mass and weight

mass and weight

What is Mass?

Mass is the quantity of matter that is contained in an object. It remains same, no matter where you take the object, either into space or another planet. Because the number of atoms and their density remains same. Mass is measured in kilograms in international standard of units.

How is Mass Measured?

There various methods for measuring the mass of an object. Two of them are described below:

  1. Inertial Mass: It is determined by the resistance of an object to change the state of rest or motion. For example, you have two smaller balls; one is made of plastic and other is made of iron. When you move each of the balls back and forth, you will notice that iron ball takes more effort to move. This is because the iron ball has more mass than the plastic ball.
  2. Gravitational Mass: Anything that has mass exerts a gravitational force on other objects. This gravitational force is measured to find out the mass of an object.

What is Weight?

Weight is actually force exerted by an object under the influence of gravity. Weight depends on the gravitational pull of our Earth. The weight of an object changes with a change in gravitational pull, but their mass remains constant. Weight also depends on the mass; the more mass you have, the heavier it will weigh under the gravity. If you carry an object to the moon, it will weigh much less because the moon has lesser gravity than the Earth. But in space, the weight of the objects will become zero.

How is weight measured?

Weight has the same unit of force; newton. It can be calculated by using the second law of motion.

F = m*a 

Here F is the weight of an object in newtons, and “a” is the gravitational acceleration of the Earth, which is 9.8 m/s^2.

Example: Calculate the weight of an object, whose mass is 100 kg.

Solution: Use the above formula to calculate the weight

F = m*a

Put m = 100 kg and a = gravity of the Earth = 9.8 m/s^2

F = 100*9.8 N = 980 N

Facts

  • The weight of the objects can change in different locations of the Earth. Because at some locations, gravity is slightly weaker.
  • A man weighing 100 pounds on the Earth would weigh only 37 pounds on the Mars.
  • Weight and Force are measured in Newtons (N), It is named after Isaac Newton.
accelerating van

accelerating van

What is Acceleration?

Acceleration is the rate of change of velocity. When the velocity of an object is changed, the object is said to be accelerated. During acceleration, the velocity of an object constantly changes.

Acceleration is measured in meter per second squared (m/s^2), which tells us that how much velocity is changing during each second. Acceleration is a vector quantity. It needs direction along with the magnitude to properly define it.

How is Acceleration measured?

Acceleration is measured by dividing the change in velocity with the amount of time.

a = ΔV/Δt = change in velocity / change in time

Example: A car is traveling at a velocity of 50 km/h. Suddenly the driver presses the accelerator to increase its velocity. The velocity of the car than changes from 50 Km/h to 80 km/h in 10 seconds. Calculate its acceleration:

Solution:

First, find the change in velocity.

ΔV = V2-V1 = (80 – 50) km/h = 30 km/h

The amount of time is already given to you, which is Δt = 10 seconds.

Now find the acceleration.

a = ΔV/Δt = 30/10 m/s^2 = 3 m/s^2

Deceleration

Deceleration is also the acceleration, but instead of increasing the velocity of an object, it decreases its velocity. You may have observed it when a car driver presses brake to slow down the car.

Deceleration is also called the negative acceleration. The method of calculating the deceleration is same as described above, but the sign will be negative.

Gravity

Gravity is the acceleration caused by planets. It constantly accelerates the objects downward. Our Earth has the gravity of 9.8 m/s^2, means if you drop an object of any mass from a height, its velocity will increase by 9.8 m/s for each passing second.

See the table below to understand, how much velocity of objects increases with each passing second.

Time period Gravity of Earth Velocity
1st second 9.8 m/s^2 9.8 m/s
2nd Second 9.8 m/s^2 19.6 m/s
3rd Second 9.8 m/s^2 29.4 m/s
4th Second 9.8 m/s^2 39.2 m/s
5th Second 9.8 m/s^2 49 m/s

However, there are certain limitations on how fast an object can fall under the influence of gravity. This is because of the air friction due to the atmosphere. Air friction opposes the moving objects in the air and makes their velocity constant at a certain velocity. This constant velocity is known as terminal velocity.

