Are you wondering what is “Force” in Physics? If yes, you are at the right place.

In this in-depth guide, we will cover What force is, its physical significance, the calculation of forces, the 4 fundamental forces in nature (and in physics), and the most common forces we encounter in Physics.

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Force in Physics: physical significance

Everyone has a basic understanding of force from everyday experiences. Although force is not visible, we do see and experience its effects.

What is Force in Physics?

Force in Physics can be defined as a push or pull that tries to change the state of rest or uniform motion or shape of a body. Alternatively, we can say force is the cause of motion or a change in shape.

It is our common observation that an object such as a chain lying on a vehicle parked outside the house remains at rest unless a push or pull is given. Such an object cannot move on its own. In other words, the force must be applied to move an object at rest. Also, if a body is moving along a straight line with some velocity, it is found that force is required to change the direction of motion or the magnitude of the velocity.

So, force is an agent which

(i) changes or tends to change the state of motion

(ii) changes or tends to change momentum

(iii) changes or tends to change the shape and size of objects.

Force as a vector used in FBD

When we study different types of problems based on force, we should analyze the different characteristics of forces, which helps draw the free body diagram and write equations of motion.

Characteristics of a force

(i) Magnitude

(ii) Direction

(iii) Point of application

(iv) Line of action

       

Example

Weight (W): The weight of a body is the force by which the earth’s gravity pulls it. Suppose a body of mass m is located at a point where the acceleration due to gravity is g, the weight W = mg.

(i) Magnitude of weight = mg

(ii) Direction will be towards the center of the earth. To show the direction on the paper plane, we draw a downward line, as shown above in the figure.

(iii) Point of application is the center of gravity of the block.

(iv) Line of action is vertically downward.

Calculation of force

Force acting on a particle or on a system of particles is defined as F = \frac{{dP}}{{dt}}

The above mathematical expression states that the rate of change of linear momentum of a body is directly proportional to the external force applied to the body. This change always takes place in the direction of applied force.

In this way, we can calculate force.

An example of the calculation of force

A bullet having a momentum of 20 kg m/s moving horizontally enters a sandbag and stops in the next 2 seconds. Find the average retarding force on the bullet.

Answer

Force acting on bullet = \frac{{{\rm{change in momentum of bullet}}}}{{{\rm{time interval}}}}

F = \frac{{{P_f} - {P_i}}}{{\Delta t}} = \frac{{m \times 0 - m{V_i}}}{{\Delta t}}

\Rightarrow \quad - F = \frac{{m{V_i}}}{{\Delta t}}\quad \Rightarrow Retarding force = \frac{{20\,kg\,{\rm{m/s}}}}{{2\sec }}

Therefore, retarding force acting on that bullet equals 10 N.

Common units of force

In the SI units: (Newton)

1 Newton = 0.225 lb

One Newton force can be defined as the force required to accelerate 1 kg of mass at a rate of 1 m/s2.

In the English system: Pound (LB)

1 LB = 4.448 N.

In the English system, a slug is the amount of mass that 1 pound of force will accelerate at 1 ft/sec2, and a pound-mass is the amount of mass that 1 LB of force will accelerate at 32 ft/sec2.

 

 

 

Fundamental forces of nature

Strong Force

The strong force is a fundamental interaction in nature that acts between different particles of the same atom.

For example, a strong nuclear force is a fundamental interaction that binds or confines quarks into protons. The strong interaction also confines neutrons and protons to form atomic nuclei.

Weak Force

The nuclear force is experienced when reactions involving protons, electrons, and neutrons take place. A neutron can change itself into a proton and, at the same time, emit an electron and a particle antineutrino. We can not think that neutrons comprise a proton, an electron, and an antineutrino. A proton can also change into a neutron and at the same time emit a positron and a neutrino. The forces responsible for these changes are different from gravitational, electromagnetic, and nuclear forces. Such forces are called weak forces.

Gravitational force in Physics

Any two bodies attract each other by virtue of their masses. The force of attraction between two point masses is F = \frac{{G{m_1}{m_2}}}{{{r^2}}} where {m_1} and {m_2} are the particles and r is the separation between them and G is a universal constant having the value 6.67 \times {10^{ - 11}}N{\rm{ - }}{m^2}{\rm{/}}k{g^2}.

We can also define gravitational force in the standard way, “The force exerted by a spherically symmetric body of mass {m_1} and another body of mass {m_2} (spherically symmetric) kept outside the first body is \frac{{G{m_1}{m_2}}}{{{r^2}}} where r is the distance between centers of two bodies. Therefore, for calculating gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centers.

