What is the relationship of force with mass and acceleration

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Do you have to consider the mass of the object while applying force on it? Does acceleration affect force?

Learn the answers to these and many more of your questions in the blog post below. 

In this post, we will first discuss mass, force, and acceleration and after that, we will see how they are interrelated by one of Newton's laws.

What is mass, force, and acceleration?

Definition of mass:

Mass is a scalar quantity and has magnitude only. It refers to the content of the body. The equation to find mass is;

m = w/g

Where w is weight and g is the gravitational force. This equation also removes the common misunderstanding that mass and weight are the same quantities. 

 It is measured in kilograms. There are some other units that are used to calculate mass such as pounds, tons e.t.c

Mass does not depend on the size of the body. A small body can have a large mass. According to NASA, it is possible for a black hole to be of the size of an atom and have the mass of a mountain. 

Definition of Force:

Force is a quantity that causes a change in the state or form of the body. It has different types i.e applied, friction, magnetic e.t.c.

Force has direction in addition to a magnitude which makes it a vector quantity. Its unit is Newton, which is equal to a force that moves the body of 1 kilogram with an acceleration of 1 meter per second square.

The formula of force will be discussed later in the article. Before digging into those details, it is better we revise what acceleration is.

Read more on the force in the post “Force Definition, Units, Types, Formula, and Applications.”

Definition of acceleration:

Acceleration is defined as:

Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity.”

Acceleration is derived from velocity so it is also a vector quantity. If it is positive it is called acceleration and if it is negative it is called retardation or deceleration.

The unit of acceleration is ms-2 and it has the same direction as the force.

Do you know? Velocity and acceleration can be opposite in direction like in the case of a ball thrown upward.

Now that you know the definition of mass, force, acceleration, it is time that we move to the actual topic of the article.

Relation between force, mass, and acceleration:

In daily life, we see numerous examples that tell us that there exists a strong relationship between mass, force, and acceleration. 

For instance, take the example of two women, namely Lisa and Britney, pushing shopping carts in the mall. If Britney is more powerful, will she be able to move the cart faster, with more acceleration? Yes!

This means that the force and acceleration are somehow related. Now, what if the masses of their carts are different. What if Britney’s cart is full to the top while Lisa has only a few items in her cart? Who will be able to move faster now?

So, now we know that the mass also has a direct or indirect relation with force. To know the nature of these relations we study Newton's second law of motion. 

Newton’s 2nd law of motion: 

Around 300 years ago, Sir Issac Newton wrote a book by the title “Principia Mathematica Philosophiae Naturalis”. In this book, he explained the effect of outside forces on the state of the body.

In the same book, he gave his all-time famous three laws of motion. The second law explained how force, mass, and acceleration depend on each other.

According to this law:

“Acceleration(a) of an object is dependent upon two variables - the net force(F) acting upon the object and the mass(m) of the object.”

a = F/m

This equation is used to find the value of acceleration using force and mass. We can rearrange it to separate force and use it as a force equation.

F = ma

F stands for force, m for mass, and a for acceleration. Looking at this equation, we can tell three things.

Force and mass:

Force and mass are directly related. If the mass of the body is more, you will need more force to accelerate it. Similarly, if it has less mass, less force will be needed.

F ∝ m

Force and acceleration:

To accelerate more you need to increase force. This means both of these quantities are also directly related. 

F ∝ a

Force and acceleration are vectors as mentioned before. Both have the same direction. Force in the opposite direction causes retardation or negative acceleration and vice versa.

Mass and acceleration:

Mass and acceleration are indirectly related. If mass increases, acceleration decreases. And inversely, when mass decreases, acceleration increases.

m ∝ 1/a

Learn through examples:

Take the example discussed before and assume some magnitudes. In the first point, we will consider the acceleration constant and mass different. In the second step, we will take the same masses while different accelerations.

This will help us to know how a change in only one quantity affects the force.

Keeping acceleration constant:

Mass of Lisa’s cart = 30 kg

Mass of Britney’s cart = 20 kg

Acceleration of Lisa’s cart = 3ms-2

Acceleration of Britney’s cart = 3ms-2

For Lisa:

F = ma

F = (30)(3)

F = 90 N

For Britney:

F = ma

F = (20)(3)

F = 60 N

Keeping mass constant:

Mass of Lisa’s cart = 15kg

Mass of Britney’s cart = 15kg

Acceleration of Lisa’s cart = 3ms-2

Acceleration of Britney’s cart = 0.5 ms--2

For Lisa:

F = ma

F = (15)(3)

F = 45 N

For Britney:

F = ma

F = (15)(0.5)

F = 7.5 N

Looking at the examples solved above, you can conclude that a change in mass or acceleration affects the force directly.

You can find the force using the force calculator.


In a nutshell, force is in direct relationship with mass and acceleration.


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