Acceleration: Newton's Second Law of Motion

Contributor: Jay Gregorio. Lesson ID: 13192

You cannot budge a cabinet. Your friend helps, and it slides across the floor. Why? Your friend stops helping, and the cabinet stops moving. Why? What about inertia? What's going on? Find out here!



learning style
personality style
Beaver, Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

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  • Have you heard the story about Isaac Newton and the falling apple?

Isaac Newton

Legend has it that the young Newton was hit on the head by an apple while sitting under an apple tree. There's no evidence that the apple really landed on his head, but his observations of a falling apple gave birth to his understanding of gravity - one of the fundamental forces in nature.

Gravity is just one of the many forces that exist in nature. There is friction force when two surfaces rub against each other, electromagnetic force that describes electric and magnetic fields, nuclear forces that hold atoms and their particles together, and the force you apply when you push or pull objects.

The different forces described above affect an object's motion in their own unique ways. Their fundamental principle, however, is a simple push or pull.

In the Related Lesson on inertia, found in the right-hand sidebar, you learned how an object wishes to remain in its current state of motion and requires an unbalanced force to alter that state.

If you push a book across a table, it will move a certain distance because the unbalanced force of your push caused it to change its state of motion. You accelerated the book.

A force that is applied to an object causing it to either speed up or slow down is called applied force.

To understand an applied force, you need to define it in terms of its direction and strength. That is, you must identify where the force is applied and the effect it has on the object at that point.

  • Is it possible for the force to change the direction of the object?
  • What is the effect of force on the speed of the object?
  • Does an object need force to continue moving at a constant speed in a specific direction?

Explore these and other questions in this lesson!

The Concept of Applied Force

Forces are all around us, and they exist in many forms. There is a force involved when you walk, move a cabinet across a wooden floor, press a key on the computer keyboard, play the drums, pluck guitar strings, and many other things.

In fact, your feet are on the ground right now because of the force of gravity! Without these forces, the world would be a lot different.

Sometimes, there may be more than one force acting on an object at the same time. Newton's first law of motion describes these forces as balanced and unbalanced forces.

To illustrate how these forces work, we will represent them as arrows:

  • The length of the arrow determines the force's strength or its amount. This means that the longer the arrow, the greater the force.
  • The arrow will also point in the direction the force is being applied.

Suppose you have a box sitting on the ground, and two forces are acting in the opposite direction as shown below:

force diagram 1

  • Are the forces balanced?
  • What will happen to the object?

In this example, the forces are balanced. If the object is at rest, it will remain at rest. The law of inertia perfectly explains this situation. The object will sit there forever until one of the applied forces increases, which will start the object moving in the direction of the greater force.

Let's look at another example below, but this time, observe the strength of force applied on each side of the object:

force diagram 2

  • Are the forces balanced?
  • What will happen to this object?

Notice that the force applied to the left side of the object is greater in strength than the force applied to its right side. This is an example of unbalanced forces.

Since the greater applied force against the left side of the object is pushing the object to the right against the weaker applied force, the object will move to the right along the surface.

It is important to emphasize that the object moved to the right as a result of a net force. The net force is the vector sum of the forces acting on an object. Remember, a force has direction. So you must add the forces together as vectors to determine their difference or net force. More on this later.

This net force will increase the object's speed at equal intervals of time. This increase in speed at equal intervals of time is called acceleration. So, when enough force is applied to an object to change its state of motion, the object will accelerate.

Force, Mass, and Acceleration

Newton's second law of motion states:

A force applied on an object is proportional to the mass of the object and its acceleration.

Conversely, acceleration of the object is only possible when there is a force applied in the direction of its motion and if the mass does not offer much resistance to the force.

To express it mathematically, use the symbols F for force, m for mass, and a for acceleration. The equation, then, is:

Fnet = ma

In this equation, Fnet is the net force, m is the mass, and a is the acceleration. The relationship among these quantities shows that the net force is directly proportional to the product of mass and acceleration.

  • What does that mean?

When an object is heavier, a greater force is needed to move it.

If you are unable to move a cabinet no matter how hard you push, its mass is too great for your level of force. When you ask someone to push with you, your combined forces are able to accelerate the mass. If your friend is able to increase his push, which would increase the net force, the cabinet's acceleration will also increase.

The unit of force applied is measured in Newtons (N). Mass is measured in kilograms (kg), and acceleration is m/s2.

Fnet = ma

Newton (N) = kilogram (kg) * m/s2

This equation may also be rearranged to solve for acceleration and mass using the triangle strategy below :

force equation triangle

a = Fnet ÷ m

m = Fnet ÷ a

A "Negative" Force

In physics, it is always important to identify the direction where force is applied. While the terms to the right and to the left are helpful, they do not make sense mathematically.

Therefore, physicists use a negative sign (-) for forces acting to the left and a positive sign (+) for forces acting to the right.

If the force is -10 N, for example, it means that a force of 10 N is applied to the left. It does not mean that the force applied is very small.

Do the Math!

Now, let's add numerical values to the examples above to put it all together!

An object with a mass of 10 kg experiences two forces:

force diagram 3

First, find the net force:

Fnet = (10 N) + (-10 N) = 0 N

Now, use the net force to find the object's acceleration:

a = Fnet ÷ m

a = 0 N ÷ 10 kg

a = 0 m/s2

This means that the object's acceleration (a) is zero, which means it will not move. Remember that a net force of zero also means that the forces acting on the object are balanced.

Now, let's look at the next example.

An object with a mass of 10 kg experiences two forces. However, the forces are not the same amount this time:

force diagram 4

First, find the net force:

Fnet = (20 N) + (-10 N) = 10 N

Now, use the net force to find the object's acceleration:

a = Fnet ÷ m

a = 10 N ÷ 10 kg

a = 1 m/s2

This means that the object above will accelerate at 1 m/s2. Since the net force is non-zero, it means that the forces are unbalanced.

Watch Newton's Second Law of Motion, from Wisc-Online, to review these concepts:

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It is important to note that balanced forces can also act on an object that is not at rest but moving at a constant speed in a specific direction. In this case, the object's motion does not increase due to Newton's first law of motion. Therefore, acceleration is zero.

If you would like to explore this concept more, read The Big Misconception by Tom Henderson at The Physics Classroom.

In the Got It? section, you will demonstrate your understanding of Newton's second law by examining some word problems!

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