Read more at Gravity

Facts

  • Galileo was the first to demonstrate that, if two objects having different weights are dropped from a height, they will reach the ground in same time.
  • Objects with acceleration can’t reach the infinite velocity. The fastest possible velocity is the velocity of light, which is around 299,792,458 m/s.
  • Acceleration is produced by the force on an object.
velocity of car

velocity of car

What is Speed?

Speed is the physical quantity for measuring the motion of a body with respect to a reference. It is defined as, the distance covered in a given amount of time.

For example, a car is traveling 50 km in an hour, then its speed would be 50 Km/h. Speed is a scalar quantity, means it doesn’t need a direction for its representation.

What is Velocity?

Velocity is a little different than the speed. Velocity is a vector quantity, means it requires direction in which the body is moving along with the magnitude.

For example, a car is moving with a speed of 30 km/h in the north direction. Here you are given the direction (north) along with the magnitude which is 30 Km/h. You can say that the speed is the magnitude of the velocity.

How are speed and velocity measured?

Velocity is measured in its standard unit which is meter per second (m/s). But, commonly we use Km/h (kilometer per hour) and mph (miles per hour). Velocity is calculated according to the following formula:

V = Δd/Δt = change in distance/change in time

or in other words

V = distance covered/amount of time

The magnitude of both speed and velocity is calculated in the same. But, velocity should also have a direction to properly define it.

Example: A car is moving towards west. It has covered 150 kilometers in 3 hours. Calculate its velocity.

Solution:

Distance covered = Δd = 150 km

Amount of time = Δt = 3 hours

Velocity = Δd/Δt = 150/3 = 50 km/h towards west

Instantaneous velocity

When the velocity is measured at any particular time, it is called instantaneous velocity. A car’s speedometer always shows instantaneous velocity. Instantaneous velocity tells us the current speed of an object.

Average Velocity

Average velocity is defined as, the total distance traveled by an object (e.g. a car) divided by the elapsed time.

For example, a car is traveling towards the north has covered a distance of 50 km in two hours. Then, its average velocity during the 50 km route will be V = 50/2 = 25 km/h. It doesn’t mean that the car was traveling all the time with the velocity of 50 km/h. Because there may be need of braking and accelerate the car, so the car may have traveled with different speed.

Facts

  • Light has the fastest possible speed. It’s speed is 299,792,458 meters/second or ‎186,000 miles/second.
  • Escape velocity is the velocity, which when an object achieves can escape the gravitational pull of the planets.
  • If you through an object towards the sky with a velocity of 11.2 kilometers/seconds, it will escape the gravitational pull of the Earth, and will never come back.
  • When two objects with different weights are dropped from a height, both objects will hit the ground at the same time with same speed. It was proved by Galileo Galilei.
earth-gravity

earth-gravityHave you ever tried to jump?

Probably, yes! And you know that when we jump from the ground, we just fall back after few seconds.children-jumping

Why? And How?

These are the questions that, almost every human had thought in his childhood. So, the simple answer to all these questions is “gravity”.

So, let’s learn something about gravity and the interesting history about it.

What is Gravity?

Gravity is the force that attracts us and other objects towards each other; much like a magnet, but not as a magnet. Then, why things in your room are not attracted to each other? It is because gravity depends on the mass; Massive objects have more gravity.

Gravitational force is so weak that the object must be very massive to have sufficiently strong gravity to attract other objects. Consider our earth, it so massive that its gravity pulls us towards the ground. When we jump, earth’s gravity pulls us and we fall back on the ground.

Importance of Gravity

What would happen, if gravity suddenly disappears? Take some time and think about it.

galaxyYou will be amazed to find out that, the current appearance of our earth, planets, and stars depends on the gravity. Without gravity, there will be no earth’s pull to attract you back to the ground when jumping. Even the planets and stars would not exist without gravity. Because planets and stars have been formed from the accumulation of cosmic dust and gas that was only possible due to gravity.

