Motion, Gravity and Pressure – Archimedes’ Principle

In this article, we will look at basic physics concepts like Motion, Gravity, Pressure, Capillary, and the Principle of Archimedes. They all are important from an exam point of view. We will look at their definition, formula, derivation, application, and much more.

These are some of the important elements of these topics. The concepts are quite easy to understand and we have used simple language to make the first time readers understand it. Let us begin with the basic concepts of physic for UPSC and other competitive exams.

Motion

The motion refers to change in an object’s position with respect to its location in an interval of time. The simplest motion is motion in a straight line. Motion takes place in everything and is mostly visible as there is a change in position.

When an object travels equal distances in equal intervals of time it becomes uniform motion. An incase of unequal distance but equal intervals, it becomes non-uniform motion.

Scalers are the quantitative terms to define dimensions like speed or mass in a single number. Vectors are the one which needs more than one number to describe themselves like velocity.

Mechanics deal with moving objects while kinetics deal with resting objects. Dynamics is the cause of force production.

Important Motion Terms

1. Distance and Displacement

Distance is a term used to describe the movement of an object in direction. The total travelled distance of an object is the total path covered.

Distance – d1 + d2 = 2d

Displacement refers to the shortest distance travelled from the initial position to the final position. The displacement magnitude may be zero but the distance covered cannot be zero.

Displacement ( Δx ) = xf − x0

2. Speed and Time

The rate at which an object travels the distance in unit time is speed. The SI of speed is meter/second or m/s. And the total time taken to travel the distance becomes the unit time.

The average speed requires division of total distance by total time. The speed can be uniform or non-uniform. When it remains the same per unit time it becomes uniform speed. And when it changes speed per unit time, it becomes non-uniform speed.

Average speed is a situation when it changes according to conditions and instantaneous speed is when it changes without any particular reason.

Average Speed – Total Distance Travelled / Total Time Taken

3. Velocity and Acceleration

The velocity is the direction of motion with speed. It is basically the speed of an object moving in a defined direction. The formula to calculate velocity is the same as speed. Velocity can be uniform and non-uniform.

When the object covers equal distance in equal time intervals, it becomes uniform velocity. And when the object covers unequal distances in equal intervals or vice versa, it becomes variable velocity.

Average Velocity – Initial Velocity + Final Velocity.

The change in velocity per unit time refers to acceleration. The SI of acceleration is m.

The acceleration is positive when velocity increases and is negative when velocity decreases. Zero acceleration is when velocity is zero. Uniform acceleration is when velocity changes in equal intervals and when it changes in unequal intervals, it becomes non-uniform acceleration.

Acceleration= Change in Velocity / Time Taken

Types of Motion

1. Translational / Translatory

This type of motion involves object movement on a path in any dimension. The object moves from one to another position mostly in a straight line. This can be in any of the directions. The straight movement of a car in a lane is an example of this motion.

2. Oscillatory / Vibratory / Periodic

This motion involves the object’s motion in a repetitive manner within a particular time frame.
If it gets mechanical in nature of movement or motion it becomes a vibration. The guitar strings are an example of this kind of motion.

Each Oscillation is a period in physics terminology.

3. Rotational / Circular / Rotatory

This type of motion involves an object’s movement in a circular path in a fixed axis. When there is a uniform speed in movement, it becomes uniform circular motion. And where the speed is not uniform, it becomes a non-uniform circular motion.

4. Linear

It comes under transnational motion as the object moves in a single direction along a single dimension. The straight-line motion is rectilinear motion and curved path motion is curvilinear motion. It follows the same principle as transnational motion mentioned above.

5. Simple Harmonic and Projectile

This motion is like the movement of a pendulum where the force is opposite to the direction of the motion. This restoring force is directly proportional to object displacement from the initial position. The projectile motion involves horizontal and vertical displacement.

Newton’s Laws of Motion

1. Newton’s First Law of Motion – Law of Inertia

This law states an object’s position will not change unless an external force acts on it. And once in motion, the velocity will not change or the object will not stop without external force interference. An external force is basically a change in the mechanical energy of an object.

Object at rest and object in motion are the two conditions of this law. Putting up a seat belt while driving is an idea based on this principle. The net force is the total force put on an object.

