> []# Futuretron EV Course_CHAPTER3

# CHAPTER 3: Pre-requisite for the course

## 3.1 Mass and Weight

Mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass.
Mass is denoted using m or M.
Weight usually is denoted by W
Weight is mass multiplied by the acceleration of gravity (g).
Then,
W = m * g

### Comparing properties of Mass and Weight

| MASS | WEIGHT |
| -------- | --------
Mass is a property of matter. The mass of an object is the same everywhere. |Weight depends on the effect of gravity. Weight increases or decreases with higher or lower gravity.
|Mass can never be zero.| Weight can be zero if no gravity acts upon an object, as in space.
|Mass does not change according to location. | Weight varies according to location.
|Mass is a scalar quantity. It has magnitude. |Weight is a vector quantity. It has magnitude and is directed toward the center of the Earth or other gravity well.
| Mass may be measured using an ordinary balance. | Weight is measured using a spring balance.
| Mass usually is measured in grams and kilograms. | Weight often is measured in newtons, a unit of force.

## 3.2 Distance and Displacement

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point. Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.

The distance tells us, how much path is traveled by the body, during motion and the displacement gives us an idea of how far the body is from its starting point, and that too in which direction.

Ref: https://tse1.mm.bing.net/th?id=OIP.gvzlSDIMtMSjGvabKIPdcQHaET&pid=Api&P=0&w=298&h=174


Where:
s = displacement
u = initial velocity
a = acceleration
t = time

The total distance can be calculated by summing up overall distance travelled irrespective of direction. The distance between two coorinate points can be calculated by using:


**Examples:**
An object moves along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.
a) Calculate the distance covered by the moving object.
b) Find the magnitude of the displacement of the object.

solution:
a) The distance covered by the moving object is calculated as follows:
AB + BC + CD + DE + EF
3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km
The distance covered by the moving object is 6.5 km.

b) The initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagora’s theorem to the triangle AHF as shown in the figure below


Applying the Pythagorean formula, we get AF2=AH2+HF2
Substituting the formula, we get
AF2=(0.5×4)2+(0.5×3)2=6.25 AF=√6.25km=2.5km
The magnitude of displacement is 2.5km.

### Comparing properties of Distance and Displacement

| DISTANCE | DISPLACEMENT
| -------- | --------
| The total or complete path travelled by a body. | The shortest distance between the final position and the intial position of the motion of the object. |
| It can never be negative or zero, always positive. |It can be positive, negative or zero depending on the context. |
| It is a scalar quantity. | It is a vector quantity. |
| Distance doesn’t decrease with time. | It decreases with time. |
| It is never less than displacement value. | It is either equal to or less than the distance value. |
| It gives complete information about the path travelled by the object. |It doesn’t give the complete information about the path travelled by the object. |

## 3.3 Uniform and Non-Uniform Motion

Uniform motion is defined as the motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.

 Ref:https:/physics/2015/12/12110655/uniform-motion.png

If the speed of a car is 10 m/s, it means that the car covers 10 meters in one second. The speed is constant in every second.

Non-Uniform motion is defined as the motion of an object in which the object travels with varied speed and it does not cover same distance in equal time intervals, irrespective of the time interval duration.

Ref:https:/physics/2015/12/12110715/non-uniform-motion.png

If a car covers 10 meters in first two seconds, and 15 meters in next two seconds.

### Comparison between Uniform and Non Uniform Motion

| BASIS FOR COMPARISON | UNIFORM MOTION | NON-UNIFORM MOTION |
| -------- | -------- | -------- |
|Meaning | Uniform motion implies the movement of a body along a straight line with steady speed. | Non-uniform motion alludes to the movement of an object along a straight line with variable speed. |
Distance | Covers equal distances in equal time interval. | Covers unequal distances in equal time interval. |
| Average speed | Is similar to actual speed of the object. | Is different from actual speed of the object. |
Graph | Distance-time graph shows a straight line | Distance-time graph shows a curved line |

#### Uniform Circular Motion
This type of motion is seen if an object is travelling at a constant speed around a fixed axis or center point, and the object travels around a curved path and it maintains a constant radial distance from the center point at any given time and it moves in a tangent to the curved path.

#### Non Uniform Circular Motion
This type of motion is inconsistent because if an object is travelling at a variable angular speed around a fixed axis or center point, then the motion of that object is said to be inconsistent because the object covers a curved path and it will have some variable radial acceleration due to which its velocity would change every second.

## 3.4 Velocity & Acceleration

Velocity and acceleration both describe motion, but there is an important difference between the two. Understanding what velocity means leads to an understanding of what acceleration means because while velocity is the rate of change of position, acceleration is the rate of change of velocity. If you’re traveling at a constant pace, you have velocity but no acceleration, but if you’re traveling and your pace is changing, you have velocity and acceleration.