Electromagnetic force in Physics

Ordinary matter is composed of electrons, protons, and neutrons. Each electron has charge - 1.6 \times {10^{ - 19}}C and each proton has charge + 1.6 \times {10^{ - 19}}C. In atoms, the electrons are bound by electromagnetic force acting on them due to protons. The atoms combine to form molecules due to the electromagnetic force. Many atomic and molecular phenomena result from electromagnetic forces between the subatomic particles.

Forces between two surfaces in contact, the tension in the string. Force due to spring is an example of electromagnetic force in daily life.

 

 

Various types of forces in Physics

Friction force in Physics

Whenever the surface of a body slides over that of another, each body exerts a force of friction on the other, parallel to the surface. The force of friction on each body is in a direction opposite to its motion relative to the other body.

The force of friction comes into action only when there is a relative motion between two contact surfaces or when an attempt is made to have it. It is a self adjusting force, it can adjust magnitude to any between zero and maximum value ; 0 \le {f_S} \le {({f_S})_{\max }}.

Spring force in Physics

The force in a spring is not constant and depends on stretch (or compression) y.

F = - ky

Where k is the spring constant and y may be elongation/compression

The greater the elongation or compression, the greater spring force and vice-versa. The negative sign indicates that the force applied by the spring is opposite to the displacement of the free end.

Drag force in Physics

The force a fluid (gas or liquid) exerts on a body moving thrown it is known as fluid resistance. The direction of fluid resistance acting on a body is always opposite the direction of motion of the body velocity relative to the fluid.

For large objects moving through the air, the resisting force is almost proportional to {v^2}. It is then called air drag or drag f = D{v^2}; D is a proportionally constant.

Viscous force in Physics

When a layer of a fluid slips or tends to slip on another layer in contact, the two layers exert tangential forces on each other. The directions are such that the relative motion between the layers is opposed. The forces between the layers opposing relative motion are known as viscous forces.

Damping force in Physics

The damping force is a function of the speed of the moving system and is directed opposite to the velocity. The damping force may be a complicated function of speed, but in several cases, the damping force is proportional to the speed. This force can be written as F = –bv. Here, b is a constant

Muscular force in Physics

Muscular force is the force that is exerted by the muscles of the body. This is a constant force because this can only be exerted on a physical constant.

Examples of muscular force: lifting, walking, running, etc.

Tension force in the Physics

Whenever a body is connected with another body or ceiling through a string, then there will be tension in the string. It acts in the opposite direction to the applied force on the string, or we can say that direction of tension force is always away from the body along the string. It means it pulls another body in contact to which it is connected.

Electromotive force in Physics

If a charge q is taken from terminal B at a lower potential to the terminal A at a higher potential, the work done by the battery force is W = {F_b}\ell where \ell is the distance between A and B.

The work done by the battery force per unit charge is

\varepsilon = \frac{{{W_b}}}{q} = \frac{{{F_b}\ell }}{q}

The quantity \varepsilon is called emf (electromotive force).

Electrostatic force in Physics

The force exerted by a charged particle on the other is given by

F = k\frac{{{q_1}{q_2}}}{{{r^2}}},

and it is known as electrostatic force or Coulomb force.

Here {q_1} and {q_2} are the charges on the particles, r is the separation between them, and k is constant.

The electrostatic force is attractive if they are of the same sign, and this force is repulsive if they are different.

The value of k = 9.89 \times {10^9}N{m^2}{C^{ - 2}}

The value of { \in _0} = \frac{1}{{4\pi k}} = 8.85 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}.

Electric force in physics

The force of interaction between two charges is known as an electric force.

 

Nuclear force in Physics

Nuclear forces are exerted only if the interacting particles are protons, neutrons, or both. These forces are mainly attractive but are short-ranged. These forces are much weaker than coulomb force if the separation between the particles is more than {10^{ - 14}}m but for a smaller separation ( \simeq {10^{ - 15}}m) the nuclear force is much stronger than coulomb force and being attractive it holds the nucleus stable. Due to being short-ranged, these forces come into the picture only if charges within the nucleus are discussed.

 

Buoyant force

When a body is partially or fully dipped into a fluid at rest, the fluid exerts an upward force of buoyancy. This type of force is known as buoyant force. We can also say that buoyant force is the net upward force on any object in any fluid.

Thrust force in Physics

Thrust force is used to control an airplane’s drag and overcome the gravitational force acting on the airplane. The engines of aircraft produce thrust through their propulsion system.

