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How does Newton’s second law of motion apply to rockets?
We know that according to Newton’s second law of motion, force is a product of mass and acceleration. When a force is applied on the rocket, the force is termed as thrust. Greater the thrust, greater will be the acceleration. Acceleration is also dependent on the mass of the rocket. Lighter the rocket faster is the acceleration.

How does Newton’s second law apply to a car crash?
According to the definition of Newton’s second law of motion, force is the dot product of mass and acceleration. The force in a car crash is dependent either on the or the acceleration of the car. As the acceleration or mass of the car increases, the force with which car crash takes place will also increase.

What are Newton’s second law examples in everyday life?
Following are Newton’s second law examples in everyday life:

Pushing a car is easier than pushing a truck with the same amount of force as the mass of the car is lesser than the mass of the truck.
In golf game, acceleration of the golf ball is directly proportional to the force with which it is hit by the golf stick. Also, the force applied is inversely proportional to the mass of the ball.
What is the other name for Newton’s second law?
The other name for Newton’s second law is a law of force and acceleration.

What are some daily life examples of Newton’s second law of motion?
Newton’s second law of motion explains how force can change the acceleration of the object and how acceleration and mass of the same object are related. Therefore, in daily life, if there is any change in the acceleration of the object due to the applied force, then they are the examples of Newton’s second law.

Acceleration of the rocket is due to the force applied known as thrust and is an example of Newton’s second law of motion.
Another example of Newton’s second law is when an object falls down from a certain height, the acceleration increases because of the gravitational force.

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Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. Objects at equilibrium (the condition in which all forces balance) will not accelerate. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

The BIG Equation

Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

a = Fnet / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Fnet = m * a

In this entire discussion, the emphasis has been on the net force. The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is important to remember this distinction. Do not use the value of merely "any 'ole force" in the above equation. It is the net force that is related to acceleration. As discussed in an earlier lesson, the net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. If necessary, review this principle by returning to the practice questions in Lesson 2.

Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written.

1 Newton = 1 kg * m/s²

The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.

Your Turn to Practice

The F net = m * a equation is often used in algebraic problem solving. The table below can be filled by substituting into the equation and solving for the unknown quantity. Try it yourself and then use the click on the buttons to view the answers.

Net Force

(N)

Mass

(kg)

Acceleration

(m/s/s)

1.

10

2

2.

20

2

3.

20

4

4.

2

5

5.

10

10

Newton's Second Law as a Guide to Thinking

The numerical information in the table above demonstrates some important qualitative relationships between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant). Similarly, comparing the values in rows 2 and 4 demonstrates that a halving of the net force results in a halving of the acceleration (if mass is held constant). Acceleration is directly proportional to net force.

Furthermore, the qualitative relationship between mass and acceleration can be seen by a comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling of the mass results in a halving of the acceleration (if force is held constant). And similarly, rows 4 and 5 show that a halving of the mass results in a doubling of the acceleration (if force is held constant). Acceleration is inversely proportional to mass.

The analysis of the table data illustrates that an equation such as F net = m*a can be a guide to thinking about how a variation in one quantity might affect another quantity. Whatever alteration is made of the net force, the same change will occur with the acceleration. Double, triple or quadruple the net force, and the acceleration will do the same. On the other hand, whatever alteration is made of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or quadruple the mass, and the acceleration will be one-half, one-third or one-fourth its original value.

The Direction of the Net Force and Acceleration

As stated above, the direction of the net force is in the same direction as the acceleration. Thus, if the direction of the acceleration is known, then the direction of the net force is also known. Consider the two oil drop diagrams below for an acceleration of a car. From the diagram, determine the direction of the net force that is acting upon the car. Then click the buttons to view the answers. ( If necessary, review acceleration from the previous unit.)

In conclusion, Newton's second law provides the explanation for the behavior of objects upon which the forces do not balance. The law states that unbalanced forces cause objects to accelerate with an acceleration that is directly proportional to the net force and inversely proportional to the mass.

We Would Like to Suggest ...

Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Force Interactive. You can find it in the Physics Interactives section of our website. The Force Interactive allows a learner to explore the effect of variations in applied force, net force, mass, and friction upon the acceleration of an object.

Rocket Science!
NASA rockets (and others) accelerate upward off the launch pad as they burn a tremendous amount of fuel. As the fuel is burned and exhausted to propel the rocket, the mass of the rocket changes. As such, the same propulsion force can result in increasing acceleration values over time. Use the Rocket Science widget below to explore this effect.

