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How To Find Normal Force With Acceleration:Several Approaches and Problem Examples

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The normal force is exerted on an object by the surface with which it is in contact. Let us learn how to find normal force with acceleration.

In physics terms, the normal force comes under the category of contact force. In order to find this force, we draw a free body diagram and then use Newton’s second law of motion. There is no other specific formula to find the normal force. Let us see several approaches and example problems.

The Normal Force

Before jumping on how to find a normal force with acceleration, we should know the formula of a force. As per Newton’s second law of motion, we already know that F propto frac{mathrm{d} p}{mathrm{d} t} . Which further drives the formula F = ma. Using this formula, we can find the force using acceleration and mass.

Know that we know that we can continue finding the normal force. An important point to remember is that the free-falling body has acceleration equal to ‘g,’ that is, acceleration due to gravity. The value of g is 9.8 m s^{-2} , or in some cases, we take it as 10 m s^{-2}.

To find the normal force, we need to follow a few simple steps:

  1. The very first step is to draw the free-body diagrams showing all the forces that act on an object.
  2. Represent the directions of all forces. The normal force always acts perpendicular to the object.
  3. The next step is to substitute the values of acceleration, mass, and forces.
  4. The last step is to do the calculation to find the normal force.

There are several approaches and cases for which we have to know how to find the normal force with acceleration.

How to find normal force with acceleration

The first case is when the object is at rest on the surface. In this case, the free body diagram is shown as above. The normal force F_N acts perpendicular to the object, and the weight W = mg acts in the downward direction.

From the diagram we get;

F_N = W

F_N = mg

Here,

F_N is the normal force

m is the mass of the object

g is the acceleration due to gravity

How To Find Normal Force With Acceleration: Several Approaches and Problem Examples

The next case is when the force acts on the object that falls at some angle theta. The free-body diagram is shown in the above figure. On splitting the F into components we get, F sintheta acting along with the weight W. On balancing, we get;

F_N = W + F sin  theta

F_N = mg + F sin theta

Here,

F_N is the normal force

F sintheta is the force acting on the object

m is the mass of the object

g is the acceleration due to gravity

How To Find Normal Force With Acceleration: Several Approaches and Problem Examples

If the force on the body acts in the upward direction, then the free body diagram should be drawn as above. On balancing, we get;

F_N = W - F sin  theta

F_N = mg - F sin theta

Here,

F_N is the normal force

F sin theta is the force acting on the object

m is the mass of the object

g is the acceleration due to gravity

How To Find Normal Force With Acceleration: Several Approaches and Problem Examples

The last case is when the object is inclined at some angle theta as shown in figure (i). The first step is to split the W into its components. On balancing, we get;

F_N = W cos theta

F_N = mg cos theta

Problems On How To Find Normal Force With Acceleration

Problem 1) An object falls down with a force of 300 N at an angle of 30°. Calculate the normal force acting on the object if its mass is 20 kg.

Solution: We are given;

Mass = 20 kg,

Force = 300 N

Angle = 30°

The normal force would be calculated from the formula;

F_N = mg + F sin theta

On substituting the given values, we get the normal force as;

F_N = 20 times 10 + 300 sin 30

F_N = 200 + 300 times frac {1}{2}

F_N = 200 + 150

F_N = 350 N

Problem 2) A box of 4 kg is kept on the table. Calculate the normal force acting on it.

Solution: We are given;

m = 4 kg

g = 9.8 m/s2

The normal force would be;

F_N = mg

F_N = 4 times 9.8

F_N = 39.2 N

Frequently Asked Questions (FAQs)

What is normal force?

There are various kinds of forces like normal force, frictional force, gravitational force, and many more that act on an object.

At the time any body is in contact with another surface, a force acts on it, known as normal force. It is this normal force that lets the object stay on the surface or avoids passing the object through each other. For example, a normal force acts on a book kept on the table to avoid it from falling.

How to find forces with acceleration?

We get the formula of force from Newton’s Second Law of Motion.

Using the law, we get F propto frac{mathrm{d} p}{mathrm{d} t} , where p is the momentum of the moving body. Further on, substituting p = mv and differentiating the formula of force becomes F = ma, a is the acceleration, and m is the mass of the body. This formula is used to find force with acceleration.

How to find normal force with acceleration?

We need to follow a few easy steps to find out the normal force acting on any object.

The first very step is to draw the free body diagram and with the directions of all the forces. Then using Newton’s Second Law ( a = F/m) computes the magnitude of the normal force.

What is the unit of normal force?

In direct terms, the normal force supports the weight of the object that is in contact with any surface.

The normal force is a kind of force that is exerted perpendicularly on the body that is in contact with the surface. For instance, the table exerts a normal force on the box kept on it. Since it is also a force, its unit is N (Newtons).

What is the direction of the normal force?

The normal force is always exerted perpendicularly to the object or the body.

In all the cases, the normal force acts perpendicularly to the object and always in the upward direction. In simple cases, the normal force balances the gravitational pull exerted by the earth’s surface.

Is normal force a contact force or a non-contact force?

The surface on which an object is placed exerts a normal force on it.

The normal force is, in all cases, a contact force. When any body touches another surface, force is exerted on it by the surface. If not so there would be no normal forces exerted by the object on each other.

About Rabiya Khalid

How To Find Normal Force With Acceleration: Several Approaches and Problem ExamplesHi,
I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: https://www.linkedin.com/mwlite/in/rabiya-khalid-bba02921a
In my free time, I let out my creative side on a canvas. You can check my paintings at:
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