Thrust = {v_{rel}}\frac{m}{{dt}}

\frac{{dm}}{{dt}} =change in mass per unit time.

 

Upthrust force in Physics

The resultant upward force acting on an object immersed in a fluid is known as the force of upthrust. Alternatively, we can say upthrust is the force with which a liquid or gas pushes up against an object that is floating in it.

 

Weight force in Physics

Another word for force of gravity in physics is weight. Weight is a force that acts all time on all objects near the earth towards the center of the earth.

 

Normal force in the Physics

When a body is pressed against a rigid surface, the body experiences a force that is perpendicular to the surface in contact. This force is called normal force or normal reaction.

The magnitude of normal reaction is given by the force perpendicular to the surface on which the body is kept.

In first figure, R = mg and in second figure, R = mg\cos \theta.

 

Net force in Physics

The resultant force acting on a particle is known as the net force.

According to Newton’s IInd law of motion, the rate of change of linear momentum of a body is directly proportional to the external force applied to the body, and this change always takes place in the direction of the applied force.

{({{\bf{F}}_{net}})_{ext}} = \frac{{d{\bf{P}}}}{{dt}}\quad \Rightarrow \quad {\bf{F}} = M{\bf{a}}

\Sigma {F_x} = \frac{{d{P_x}}}{{dt}} = {{\mathop{\rm ma}\nolimits} _x}

and \Sigma {F_y} = \frac{{d{P_y}}}{{dt}} = {{\mathop{\rm ma}\nolimits} _y}

and \Sigma {F_z} = \frac{{d{P_z}}}{{dt}} = {{\mathop{\rm ma}\nolimits} _z}

Ex. 

\Sigma {F_x} = {F_1} + {F_2}\cos \theta - {f_s}

and \Sigma {F_y} = N + {F_2}\sin \theta - mg

and \left| {\bf{F}} \right| = \sqrt {{{\left( {\Sigma {F_x}} \right)}^2} + {{\left( {\Sigma {F_y}} \right)}^2}}

Body of mass m is in rest.

\Sigma {F_x}: net force acting on the body along x-axis

\Sigma {F_y}: net force acting on the body along the y-axis

\left| {\bf{F}} \right|: net force acting on the body

 

External force

With the help of ‘system,’ we can describe which one is an external force and an internal force.

Forces applied on any part of the system by some objects outside it are called external forces.

Ex. 

All surfaces are rough; body B does not ship over body A; system (A+B) is accelerating along +ve x-axis with constant acceleration.

System : A + B

Internal forces : {f_s},\,\,{N_A}

External forces : {f_k},\,\,{N_B},\,\,{m_A}g,\,\,{m_B}g\,\,\& \,\,F

 

Applied force in Physics

An applied force is a force that is applied to an object with the help of an external agent.

Example: A person is pushing a heavy box across the room. Here an applied force is acting on the box.

Examples of applied forces may be

(i) frictional force

(ii) tension force

(iii) normal force

(iv) constant force

 

Constant force in Physics

When a force’s magnitude and direction remain constant with position and time, that force is said to be a constant force.

Examples :

(i) gravitational force acting on the body near the earth’s surface

(ii) kinetic frictional force

(iii) normal reaction force acting on a body placed on a smooth horizontal surface.

 

Variable force in Physics

When a force’s magnitude and direction vary with position and time, that force is said to be a variable force.

Examples : (i) spring force \left( {\frac{1}{2}k{x^2}} \right); Here x may be elongation or compression developed in the spring.

(ii) viscous force acting on a spherical ball.

{F_v} = 6\pi \eta rv

As the speed of the spherical body changes, the viscous force acting on that body changes.

(iii) electrostatic force {F_{el}} = \frac{{k\left| {{Q_1}} \right|\left| {{Q_2}} \right|}}{{{r^2}}}; Here we see that, \left| {{{\bf{F}}_{el}}} \right| is a function of r.

Where r is the separation between two charged particles.

 

Reaction force in the Physics

If two bodies interact, the force exerted on body 1 by body 2 is equal to and opposite the force exerted on body 2 by body 1.

According to Newton’s IIIrd law,

{{\bf{F}}_{12}} = - \,{{\bf{F}}_{21}}

The force that body 1 exerts on body 2 is sometimes called action force, whereas the force body 2 exerts on body 1 is called the reaction force. In reality, however, either force can be labeled the action or reaction force.

 

Conservative force in Physics

If work done by a force around a closed path is zero and is independent of the path, then the force is said to be a conservative force.