Check Your Understanding

1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object.

2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s ². Determine the mass of the encyclopedia.

3. Suppose that a sled is accelerating at a rate of 2 m/s ². If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?

4. Suppose that a sled is accelerating at a rate of 2 m/s ². If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?

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Newton's second law describes the affect of net force and mass upon the acceleration of an object. Often expressed as the equation a = Fnet/m (or rearranged to Fnet=m*a), the equation is probably the most important equation in all of Mechanics.

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The first part of Newton's law of inertia is pretty straightforward. An object at rest will stay at rest, unless and until it comes in contact with an unbalanced force.

That means that this baseball isn't going anywhere, unless it encounters another force. Say a wind gust knocks it over, or someone picks it up, like this.

So the ball stays at rest, until someone or something moves it, or hits it.

The second part of the law-an object in motion will stay in motion, until and unless it comes into contact with an unbalanced force-might take a bit more imagination.

There are many unbalanced forces in baseball: friction, gravity, air currents, to name a few. For this example we can use friction. A grassy infield has a great deal of friction, since grass growing out of dirt is rough and can be a little bumpy.

So if I hit a ground ball, the friction from the field is gonna stop the motion, pretty quickly.

Okay, let's say we were playing this game on ice.

Ice is a smooth surface and slicker than grass and dirt, so it has a lot less friction, though it still has some.

Less friction, so the ball goes farther before it stops.

So what if I hit this ball, but in a place where there is no unbalanced force at all-no gravity, no air currents, and no friction?

With nothing there to stop it, the ball's inertia continues, and the ball stays in motion, forever.

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Space Pause/Play video playback Enter Pause/Play video playback m Mute/Unmute video volume Up and Down arrows Increase and decrease volume by 10% Right and Left arrows Seek forward or backward by 5 seconds 0-9 Fast seek to x% of the video. f Enter or exit fullscreen.

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The rate of change of linear momentum is directly proportional to the impressed force and takes the direction in which the force acts.

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Dementieva Zvonareva Jankovic Azarenka Stosur

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Ball bouncing in slow motion: Tennis ball

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Recorded at 10'000 FPS, played back at 25 FPS = 400x slower.

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The normal force is an everyday force that is felt when a surface pushes against an object that is placed on that surface. For example, when a book is placed on a table, the normal force keeps the book from falling through the table. Gravity is pulling the book downward, but since the book isn't actually falling, something must be pushing it up. This force is called the normal force. The name 'normal' means perpendicular to the surface. Figure 1 and Figure 2 show how the the normal force acts on the object. Contrast to the gravitational force (whose force starts at the centre of the object)-the normal force begins at the surface.

The normal force arises from the electromagnetic force; specifically, the electrons in the book push against the electrons in the table. Since the electrons don't want to get any closer to each other, the book stays on top of the table.

The normal force is closely related to the friction force. Both are non-conservative forces, which can be seen when a ball bounces. The ball falls; gravity pulls it down, so it speeds up, while air drag somewhat slows the fall. When the ball hits the ground a huge normal force pushes upwards, making the ball bounce not quite as high as when it started. There is energy lost to changing the shape of the ball, which becomes thermal energy (warming the ball) and sound. The normal force can also be seen as non-conservative in the case of rolling resistance. The deformation of the tire (or wheel) means that energy is being lost to that change of shape.

See Florian Knorn's video below for an example of how the normal force deforms a tennis ball while bouncing:

Please see UC Davis's Phys wiki or hyperphysics for more information about the normal force.

For Further Reading

References

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The normal force is an everyday force that is felt when a surface pushes against an object that is placed on that surface. For example, when a book is placed on a table, the normal force keeps the book from falling through the table.

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→ Force can make a stationary body in object.
For example: a football can be set to move by kicking it i.e. by applying a force.

→ Force can stop a moving body. For example, by applying brakes, a running cycle or a running vehicle can be stopped.

→ Force can change the direction of a moving object.
For example: by applying force i.e. by moving handle, the direction of a running bicycle can be changed. Similarly by moving steering, the direction of a running vehicle is changed.

→ Force can change the speed of a moving body. By accelerating, the speed of a running vehicle can be increased or by applying brakes the speed of a running vehicle can be decreased.