2. Newton’s Second Law of Motion

The second law of motion states “Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.” it is quantitative in nature and studies the motion behavior. This law depends on the net force and mass of the object.

The “F” represents the force and ”m” is the mass and acceleration is “a”.
a = net F / m

3. Newton’s Third Law of Motion

This law of motion states “For every action, there is an equal and opposite reaction.” The interaction of objects is because of force. The force is of two types – frictional force and non-contact force. Friction is when there is contact between two objects and the force between them. And normal force is when an object touches the surface.

Force of AB = Force of BA

This law explains that two bodies interact, they exert equal force on each other. Mass and Weight are other important terms here. Mass is the quantity and weight is the gravity size. Newton denotes mass and kg denotes weight.

W = mg ( W – weight in newton, m – mass in kg and g- acceleration of gravity )

Gravity

Gravity refers to the force that attracts the body to the earth and any physical body with mass. All the objects in this world have mass thus exert gravitational pull and strength increase with mass. This is the reason why planets revolve around the sun in orbits.

Gravity is a discovery of Isaac Newton in 1687 when he was sitting under an apple tree. The falling of the apple excited Newton and he recognized the idea of gravity or Newton’s law of Universal Gravitation.

Gravity in the Universe is the reason for sustaining life. The gravitational pull keeps all the elements in place on earth and in the atmosphere. The sun is at a distance because of gravity and keeps the earth secure with proper air and light.

Newton denied gravity as “Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.”

Force = Gravitational Constant ( mass 1 mass 2 / distance between centre of 2 masses ) Or F = G (m1m2/r2)

Anything which has gravity and more massive mass means more gravity. And the gravitational pull is strongest in closer objects. The distance usually weakens the gravity. This formula is to find gravity between 2 objects.

Examples of Gravity

• The gravity holds the sun gases together.
• The water rests at the glass bottom because of gravity.
• The tides in the ocean are because of the moon and earth attraction due to gravity.
• Gravity allows the moon to revolve around the earth.
• There are millions of similar examples but the bottom line is that the effect of gravity is the same on all objects. The only change is that it
• depends on the size and the mass.

Relationship Between Gravity and Weight

The force that attracts the body to earth by gravitation is the weight. It is the force of gravity or Fg. It is applicable to all the objects near earth. The weight of the object is the mass of the body multiplied by acceleration by gravity.

Fg = mg (Fg – the force of gravity, m – the mass of the object and g – acceleration due to gravity)

Facts about Gravity

• The weakest fundamental force of nature is gravity and also the dominant force.
• The speed of all the falling objects remains the same on earth i.e. 9.8 m/s.
• G = 6.67259×10−11 N Sqm / Sq kg.
• Your weight is the force of attraction between you and the Earth.
• To leave earth’s gravitational pull, an object has to travel 7 miles per second.
• The moon has 16% of gravitational pull compared to earth and mars has 28%. And Jupiter 2.5 times more than earth.
• The black holes have maximum gravity on the universe that even light cant escape.
• Gravity is capable of bending with light with unlimited range.

Capillary

Capillary refers to the rise or fall of liquid in small tube passage and is not limited to the vertical direction. A towel is an example of this as water enters the fibers no matter the direction.

Liquid wets the tube when it rises in small-bore tubes and does not wet the tube when it depresses within tubes below the surface.

The capillary occurs when the tube gets wet. Water wets the line while mercury does not. The interfacial force allows capillary-like water inside a tube is due to the interaction between molecules of water and the glass walls.

The narrower the capillary tube, the higher the water rise and vice versa for mercury. This concept often follows Newton’s Second Law.

Important Points Regarding Capillary

• The nature of the liquid and solid will have an impact on capillary as we saw in the water and mercury example above.
• The angle of contact is the angle of the tangent to the liquid surface and solid inside the liquid. The solid and liquid nature impacts this like concave meniscus has an acute angle while a convex meniscus of the liquid has an obtuse angle.
  P, T, O, and G remain constant in liquid or solid at a point of time.
• The height of the liquid rise is independent of capillary shape until the radius remains the same.
• The liquid meniscus in Capillarity are of three types –

1. Concave meniscus
2. Convex meniscus
3. Plane meniscus

Forces in Capillary

1. Adhesion
This is a force between two substances that are different in nature. This is the reason behind water sticking on a glass.

