4.4 Newton's Third Law of Motion: Symmetry in Forces

From Figure 4.8, we can see that the engine thrusts add.

The numbers are large and might surprise you.

Experiments such as this were performed in the early 1960s to test the limits of human endurance and the setup designed to protect human subjects in jet fighter emergency ejections.
The speeds of 1000 km/h were obtained.
Land speeds of 10,000 km/h have been obtained with rocket sleds.
The system of interest is obvious in this example.
The choice is not always obvious when choosing the system of interest.

The second law of motion is more than a definition, it is a relationship between acceleration, force, and mass.

We can use it to make predictions.
The second law tells us something basic and universal about nature.
The third and final law of motion is introduced in the next section.

The musical Man of la Mancha talks about the third law of motion.

When one body exerts a force on another, the first also experiences a force, equal in magnitude and opposite in direction.
Many common experiences, such as stubbing a toe or throwing a ball, confirm this.

The first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.

One body can't exert a force on another without experiencing a force of its own.

The law is sometimes referred to as "action-reaction," where the force is the action and the force experienced as a consequence is the reaction.
Understanding which forces are external to a system is one of the uses of the third law.

We can see how people move by looking at how they move.

She pushes against the pool wall with her feet and goes in a different direction.
The wall exerts an equal force on the swimmer.
You might think that two equal and opposite forces would cancel, but they don't because they act on different systems.
There are two systems that we could investigate in this case.
If we choose the swimmer to be the system of interest, the external force on this system will affect its motion.
Our system of interest is not affected by the force on the wall.
It does not affect the motion of the system.
The swimmer pushes in the opposite direction to where she wants to go.
The reaction to her push is what she wanted.

The swimmer goes in the opposite direction of her push when she exerts a force on the wall.

The net external force on her is in the opposite direction.
The wall exerts a force on her equal in magnitude but in the opposite direction as she exerts on it.

The system of interest is indicated by the line around the swimmer.

The swimmer does not act on this system and thus does not cancel.
The free-body diagram only shows the force of the water on the swimmer's body.

There are many examples of the third law.

A professor exerts force backward on the floor as she paces in front of a whiteboard.
The professor is forced to accelerate forward by the floor's reaction force.
The ground pushes forward on the drive wheels in reaction to the drive wheels pushing back on the ground.
There is evidence of the wheels pushing back when the tires spin on a gravel road.
In another example, rockets move forward by expelling gas.
The gas in the rocket combustion chamber exerts a large reaction force on the rocket, because it exerts a large backward force on the rocket.
It's a common misconception that rockets propel themselves by pushing on the ground or in the air behind them.
They work better in a vacuum.

Helicopters experience an upward force reaction when they push air down.

Birds and airplanes exert force on air in a different direction than they need.
The wings of a bird force air downward and backwards in order to move forward.
An octopus propels itself in the water by expelling water through a funnel from its body, like a jet ski.
Professional cage fighters experience reaction forces when they punch, sometimes breaking their hand by hitting an opponent's body.

A professor pushes a cart.

The lengths of the arrows are determined by the magnitude of the forces.
The system of interest needs to be defined differently for each example.
System 1 is appropriate for this example since it asks for the entire group of objects to be accelerated.

External forces are acting on System 1 along the line of motion.

System 2 will be an external force and enter into the second law.

The free-body diagrams allow us to apply the second law.

The system is defined as the professor, cart, and equipment since they accelerate as a unit.

The floor exerts a forward reaction force of 150 N on System 1.
We can assume that there is no net force in the horizontal direction.
The problem is one-dimensional in the horizontal direction.

System 1 has no other significant forces acting on it.

If the net external force can be found, we can use the second law to find the acceleration.
There is a freebody diagram in the figure.

The forces between the professor's hands and the cart are internal to System 1 and do not contribute to the net external force.

There are forces between components of a system that are equal in magnitude and opposite in direction.
The professor's force on the cart results in an equal and opposite force back on her.

It was important to choose System 1 to solve the problem.

An external force is acting on System 2 when she exerts force on the cart.

The second law can be used.

We have to calculate net because the value of is given.

The mass and acceleration of System 2 are known.

The previous example shows that the mass of System 2 is 19.0 kg and that it has an acceleration of 12.0 km/h.

This force is not as strong as the 150-N force that the professor exerts on the floor.

Some of the 150-N force is not transmitted to the cart.

The choice of a system is an important analytical step in both solving problems and understanding the physics of the situation.

The force that two objects exert on each other is visualized.

The gravity force can be changed by changing the properties of the objects.

There are many names for forces, such as push, pull, thrust, lift, weight, friction, and tension.

Traditionally, forces have been grouped into several categories and given names relating to their source, how they are transmitted, or their effects.
The most important of these categories are discussed in this section.
Later in the text, more examples of forces are discussed.

The table is slightly under load when a bag of dog food is placed on it.

If the load were placed on a card table, it would be noticeable, but rigid objects would change shape when a force is applied to them.
The object will exert a restoring force if it is beyond its limit.
The restoring force is greater when the deformation is greater.
When the load is placed on the table, it causes the table to fall until it becomes as large as the weight of the load.
The load's net external force is zero.
The load is on the table.
The table is small so we don't notice it.
It is similar to a trampoline when you climb on it.

The elastic restoring forces in the table grow until they are equal in magnitude and opposite in direction to the weight of the load.

We assumed in a few of the previous examples that whatever supports a load must supply an upward force equal to the weight of the load.

If the object is on an incline, the normal force can be less than the object's weight.

The quantity normal force is represented by the variable.