→ Force can change the shape and size of an object.
For example: by hammering, a block of metal can be turned into a thin sheet. By hammering, a stone can be broken into pieces.

* Forces are mainly of two types:

→ If the resultant of applied forces is equal to zero, it is called balanced forces.

Example: In the tug of war if both the team apply similar magnitude of forces in opposite directions, rope does not move in either side.
This happens because of balanced forces in which resultant of applied forces become zero.

→ Balanced forces do not cause any change of state of an object. Balanced forces are equal in magnitude and opposite in direction.

→ Balanced forces can change the shape and size of an object.

For example: When forces are applied from both sides over a balloon, the size and shape of balloon is changed.

→ If the resultant of applied forces are greater than zero, the forces are called unbalanced forces.

→ An object in rest can be moved because of applying balanced forces.

* Unbalanced forces can do the following:

→ Move a stationary object

→ Increase the speed of a moving object

→ Decrease the speed of a moving object

→ Change the shape and size of an object

* Galileo Galilei: Galileo first of all said that object move with a constant speed when no foces act on them.

→ This means if an object is moving on a frictionless path and no other force is acting upon it, the object would be moving forever. That is, there is no unbalanced force working on the object.

→ But practically it is not possible for any object. Because to attain the condition of zero, unbalanced force is impossible.

→ Force of friction, force of air and many other forces are always acting upon an object.

→ Newton studied the ideas of Galileo and gave the three laws of motion. These laws are known as Newton's laws of motion.

Newton's First Law of Motion (Law of Inertia)

→ Any object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change the state by applying external force.

Explanation: If any object is in the state of rest, then it will remain in rest until a external force is applied to change its state. Similarly, an object will remain in motion until any external force is applied over it to change its state.
This means all objects resist to in changing their state. The state of any object can be changed by applying external forces only.

* Newton's First Law of Motion in Everyday Life

(i) A person standing in a bus falls backward when bus starts moving suddenly.

→ This happens because the person and bus both are in rest while bus is not moving, but as the bus starts moving, the legs of the person start moving along with bus but rest portion of his body has the tendency to remain in rest. Because of this, the person falls backward; if he is not alert.

(ii) A person standing in a moving bus falls forward if driver applies brakes suddenly.

→ This happens because when bus is moving, the person standing in it is also in motion along with bus. But when driver applies brakes the speed of bus decreases suddenly or bus comes in the state of rest suddenly, in this condition the legs of the person which are in contact with the bus come in rest while the rest part of his body have the tendency to remain in motion. Because of this person falls forward if he is not alert.

(iii) Before hanging the wet clothes over laundry line, usually many jerks are given to the clothes to get them dried quickly. Because of jerks, droplets of water from the pores of the cloth falls on the ground and reduced amount of water in clothes dries them quickly.

→ This happens because when suddenly clothes are made in motion by giving jerks, the water droplets in it have the tendency to remain in rest and they are separated from clothes and fall on the ground.

(iv) When the pile of coin on the carom-board is hit by a striker, coin only at the bottom moves away leaving rest of the pile of coin at same place.

→ This happens because when the pile is struck with a striker, the coin at the bottom comes in motion while rest of the coin in the pile has the tendency to remain in the rest and they vertically falls the carom-board and remain at same place.

→ The property of an object because of which it resists to get disturb its state is called inertia.

→ Inertia of an object is measured by its mass. Inertia is directly proportional to the mass. This means inertia increases with increase in mass and decreases with decrease in mass.

→ A heavy object will have more inertia than the lighter one. In other words, the natural tendency of an object that resists the change in state of motion or rest of the object is called inertia.

→ Since a heavy object has more inertia, thus it is difficult to push or pull a heavy box over the ground than the lighter one.

→ Momentum is the power of motion of an object.

→ The product of velocity and mass is called the momentum. Momentum is denoted by 'p'.

→ Therefore, Momentum of the object = Mass × Velocity (p = m × v)

where, p = momentum, m = mass of the object and v = velocity of the object.

* Some explanations to understand the momentum:

→ A person get injured in the case of hitting by a moving object, such as stone, pebbles or anything because of momentum of the object.

→ Even a small bullet is able to kill a person when it is fired from a gun because of its momentum due to great velocity.

→ A person get injured severely when hit by a moving vehicle because of momentum of vehicle due to mass and velocity.