Here are some of the effects of gravity on our everyday life

  • We can stand, jump, walk, and run on the ground due to gravity. If the earth doesn’t pull you back while jumping, then you would never come back to the ground, and you may reach space in a single jump! Wow!
  • On the earth, gravity keeps the air around us as a blanket, and it prevents air from escaping into space.
  • Tides in the oceans are caused by the gravitational pull of moon and sun.

Universal Law of Gravitation

law-of-gravitationDon’t be afraid!

It is just a simple law that was proposed by a famous scientist Sir Isaac Newton. This law gives us the relation between the gravitational force, the mass of objects, and the distance between objects.

Here are two simple points that explain the law:

  • The gravitational force between massive objects is more as compared to light objects.
  • The gravitational force between two objects decreases exponentially as they go away from themselves.

Here is the mathematical expression of the universal law of gravitation:

F = G*M1*M2/r^2

G = Gravitational constant, whose value is equal to
M1 = mass of the first object
M2 = mass of the second object
r = distance between two objects

By knowing gravity, you can calculate when a ball will touch the ground after being released into the air. You can measure and graph the path of a projectile. You can calculate how much propellant is required to push a rocket into space, and many more.

Do Heavy and Light Objects Fall at the Same Time?

galileo-galilei-gravity-experimentThe simple answer is, yes. But let’s understand, why it happens.

Gravity at the surface of the earth is 9.8 m/s, which means an object falling towards earth gains 9.8 m/s speed in every second. If a ball is dropped from a building it will have 9.8 m/s speed at the end of the 1st second, 19.6 m/s at end of the 2nd second, and 29.4 at the end of the 3rd second and so on. Every object is accelerated at the same rate towards earth, whether it is a paper clip or a stone. If two objects are dropped from a height, they both will hit the ground at the same time.

But, wait a minute!

You may be thinking, why a paper falls slower than a paper clip when both are dropped from the same height? It is because of the air resistance. The paper clip has lower surface area than the paper, which results in higher air resistance for the paper. But, if you drop paper and paper clip into a vacuum chamber both will hit the bottom at the same time. It is because vacuum chamber does not have air, so there will be no air friction to slow any object.

Difference between Mass and Weight

mass and weightIn everyday life, you may have used the term mass and weight interchangeably. But in physics, mass and weight are two different quantities.

The mass of an object is the quantity of matter in it; usually measured in kilograms. But, weight is the force of an object that it is putting on a platform due to gravity.

For example, if you hold a brick in your hand you will feel a downward force. If you somehow take that brick to the moon, you will notice much less downward force. Because the moon has less gravitation than the earth. In both cases, the amount of the matter in the brick will be same on the earth and the moon.

Difference between Gravity and Gravitation

There is a difference between gravity and gravitation. Gravitation is the force of attraction between objects that have mass. But, gravity is the gravitational force between earth and other objects. It means that gravity is the special case of gravitation.

Gravitational force exists since the formation of our universe. It is one of the four fundamental forces of nature. It is the force that attracts atoms together to form stars and planets. It keeps the moon in orbit around the earth and the earth around the sun.

Fun Facts

  • Gravity keeps all the planets in the orbit of the sun, and it keeps our moon in orbit of the earth.
  • If any object goes upward with a velocity of 11 km/s, it will escape the gravitational pull of the earth. This velocity is called the escape velocity, and it is different for different planets and moon.
  • The gravity of our sun is about 274 m/s^2. Anything weighing 1 kg on the earth will weigh about 28 kg (If it was possible!).

A Brief History

Let’s learn something about the history of gravity, and find out about the people who contributed to explaining the gravity.

Who first pointed to the presence of gravity? And when? It is still unknown. But you may consider that early human beings had probably thought about it. Because, it is the force whose effects we can clearly see, like falling back to the ground after jumping.

  • The first person who gave the hypothesis about gravity was, Aristotle. He hypothesized that “heavier objects are accelerated more towards ground than lighter objects”. He was actually wrong because he didn’t know about air resistance which slows down the objects. But, he at least provided the ground for the great scientists to think and research about gravity.