The symbol for the newton is also represented by the letter N. The normal force that the floor exerts on a chair might be.
The newton is simply a unit, while normal force is a vector.
As you progress in physics, you will see more similarities between variables and units.
The quantity work is an example of this.

Her mass is 60.0 kilograms.

It is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is the opposite.

The forces on the skier are not parallel, so this is a two-dimensional problem.

The approach we have used works well here.
If you choose a convenient coordinate system, you can create two connected one-dimensional problems.
One of the most convenient coordinate systems for motion on an incline is one that has one coordinate parallel to the slope and another parallel to the slope.
The symbols are used to represent parallel and perpendicular.
This type of problem is simplified by the choice of axes because there is no motion between the two objects.
The component of weight parallel to the slope and the component of weight parallel to the slope are defined as the components of weight by the chosen axes.
There are two problems of forces parallel to the slope and parallel to the slope.

The magnitude of the component of the weight parallel to the slope and the magnitude of the component of the weight parallel to the slope are related.

We only need to consider forces parallel to the slope since the acceleration is parallel to the slope.

The amount of the skier's weight is parallel to the slope.

The acceleration is 4.32.

We now know that the value for friction is related to the slope and the motion between the surfaces.

The acceleration is smaller when there is friction than when there is no.

It is a general result that if there is no friction on an incline, the acceleration down the incline is the same regardless of mass.
This is related to the fact that all objects fall in the same way without air resistance.
If the angle is the same, all objects will slide down the incline with the same speed.

An object rests on an incline with a horizontal angle.

The object goes down the incline because of the force acting parallel to the plane.

The force of force on the object causes it to move upward along the plane.

When resolving the weight of the object into components, it is important to be careful.

It is helpful to be able to reason with these equations.

The right triangle is formed by the three weight vectors.

A rubber band, some objects to hang from the end of the rubber band, and a board can be used to investigate how a force parallel to an inclined plane changes.

Place the board at an angle so that the object slides off.

Try two more angles.

The flexible cords that carry muscles to other parts of the body are called tendons.

A force carried by a flexible connector can only be pulled parallel to the length of the string, rope, chain, wire, or cable.
It is important to understand that tension is a pull.
The force of the tension pulls on the ends of the rope.

The force that is transmitted by this rope must be parallel to the length of the rope, as shown.

A tension is caused by the pull that a flexible connector exerts.
The rope pulls with equal force but in different directions on the hand and the supported mass.
This is an example of a third law.

The rope is used to carry the opposite and equal forces between objects.

The rope has the same tension between the hand and mass.
You have determined the tension at all locations along the rope once you have determined the tension in one location.

The weight of the supported mass must be equal to the tension in the rope.

The figure's acceleration is zero if the mass is stationary.
The tension supplied by the rope is the only external force acting on the mass.
The magnitudes of the tension and weight and their signs indicate direction, with up being positive here.

If we cut the rope and put a spring in it, we can see the tension force in the rope.

A hospital traction system, a finger joint, and a bicycle brake cable are just a few of the places where flexible connections are used.

The tension is transmitted undiminished if there is no friction.
It is always parallel to the flexible connector.

Again, the direction but not the magnitude is the same.

The wire is affected by the weight of the tightrope walker.

The point at which the tightrope walker is standing is of interest.

The tension on either side of the person can support his weight.

The forces are represented by arrows with the same directions and lengths as the magnitudes of the forces.
The system is a tightrope walker, and the only external forces acting on him are his weight and the two tensions.
It's reasonable to ignore the weight of the wire.
Since the system is stationary, the net external force is zero.
It is possible to find the tensions using a little trigonometry.
We can see from part b of the figure that the magnitudes of the tensions must be equal.

To cancel each other out, the magnitude of those forces must be equal.

Pick a convenient coordinate system and project the vectors onto its axes is the easiest way to solve two-dimensional vector problems.

The best coordinate system has one axis horizontal and one axis vertical.
We call it the horizontal and the vertical axis.

We need to resolve the tension into the horizontal and vertical components.

A new free-body diagram shows all of the horizontal and vertical components of the system.

Since the tightrope walker is stationary, the components along the axes must add to zero.

The small angle is greater than.

The person is stationary.

Figure 4.18 can be observed.

We can solve for it considering the vertical components.

Since the person is stationary, the second law implies that net.

The weight of the tightrope walker is supported by the vertical tension in the wire.

The weight of the tightrope walker is 686-N.
The vertical component of the wire's tension is a small fraction of the tension in the wire.
Most of the tension in the wire is not used to support the weight of the tightrope walker because the horizontal components are in opposite directions.

The weight of the tightrope walker acted as a force to the rope.

There is an angle between the horizontal and the bent one.

As approaches zero, this becomes very large.

We can create a very large tension in the chain by pushing on it.

When no tow truck is available, we might want to pull the car out of the mud.
The chain is tightened when the car moves forward.
Since the chain is small, the tension is very large.

The chain at the bottom of the picture will fall under its own weight if the weight is evenly distributed along the length.

The Golden Gate Bridge is a very heavy flexible bridge.
The weight of the bridge is evenly distributed along the length of the cables.
There is more than one distinction among forces.
Some forces are real and others are not.
The real forces are those that have a physical origin.
There are forces that arise because an observer is in an accelerated frame of reference, such as a merry-go-round or a car slowing down.
If a satellite is heading north above Earth's northern hemisphere, it will appear to an observer on Earth to be a force to the west that has no physical origin.
Earth is moving east under the satellite because it is rotating toward the east.
This appears to be a westward force on the satellite, or it may be a violation of the law of inertia.