→ Since momentum is the product of mass and velocity (p = m × v) of an object. This means momentum is directly proportional to mass and velocity. Momentum increases with increase of either mass or velocity of an object.

→ This means if a lighter and a heavier object is moving with same velocity, then heavier object will have more momentum than the lighter one.

→ If a small object is moving with great velocity, it has tremendous momentum. And because of momentum, it can harm an object more severely.

Example: a small bullet having a little mass even kills a person when it is fired from a gun.

→ Usually, road accidents prove more fatal because of high speed than in slower speed. This happens because vehicles running with high speed have greater momentum compared to a vehicle running with slower speed.

Momentum of an object which is in the state of rest

Let an object with mass 'm' is in the rest.

Since, object is in rest, therefore, its velocity, v = 0

Momentum = mass × velocity

Thus, the momentum of an object in the rest i.e. non-moving, is equal to zero.

→ SI unit of velocity = m/s

We know that,
Momentum (p) = m × v

∴ p = kg × m/s ⇒ p = kgm/s

Numerical Problems Based on Momentum

Type I: Calculation of Momentum

Example 1: What will be the momentum of a stone having mass of 10 kg when it is thrown with a velocity of 2 m/s?

Solution

Mass (m) = 10 kg

We know that,
Momentum (p) = Mass (m) × Velocity (v)

∴ p = 10 kg × 2 m/s = 20 kg m/s

Thus, the momentum of the stone = 20 kg m/s.

Example 2: Calculate the momentum of a bullet of 25 g when it is fired from a gun with a velocity of 100 m/s.

Solution

Given,
Velocity of the bullet (v) = 100 m/s

Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025 kg

∴ p = 0.025 × 100 = 2.5 kg m/s

Momentum of the bullet = 2.5 kg m/s.

Example 3: Calculate the momentum of a bullet having mass of 25 g is thrown using hand with a velocity of 0.1 m/s.

Solution

Given,
Velocity of the bullet (v) = 0.1 m/s

Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025 kg

Momentum (p) = Mass (m) × Velocity (v)

Momentum of the bullet = 0.0025 kg m/s.

Example 4: The mass of a goods lorry is 4000 kg and the mass of goods loaded on it is 20000 kg. If the lorry is moving with a velocity of 2 m/s, what will be its momentum?

Solution

Given,
Velocity (v) = 2 m/s

Mass of lorry = 4000 kg
Mass of goods on the lorry = 20000 kg

∴ Total mass (m) on the lorry = 4000 kg + 20000 kg = 24000 kg

Momentum (p) = Mass (m) × Velocity (v)

Momentum of the lorry = 48000 kg m/s.

Example 5: A car having mass of 1000 kg is moving with a velocity of 0.5 m/s. What will be its momentum?

Solution

Given,
Velocity of the car (v) = 0.5 m/s

Mass of the car (m) = 1000 kg

Momentum (p) = Mass (m) × Velocity (v)

∴ p = 1000 kg × 0.5 m/s = 500 kg m/s

Momentum of the car = 500 kg m/s.

Statement of Second Law of Motion

→ Rate of change of momentum of an object is proportional to applied unbalanced force in the direction of force.

Suppose,
Mass of an object = m kg

Initial velocity of an object = u m/s

Final velocity of an object = v m/s

∴ Initial momentum, p ₁ = mu
Final momentum, p ₂ = mv

∴ Change in momentum = Final momentum - Initial momentum

∴ Rate of change of momentum = Change in momentum/Time taken

* According to 2nd law, this rate of change is momentum is directly proportional to force.

We know that, a = (v-u)/t (From 1st equation of motion)

where, k is a constant. Its value can be assumed as 1.

* SI unit = kg m/s 2 or Newton

1 Newton: When an acceleration of 1 m/s ² is seen in a body of mass 1 kg, then the

force applied on the body is said to be 1 Newton.

Proof of Newton's First Law of Motion from Second Law

→ First law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.

(i) A body is moving with initial velocity u then,

Thus, final velocity is also same.

(ii) A body is at rest i.e., u = 0

Therefore, from above u = v = 0

So, the body will continue to be at rest.

→ For every action there is an equal an opposite reaction.

(i) Walking is enabled by 3rd law.

(ii) A boat moves back when we deboard it.

(iii) A gun recoils.

(iv) Rowing of a boat.

Law of Conservation of Momentum

→ When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting.

