object downward, right? But then according to Archimedes principle, the ship will stop sinking when it displaces the weight of water equal to its weight. In this case, won't the ship decelerates to a stop? How exactly does it get decelerated?

jbriggs444
Homework Helper
How about the case of the glue. The book was brought to a stop. If we say the force acted by the glue was greater, that would imply the book is supposed to accelerate upwards. Why did an equal force brought the book to a rest?
The glue does not amount to a fixed force. It is an available force. The more strain you put on the glue joint, the more force it resists with. [Up until the glue joint breaks].

The reason the book comes to rest is because a stable equilibrium exists between the downward force of gravity and the strain that results in an upward force from the glue.

Zaya Bell
ZapperZ
Staff Emeritus
Alright, but let me clear my confusions. Say I have a toy ship. If I were to hold the ship on the surface of water(no fraction of ship underwater, zero velocity), then left it to sink. Instantaneously, the force of gravity accelerates the object downward, right? But then according to Archimedes principle, the ship will stop sinking when it displaces the weight of water equal to its weight. In this case, won't the ship decelerates to a stop? How exactly does it get decelerated?

Your thread has become quite confusing, because now it appears that you're asking for the origin of these various forces.

Let's start from Chapter 1. Do you understand that in Newton's second law, F = ma, the "F" in this case is the vectorial sum of ALL the forces acting on a body? And that if this vectorial sum is zero, then the object will experience no acceleration?

Note that it doesn't mean that there are no forces acting on the object. It is just that the sum of all these forces come out to zero.

This is what I still am not sure that you have understood clearly.

Zz.

Zaya Bell
Merlin3189
Homework Helper
Gold Member
... I have a toy ship. .. I ...hold the ship on the surface of water(no fraction of ship underwater, zero velocity), then left it to sink. Instantaneously, the force of gravity accelerates the object downward, right?
yes
But then according to Archimedes principle, the ship will stop sinking when it displaces the weight of water equal to its weight.
No
In this case, won't the ship decelerates to a stop?
yes
How exactly does it get decelerated?
As it starts to sink, it displaces some water and there is an upward buoyant force which reduces its downward acceleration.
When it gets to a depth where the displacement makes the buoyant force equal to the weight, then the acceleration becomes zero.
It continues to go down, but as the depth increases, the buoyant force is greater than the weight and the acceleration is now upwards.
Gradually the downward velocity reduces to zero and the continuing upward acceleration starts it moving upward.
It accelerates upward until it again reaches the depth where buoyancy equals weight and the acceleration becomes zero.
It continues to go up , but as the depth decreases, the buoyant force is less than the weight and the acceleration is now downwards.

Ie. the boat bobs up and down about the equilibrium depth.

But I haven't mentioned the other effects, like the water level changing around the boat and dissipating energy as waves, turbulence, viscosity. Energy is being dissipated and the amplitude of bobbing decreases until the boat settles at its equilibrium level.

Dale, Zaya Bell and jbriggs444
russ_watters
Mentor
Alright, but let me clear my confusions. Say I have a toy ship. If I were to hold the ship on the surface of water(no fraction of ship underwater, zero velocity), then left it to sink. Instantaneously, the force of gravity accelerates the object downward, right? But then according to Archimedes principle, the ship will stop sinking when it displaces the weight of water equal to its weight. In this case, won't the ship decelerates to a stop? How exactly does it get decelerated?
You should actually try this. It should be clear that the toy initially sinks lower in the water than its steady state displacement. That's where the extra force required to decelerate it comes from.

Zaya Bell
Dale
Mentor
2020 Award
Instantaneously, the force of gravity accelerates the object downward, right?
Yes.

But then according to Archimedes principle, the ship will stop sinking when it displaces the weight of water equal to its weight.
Archimedes principle says no such thing. It says “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.” Nothing about stopping is involved in the principle.

In this case, won't the ship decelerates to a stop? How exactly does it get decelerated?
The buoyant force will exceed the weight as the ship passes the equilibrium position.

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Zaya Bell
How about the case of the glue. The book was brought to a stop. If we say the force acted by the glue was greater, that would imply the book is supposed to accelerate upwards. Why did an equal force brought the book to a rest?