2. Cohesion
Cohesion is the force between liquid molecules specifically. Raindrops cohesion is one example before touching any surface.

Application of Capillary In Everyday Life

• Wetting of paper towel due to water capillary movement
• A cloth towel uses the same concept
• The roots of trees use this concept to transport water and liquid throughout the plant
• The oil in a lamp wick rises due to the concept of capillary
• Water retains in a piece of sponge is due to this

Pressure

The pressure is a term for physical force put on an object. The force is perpendicular to the object surface per unit area. When force is put on an object, the pressure becomes equal to force and area ratio.

The SI unit of pressure is pascal or Pa and is the force of 1N applied / surface area of 1m sq. the pressure has y

The formula of pressure (P) becomes – P = F / A

Factors Affecting Pressure

The area is one most important factor that decides the pressure of the force. The force remains the same but pressure changes with the change in surface size.

The pressure increases with a decrease in the surface size with the same amount of force and vice versa. The physics behind sharpening the knives is related to pressure.

Sharpening a sharp knife requires less pressure as the force is reaching just the edges but in the case of blunt knives, the force reaches a larger surface requiring more pressure. Another example is of karate methods.

The karate chop applies all the force at one point thus the pressure is more and the surface is less. And the open-handed slap looks at a larger surface thus the pressure drops.

Types of Pressure

The pressure that air exerts in the atmosphere is the atmospheric pressure. The atmosphere has a gas layer around it that exerts pressure. 101325 Pa is the value of atmospheric pressure at sea level. The mercury barometer measures this with the height of a mercury column.

The millimeters of mercury, pounds per square inch (psi), dynes per square centimeter, etc can measure this pressure. This pressure tends to drop near the earth’s surface with a rate of 3.5 millibars / every 30 meters.

The pressure relative to atmospheric pressure is the gauge pressure. It is positive above atmospheric pressure and negative below it.

The gauge is zero at atmospheric pressure and thus blood pressure or gas pressure machines are relative to atmospheric pressure. And it also doesn’t add to closed container fluid pressure.

Thus the total of atmospheric and gauge pressure gives rise to absolute pressure. And the differential pressure is the difference between the pressure on point A and pressure on point B.

The fluid or hydrostatic pressure is not a basic type but it is the pressure by increasing the quantity of fluid.

Archimedes Principle

The force of thrust is opposite to the force of gravity. When pressure is put on any fluid, the body submerged in it, this force is thrust. The force reduces as it goes down because of gravity and thus the body feels light. Swimming is an example of this concept.

Thrust = Pressure × Area

The principle of Archimedes states that “The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid”.

Archimedes of Syracuse of Greece is the founder of this law. Buoyancy is the force that allows an object to float. The buoyant force is equal to the fluid weight displaced by the object.

The formula for this force is – Fb = ρ x g x V ( Fb is buoyant force, ρ is density, g is gravity acceleration and V is submerged volume. )

Derivation of Archimedes Principle

• The mass of the liquid displaced – Mass = Density × Volume = ρ × V.
• Density is ρ = MassVolume = MV
• Weight of displaced liquid becomes – Weight = Mass × Acceleration due to gravity or W = M × g
• And the Archimedes principle says – loss of weight = weight of water displaced = ρ×V×g
• The thrust force or buoyant force becomes – Fb = ρ × V × g

Archimedes Principle Applications

• Submarine – Ballast tank inside the submarine makes the weight of the submarine greater than the buoyant force.
• Hot Air Balloon – The buoyant force of a balloon is less than the surrounding air by varying the quantity of hot air in the balloon.
• Hydrometer – They have lead shots that help them flow to measure liquid’s relative density.

Conclusion

This article was about some important physics concepts. The most important elements were their application and formula to calculate them. They are an important part of physics as well as general science. They are essential for knowing how the world functions.

The UPSC Prelims General Study paper can have a question from this topic. This is because it comes under the basic science module. It is also important for UPSC Mains Physics as it is building a basic understanding of the subject.

Aspirants preparing for other competitive exams like SSC, RRB, and more can refer to it as well. UPSC candidates can look at this topic before appearing for the exams.