* Initial momentum = Final momentum

Suppose, two objects A and B each of mass m ₁ and mass m ₂ are moving initially with velocities u ₁ and u ₂, strike each other after time t and start moving with velocities v ₁ and v ₂ respectively.

Initial momentum of object A = m ₁u ₁

Initial momentum of object B = m ₂u ₂

Final momentum of object A = m ₁v ₁

Final momentum of object B = m ₂v ₂

Rate of change of momentum in A,

Rate of change of momentum in B,

We know from 3rd law of motion,

Thus, Initial momentum = Final momentum

Example 1: A bullet of mass 20 g is fired horizontally with a velocity of 150 m/s from a pistol of mass 2 kg. Find the recoil velocity of the pistol.

Mass (m ₁) of bullet = 20 g = 0.02 kg

Mass (m ₂) of pistol = 2 kg

Initially bullet is inside the gun and it is not moving.

∵ Mass = m ₁+m ₂ = (0.02 + 2) kg = 2.02 kg

∴ Initial momentum = 2.02 × 0 = 0 ....(i)

Let the velocity of pistol be v ₂ and v ₁ for bullet = 150

Initial momentum = Final momentum

∴ (0.02×150)/100 + 2v ₂ = 0 [From equations (i) and (ii)]

(−)ve sign indicates that gun recoils in direction opposite to that of the bullet.

Example 2: Two hockey players viz A of mass 50 kg is moving with a velocity of 4 m/s and another one B belonging to opposite team with mass 60 kg is moving with 3 m/s, get entangled while chasing and fall down. Find the velocity with which they fall down and in which direction?

Initial momentum A = m Au A = 50 × 4 = 200 kgm/s

Initial momentum B = m Bu B = 60 × 3 = 180 kgm/s

∴ Total initial momentum = 200 + 180 = 380 kgm/s ....(i)

Final momentum = (m A + m B)v = (50 + 60)v = 110v ....(ii)

According to the law of conservation of momentum,

⇒ v = 380/110 = 3.454 m/s

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Notes of Ch 9 Force and Laws of Motion| Class 9th Science

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→ Force can make a stationary body in object. For example: a football can be set to move by kicking it i.e. by applying a force. → Force can stop a moving body. For example, by applying brakes, a running cycle or a running vehicle can be stopped.

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"The tendency of the body  to oppose any changes in the  direction of its motion."

If we  observe the  video,  Bus is travelling on the road with passenger.  Passenger standing inside the bus with the help of grab handle.
Bus is moving fast on the road, suddenly bus should cross the curved road, Than the bus negotiates right hand curve on the road the passenger will tilt to the left side . In the same manner , if the bus negotiates left hand curve on the road the passenger will tilt to the right side, This is because of " inertia of direction".

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Uploaded by annapureddy venkat on 2016-12-29.

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:The force which act on a body for a short time are known as Impulsive forces.

For eg. Hitting a ball with bat fining a gun etc.

An Impulsive force doe snot remain constant but changes, firstly from zero to max and then from max. to zero.

So it is not possible to measure the exact value of force. Hence in such cases, we measure the total effect of force known as Impulse.

So Impulse of a force is defined as the measure of total effect of force. It is given by the product of force and time.

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https://youtu.be/d7iYZPp2zYY "The tendency of the body  in uniform motion to continue to travel a longer straight line unless an external force  acts on it."

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Newton's third law: All forces in the universe occur in equal but oppositely directed pairs. There are no isolated forces; for every external force that acts on an object there is a force of equal magnitude but opposite direction which acts back on the object which exerted that external force. In the case of internal forces, a force on one part of a system will be countered by a reaction force on another part of the system so that an isolated system cannot by any means exert a net force on the system as a whole. A system cannot "bootstrap" itself into motion with purely internal forces - to achieve a net force and an acceleration, it must interact with an object external to itself.

| Without specifying the nature or origin of the forces on the two masses, Newton's 3rd law states that if they arise from the two masses themselves, they must be equal in magnitude but opposite in direction so that no net force arises from purely internal forces.

Newton's third law is one of the fundamental symmetry principles of the universe. Since we have no examples of it being violated in nature, it is a useful tool for analyzing situations which are somewhat counter-intuitive. For example, when a small truck collides head-on with a large truck, your intuition might tell you that the force on the small truck is larger. Not so!