Force and Pressure: All our daily activities such as running, lifting, opening a door, playing games require force to be applied. How can we define force in simple terms? Do we always need physical contact to apply a force, or can we apply a force without any physical contact? Also, what is pressure? What are the laws associated with it? Let us read this article to understand more about force and pressure.

What is Force?

All the activities in our daily life, like running, walking, holding, lifting, etc., require us to apply some force. But what is force?

In simple words, we can say that a push or a pull is known as force. Force is a vector quantity; that is, it has both a direction and some magnitude. The SI unit of force is Newtons \(N\) The CGS unit of the force is dyne.

Newton’s Second Law of Motion

Newton’s second law of motion defines force as the rate of change of momentum with respect to time.

\(F = \,\frac{{{P_f} – {P_i}}}{{\Delta t}} = m\left( {\frac{{v – u}}{{\Delta t}}} \right)\)

Where,

\({p_f}\) is the final momentum of the body.

\({p_i}\) is the initial momentum of the body.

\(m\) is the mass of the body.

\(v\) is the final velocity of the body

\(u\) is the initial velocity of the body.

\(\Delta t\) is the time interval.

\(F = \,ma\)

Here,

\(a\) is the acceleration of the body.

In differential form, we can write,

\(F\, = \,\frac{{dp}}{{dt}} = \frac{{mdv}}{{dt}}\)

\( \Rightarrow \,F\, = \,ma\)

Effect of Force

Force can bring out various changes in the body, such as an increase or decrease in speed or deforms it.

Force can change the state of the body; that is, it can increase the velocity, decrease the velocity or change the direction of the velocity. It can bring the body to rest from motion or from motion to rest.

For rigid bodies, the force cannot change the shape of the body, but if the body is not rigid, for example, foam, sponge, etc., a force can change the shape of the object.

Types of Force

Based on the mode of application, the force can be classified into two types.

1. Contact Forces
2. Non-contact Forces

1. Contact Force

Contact forces are forces that require physical contact to apply. Example: Friction, muscular force, viscous force.

Friction

Frictional force exists between any two bodies or surfaces in contact when they tend to move relative to each other. Friction opposes the relative motion between any two surfaces.

\(f = \mu N\)

Where,

\(f\) is the frictional force,

\(\mu \) is the coefficient of friction.

\(N\) is the normal force to the surface.

Viscous Force

Viscous force is defined as the opposition offered by the fluid to any relative motion between the different layers of a fluid or with the container. It is analogous to friction. The viscous force is given by,

\(F\, = \,\mu A\frac{{{V_{\max }}}}{{\Delta h}}\)

Where,

\(\mu \) is the viscosity of the fluid.

\(A\) is the area under consideration.

\({v_{\max }}\) is the velocity of the top layer under consideration.

\(\Delta h\) is the height of the fluid.

\(\frac{{{V_{\max }}}}{{\Delta h}}\) is the velocity gradient of the fluid.

2. Non-contact Force

Non-contact forces are the force that does not require physical contact to apply the force. Example: Gravitational force, magnetic force, electrostatic force, etc.

Gravitational Force

Gravitational force exists between any two bodies in the universe that have mass. It is always attractive in nature. The magnitude of this force is given by Newton’s law of gravitation; that is, the magnitude of the force is directly proportional to the product of the mass of the bodies and inversely proportional to the square of the distance between them.

\(F\propto {m_1} \times {m_2}\)

\( \Rightarrow F = \frac{{G{m_1}{m_2}}}{{{r^2}}}\)

Where,

\(G\) is the proportionality constant known as the universal gravitational constant.

Magnetic Force

Magnetic force can be exerted on magnetic material without the need for any physical contact. A magnet attracts iron or a current-carrying conductor when kept nearby. Magnetic force is also experienced by charges that are in motion.

The force on a charge in motion is given by the charge multiplied by the cross-product of the velocity and magnetic field.

\(\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)\)

\(q\) is the value of the charge.

\({\overrightarrow v }\) is the velocity of the charge.

Field or a force field is a concept that we use to explain these Non-contact forces. Examples of fields are gravitational field, electric field, magnetic field, etc.

Electrostatic Force

electrostatic force exists between any two charges in the universe. It can be both attractive and repulsive in nature. Coulomb’s law of electrostatics; that is, the magnitude of the force is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.

\(F\,\propto \,{q_1}\, \times \,{q_2}\)

\(F\propto \,\frac{1}{{{r^2}}}\)

\( \Rightarrow F = \frac{{K{q_1}{q_2}}}{{{r^2}}}\)

Where,

\(K\) is the proportionality constant known as the universal gravitational constant.

\({q_1}\) and \({q_2}\) is the magnitude of the charge.

\(r\) is the distance between the two charges.

Pressure

Thrust is the net effective force experienced by the surface or the component of the force acting normal to the surface.