What is really happening in that case is that the glue (and the wall, and the book too) is elastic. When you push on it in some direction it stretches like a spring. It takes force to stretch the material, and the force is directly proportional to the amount of stretch. The material will stretch until the force is equal to the gravitational force.

As you noted, if the book was already in motion and somehow the glue “caught” and stopped it, the elastic stretching would go past where it equaled gravity and would increase until the net upward force stops the book. The material would then snap back and the book would oscillate until the energy damped and you wind up in the equilibrium condition. This isn’t just true of glue. Apparently rigid materials are flexing and moving all the time as the forces change, say, when you sit on a chair or swing a golf club. When you lean on a rock wall, believe it or not, the rock wall bends a little until the elastic restoring force equals the force with which you are pushing on the wall.

The reason you don’t always see this is because materials can be very stiff and the stretching may be small. On the other hand if your glue is something like silly putty a high speed camera will show all kinds of fun macroscopic distortions and stretching when you toss it against a wall.

A lot of times the physics problem isn’t about a rigid object or a rigid connection. We don’t want to (or perhaps can’t) work out all of the elastic bending and stretching involved. We just know that, say, some rod is attached to some wall and it isn’t going to bend or move significantly. We call these forces of constraint. We know the rod will produce whatever force is necessary to keep from moving, so we just go ahead and use that. In the case of your book the glue provides enough force to stop the book and then enough force to counter gravity and keep it stationary. When stated that way it sounds like magic, but we are just ignoring the details of elastic stretching or compressing that make it true.

Zaya Bell
Let's start from Chapter 1. Do you understand that in Newton's second law, F = ma, the "F" in this case is the vectorial sum of ALL the forces acting on a body? And that if this vectorial sum is zero, then the object will experience no acceleration?

Note that it doesn't mean that there are no forces acting on the object. It is just that the sum of all these forces come out to zero.

This is what I still am not sure that you have understood clearly.
Yes, I do.

Got it. Thanks

yes
No
yes
As it starts to sink, it displaces some water and there is an upward buoyant force which reduces its downward acceleration.
When it gets to a depth where the displacement makes the buoyant force equal to the weight, then the acceleration becomes zero.
It continues to go down, but as the depth increases, the buoyant force is greater than the weight and the acceleration is now upwards.
Gradually the downward velocity reduces to zero and the continuing upward acceleration starts it moving upward.
It accelerates upward until it again reaches the depth where buoyancy equals weight and the acceleration becomes zero.
It continues to go up , but as the depth decreases, the buoyant force is less than the weight and the acceleration is now downwards.

Ie. the boat bobs up and down about the equilibrium depth.

But I haven't mentioned the other effects, like the water level changing around the boat and dissipating energy as waves, turbulence, viscosity. Energy is being dissipated and the amplitude of bobbing decreases until the boat settles at its equilibrium level.
And this cleared the confusion. Thank you.

What is really happening in that case is that the glue (and the wall, and the book too) is elastic. When you push on it in some direction it stretches like a spring. It takes force to stretch the material, and the force is directly proportional to the amount of stretch. The material will stretch until the force is equal to the gravitational force.

As you noted, if the book was already in motion and somehow the glue “caught” and stopped it, the elastic stretching would go past where it equaled gravity and would increase until the net upward force stops the book. The material would then snap back and the book would oscillate until the energy damped and you wind up in the equilibrium condition. This isn’t just true of glue. Apparently rigid materials are flexing and moving all the time as the forces change, say, when you sit on a chair or swing a golf club. When you lean on a rock wall, believe it or not, the rock wall bends a little until the elastic restoring force equals the force with which you are pushing on the wall.

The reason you don’t always see this is because materials can be very stiff and the stretching may be small. On the other hand if your glue is something like silly putty a high speed camera will show all kinds of fun macroscopic distortions and stretching when you toss it against a wall.

A lot of times the physics problem isn’t about a rigid object or a rigid connection. We don’t want to (or perhaps can’t) work out all of the elastic bending and stretching involved. We just know that, say, some rod is attached to some wall and it isn’t going to bend or move significantly. We call these forces of constraint. We know the rod will produce whatever force is necessary to keep from moving, so we just go ahead and use that. In the case of your book the glue provides enough force to stop the book and then enough force to counter gravity and keep it stationary. When stated that way it sounds like magic, but we are just ignoring the details of elastic stretching or compressing that make it true.
Perfect. Thanks