Under conservative force F = - \frac{{dU}}{{dr}}; where U is potential energy.

U = \int {dU} = - \int {{\bf{F}} \cdot d{\bf{r}}}

Examples of a conservative force

  • A gravitational force is a conservative force.
  • Elastic force in a stretched spring is a conservative force.

 

Non-conservative forces

If the work done by a force around a closed path is not equal to zero.

\oint {{\bf{F}} \cdot d{\bf{r}}} \ne 0,

and is dependent on the path then the force is a non-conservative force.

Example of a non-conservative force

  • Force of friction
  • Viscous force

Note: Work done by the non-conservative force will not be stored in the form of potential energy.

 

Moment of a force in Physics (also called Couple, Torque, etc.)

Consider a force {\bf{F}} acting on a particle P. choose an origin O and let {\bf{r}} be the position vector of the particle experiencing the force. We define the moment of a force F about O as {\bf{\Gamma }} = {\bf{r}} \times {\bf{F}}

This is a vector quantity having its direction perpendicular to {\bf{r}} and {\bf{F}}. According to the right-hand thumb rule or right-hand screw rule, we can find the direction of the moment of force.

 

Average force in Physics

Over a time interval (\Delta t), the rate of change of momentum of a particle or a system of particles is known as average force.

Mathematically, average force is expressed as

{{\bf{F}}_{av}} = m\left( {\frac{{{{\bf{V}}_f} - {{\bf{V}}_i}}}{{\Delta t}}} \right); Where m is mass of particle

{{\bf{V}}_f} is the final velocity of the particle

{{\bf{V}}_i} is the initial velocity of the particle and

\Delta t is the time interval.

 

Balanced force in Physics

If the sum of all the forces acting on a body equals zero, then the forces acting on the body are called balanced forces.

Here, a body is pulled with the help of an external agent, but the body is unaccelerated.

{a_x} = 0\quad \Rightarrow \quad \Sigma {F_x} = 0\quad \Rightarrow \quad {F_{ext}} = {f_k}

Similarly, {a_y} = 0\quad \Rightarrow \quad \Sigma {F_y} = 0\quad \Rightarrow \quad N = mg

 

Unbalanced force in Physics

When the resultant of the forces acting on the body is not zero, the forces acting on the body are called unbalanced forces.

Here, {a_y} \ne 0\quad \Rightarrow \quad \Sigma {F_y} \ne 0\quad \Rightarrow \quad T - mg \ne 0

Also, T - mg = ma

Or, T - mg > 0

\Rightarrow T > mg unbalanced force.

 

Restoring force in Physics

A force that takes the particle back towards the equilibrium position is called restoring force.

Example

A block of mass m is attached to one end of the spring. Another end of the spring is fixed with the wall. Then the block is pulled away with the help of an external agent. In this process, spring elongates by an amount (\Delta x) but spring always tries to maintain its natural length. As external force is removed, spring force becomes restoring force in this situation.

 

Impulsive force in Physics

When two bodies collide, they exert force (action/reaction) forces on each other while in contact. The momentum of each body is changed due to the force exerted by one another. Typically, the time duration in contact is minimal. This means that the magnitude of the force must be enormous. We call such large forces acting for a very short duration impulsive forces.

As we know {{\bf{F}}_{ext}} = \frac{{d{\bf{P}}}}{{dt}}

If (dt) will be small, \left| {{{\bf{F}}_{ext}}} \right| will be large.

 

Pseudo force in Physics

In the non-inertial frame, Newton’s second law is not applicable. We introduce a “pseudo force” to apply Newton’s second law in the non-inertial frame.

If {\bf{a}} is the acceleration of non-inertial frame of reference, the pseudo force acting on an object of mass m, as measured by an observer in the given non-inertial frame is {{\bf{F}}_{Pseudo}} = - \,m{\bf{a}}.

This means pseudo force acts on an object opposite to the direction of acceleration of the non-inertial frame.

Equation of motion relative to non-inertial frame is \sum {\left( {{{\bf{F}}_{real}} + {{\bf{F}}_{Pseudo}}} \right) = m{\bf{a}}}.

Here ‘a’ is the acceleration of the body as measured with respect to a non-inertial frame of reference.

Author
  • Rajesh Kumar

    20 years of experience teaching high school and college physics to students across the globe.

    When not teaching or mentoring, I write informative articles in physics and related subjects. So far, I have written more than 200 articles on different topics in physics. Apart from physics, I am proficient in engineering statics, dynamics, and calculus. I love spending time with my kids and listening to old Hindi songs.

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