    Aristotle
    Aristotle
  • In late 16th century, a famous scientist Galileo Galilei performed an experiment. In this experiment, he dropped two balls from a height and proved that light objects and heavy objects fall at the same rate.

    galileo-galilei
    Galileo Galilei
  • In 1687, Sir Isaac Newton developed the universal law of gravitation. Which explained that lighter objects have less gravitational force of attraction than massive objects. Also, the gravitational force decreases exponentially as the distance between two objects increase. This is also known as the inverse square law.

    isaac-newton
    Isaac Newton
  • The modern understanding of gravity was described by Albert Einstein. He described the gravity as a curvature in space and time. This curvature is caused by the objects with mass; the massive objects cause more curvature than the lighter objects.

    albert-einstein
    Albert Einstein
bicycle-friction

Friction-forceYou may be listening to the word friction from your childhood that it slows down the vehicles and wear out the machine part. That is true! Friction causes resistance in motion. It is also a force that acts in opposite direction of motion.

When you put a brake on your bicycle, it stops suddenly because you increase the friction between the wheels and road. It is hard to push a box on a cemented surface than a smooth surface because cemented surface causes more friction due to its irregular surface. On the other hand, if you push the same box on a glass table, it will slide very easily because it has a very smooth surface that causes lower friction.

Types of friction

Friction has been divided into 3 types; static friction, kinetic friction, and fluid friction. All the three types of friction act on any object differently. Let’s see!

  1. Static Friction

    Static friction, as the name suggests occurs between the objects that are in contact with each other but not moving. So, that means if you place a heavy box on a table, will it experience the static friction? No!

    pushing-box-sliding-friction

    OK so, when static friction actually occurs? Static friction will only occur between two static objects that are not moving even when the force is applied on them. For example, When you put a box on the table it won’t experience static friction until you apply a force to slide it but it still doesn’t move, then it is experiencing the static friction. But when you push the box even harder, the box will move. Now the static friction will be converted to kinetic friction.

  2. Kinetic Friction

    Now it is time learn about the kinetic friction. Let’s start with an example. Suppose you are riding a bicycle very fast. Tell me what will happen when you suddenly stop paddling? You will notice that the bicycle will start to slow down until it comes to stop completely. This is what you might guess, the kinetic friction!
    bicycle-friction

    If one object is moving on another object than both objects will experience kinetic friction. Kinetic friction always occurs between moving objects (In our case, the wheels of bicycles and the road). Normally kinetic friction is less than the static friction due to the motion of the objects.

    Kinetic friction is further divided into two types.

    1. Sliding friction: When two objects slide on each other, both will feel the sliding friction. Pushing a box and rubbing your hands both are the examples of sliding friction.
    2. Rolling friction: When one object rolls on another object or both are rolling on each other, they will experience rolling friction. It is less than the Sliding friction that is why pushing a weight on wheels is easier than sliding it. The bicycle that you were riding was experiencing rolling friction.
      wheel-rolling-friction
  3. Fluid Friction

    Solids offer two kinds of friction to an object, but there is also another type of friction that is provided by the fluids, e.g. liquids and gases. Let’s see an example to understand the concept more easily.
    coin-droping-in-liquid-fluid-friction

    What will happen when you drop a coin in oily liquid (your cooking oil)? It will sink slowly to the bottom. Can you tell me why? Yes, you guessed correctly. This is because of the fluid friction. The fluid (oil) is resisting the motion of the coin. Fluid friction increases with two things; one is the velocity of an object and other is viscosity (thickness of liquid) of the fluid. The honey is more viscous than the cooking, so it will provide more friction to the coin. Try it!

The importance of Friction in Everyday Life.

  • It helps us to walk on the road. Otherwise, we would skid away.
  • You warm your hand by rubbing them together.
  • We can stop of vehicles suddenly by putting brakes on them.
  • It helps you to hold a pencil or anything tightly. Without friction, the object you hold would easily slip away from your hand.

Why is Friction Avoided?

  • Friction cause wears in the machinery parts. So, we lubricate the machines to reduce friction
  • Our body joints are well lubricated to reduce friction.
  • Reduced fluid friction can increase the mileage of your car. After the speed of 80 km/h, we spend the majority of our fuel to fight friction.
    moving-car-friction