The SI unit of thrust is Newton \({\rm{N}}\)

The thrust experienced per unit area is known as pressure. The pressure is given as,

\(P = \frac{T}{A}\)

Where,

\(T\) is the thrust on the area.

\(A\) is the magnitude of the area.

From the expression of the pressure, we can say that the larger the area on which the force is acting, the lesser the pressure will be. This means that a pin can exert greater pressure than a hammer.

Atmospheric Pressure

Earth is surrounded by a blanket of air known as the atmosphere. Air is a fluid and exerts pressure on the surface of the earth. This pressure is due to the thrust due to the weight of the air column above the earth’s surface.

From the law of hydrostatics,

The rate of change of pressure with height is given by,

\(\frac{{dP}}{{dh}} = \rho g\)

Where,

\(\rho \) is the density of the fluid

\(g\) is the acceleration due to gravity

Pressure in Liquids

A liquid also applies some pressure on the object submerged.

\(P = {P_0} + \rho gh\)

Where,

\({P_0} \) is the pressure of the surface of the liquid.

\(\rho \) is the density of the liquid.

\(g\) is the acceleration due to gravity.

depth of the point where the pressure is to be determined.

Solved Examples on Force and Pressure

Q.1. The mass of a man is \(30\,{\rm{kg}}\) The man is standing on the podium with a base area of \({\rm{.02}}\,{{\rm{m}}^2}\) Find the pressure on the surface.
Ans: Given,
The mass of the man is \(30\,{\rm{kg}}\)
The area of the podium is \({\rm{.02}}\,{{\rm{m}}^2}\)
We know that pressure is given by,
\({\rm{P}}\,{\rm{ = }}\,\frac{T}{A}\)
Where,
\(T\) is the thrust on the area.
\(A\) is the magnitude of the area.
Putting in the values we get,
\( \Rightarrow P = \frac{{mg}}{A}\)
\( \Rightarrow P = \frac{{30 \times 10}}{{02}}\)
\( \Rightarrow P = 1.5 \times {10^4}\;{\rm{N}}\,{{\rm{m}}^{ – 2}}\)

Q.2. If the momentum of the car changes from \(10\,{\rm{Kg}}\,{\rm{m}}{{\rm{s}}^{ – 1}}\) to \(20\,{\rm{Kg}}\,{\rm{m}}{{\rm{s}}^{ – 1}}\,\) then find the force applied.
Ans: Given,
The initial momentum of the car is, \({p_1} = 10\,{\rm{Kg}}\,{\rm{m}}{{\rm{s}}^{ – 1}}\)
The final momentum of the car is \({p_f}\, = \,\,20\,{\rm{Kg}}\,{\rm{m}}{{\rm{s}}^{ – 1}}\)
The time taken to change the momentum is \(t\, = \,2\;{\rm{s}}\)
From Newton’s second law, we know that,
\(F = \,\frac{{{p_f} – {p_i}}}{{\Delta t}}\)
Where,
 \({p_f}\) is the final momentum of the body.
\({{p_i}}\) is the initial momentum of the body.
\(\Delta t\) is the time interval
Putting in the values and solving we get,
\(F\, = \,\left( {\frac{{20 – 10}}{2}} \right) = 5\;{\rm{N}}\)

Summary

Our everyday daily activities require force. Our muscles generate the required force for doing our daily activities. We need to have physical contact to apply force, but that is not always the case. Forces that require physical contact to use are known as contact forces—examples: friction, viscous. Forces that do not require contact to apply are known as non-contact forces. Example: magnetic force, electrostatic force, gravitational force.

Thrust is the effective force or the component of the force perpendicular to the area. Pressure is the thrust per unit area. The atmospheric pressure exists due to the weight of the air column present before the surface of the earth.

FAQs on Force and Pressure

Q.1. What is force?
Ans: A push or a pull is known as force. Force can also be defined by Newton’s second law of motion; force is the rate of change of momentum with respect to time.
\(F\, = \,\frac{{{p_f} – {p_i}}}{{\Delta t}} = m\left( {\frac{{v – u}}{{\Delta t}}} \right)\)
Where,
\({p_f}\) is the final momentum of the body.
\({p_i}\) is the initial momentum of the body.
\(m\) is the mass of the body.
\(v\) is the final velocity of the body.
\(\Delta t\) is the time interval.

Q.2. Is a normal reaction force a contact force?
Ans: Yes, the normal reaction force is a contact force as it gets applied only when the two surfaces are in contact.

Q.3. What is thrust?
Ans. Thrust can be defined as the net effective force on the surface or the component of the force in the direction perpendicular to the area. The SI unit of thrust is the same as that of force.

Q.4. What is pressure?
Ans: The thrust per unit area is known as pressure.
\(P = \,\frac{T}{A}\)
Where,
\(T\) is the thrust on the area.
\(A\) is the magnitude of the area.

Q.5. On what factors does pressure depend?
Ans: Pressure depends on the thrust and the area of the surface on which it acts.

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