### Velocity

The rate of change of your position with time defines your velocity. While velocity means the same thing as speed. In physics there is an important distinction between the two terms. Speed is a “scalar” quantity, and it’s measured in units of distance/time, so in meters per second or miles per hour. Velocity is a “vector” quantity, so it has both a magnitude and a direction.

Technically, if you’re traveling at 5 meters per second is a speed and saying you’re traveling at 5 meters per second towards the north is a velocity, because the latter has a direction too.
The formula for velocity is:

#### Velocity = distance traveled ÷ time taken**

### Acceleration

Acceleration is the rate of change of velocity with time. Like velocity, this is a vector quantity that has a direction as well as a magnitude. An increase in velocity is commonly called acceleration while a decrease in velocity is sometimes termed deceleration.

Technically, since velocity includes a direction as well as a speed, a change in direction at a constant speed is still considered acceleration. Acceleration can be defined simply as:

#### Acceleration = change in velocity ÷ time taken for velocity to change.

Acceleration has units of distance/time squared – for example, meters/second2.

#### Constant Acceleration vs Constant Velocity

Traveling with a constant velocity means you’re going at the same speed in the same direction continuously. If you have a constant velocity, this means you have zero acceleration. You can imagine this as driving down a straight road but keeping your speedometer on the same value.

A constant acceleration is quite different. If you travel with a constant acceleration, your velocity is always changing, but it’s changing by a consistent amount each second. The acceleration due to gravity on the Earth has the constant value 9.8 m/s2, so you can imagine this like dropping something from a skyscraper. The velocity starts low, but increases by 9.8 m/s for every second it is falling under gravity.

## 3.5 Force
Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction. The direction towards which the force is applied is known as the direction of the force, and the application of force is the point where force is applied.

The Force can be measured using a spring balance. The SI unit of force is Newton(N).

### Effects of force
In physics, motion is defined as the change in position with respect to time. In simpler words, motion refers to the movement of a body. Typically, motion can either be described as:

1. Change in speed
2. Change in direction

The Force has different effects and here are some of them.
• Force can make a body which is at rest to move.
• It can stop a moving body or slow it down.
• It can accelerate the speed of a moving body.
• It can also change the direction of a moving body along with its shape and size.

The quantity of force is expressed by the vector product of mass (m) and acceleration (a). The equation or the formula for force can mathematically be expressed in the form of:

#### F = ma

Where,
m = mass
a = acceleration
It is articulated in Newton (N) or Kgm/s2.

#### Acceleration a is given by
a = v/t
Where
v = velocity
t = time taken

So Force can be articulated as:

### F = mv/t

Inertia formula is termed as p = mv which can also be articulated as Momentum.

Therefore, Force can be articulated as the rate of change of momentum.
### F = p/t = dp/dt

Force formulas are beneficial in finding out the force, mass, acceleration, momentum, velocity in any given problem.

**Unit of Force**
In the centimetre gram second system of unit (CGS unit) force is expressed in dyne.
In the standard international system of unit (SI unit) it is expressed in Newton (N).

**Types of force**

Force is a physical cause that can change the state of motion or the dimensions of an object. There are two types of forces based on their applications:

1. Contact Force
2. Non-Contact Force

**Contact force**
Forces which act on a body either directly or through a medium are called contact forces.

Examples of contact forces are:
Muscular Force
Mechanical Force
Frictional Force

We can make use of muscular force of animals like bullocks, horses and camels to get the activities done. The frictional force is another type of contact force which acts between a pair of a surface in contact and tends to oppose the motion of one surface over the other.

**Non-contact Force**
Forces which act through spaces without making direct contact with the body are called non-contact forces.

Examples of non-contact forces are:
Gravitational Force
Electrostatic Force

**Magnetic Force**
The force exerted by a magnet on other magnets is called magnetic force. Magnetic force and electrostatic force act on an object from a distance, that’s the reason they are non-contact forces.

The strength of gravity is an attractive force which is exerted by the Earth on objects which make them fall to the land. The weight of a body is the force which is pulled by the earth towards the centre.

### Examples:

1. How much net force is required to accelerate a 1000 kg car at 4.00 m/s2?

Solution:
Given,
a = 4.00 m/s2
m = 1000kg
Therefore,
F = ma
= 1000 × 4
= 4000N

2. Aimee has a toy car of mass 2kg. How much force should she apply on the car so that it should travel with the acceleration of 8m/s2?

Solution:
Known,
m (Mass of toy car) = 2 Kg,
a (Acceleration) = 8m/s2,
F is Force to be applied by aimmee = m × a
= 2 Kg × 8 m/s2 = 16 Kgm/s2 = 16N.

3. A hammer having a mass of 1 kg going with a speed of 6 m/s hits a wall and comes to rest in 0.1 sec. Compute the obstacle force that makes the hammer stop?

Solution:
Given,
Mass of Hammer, m = 1 kg
Initial Velocity, u = 6 m/s
Final Velocity, v = 0 m/s
Time Taken, t = 0.1 s
The acceleration is: a = (v – u)/t
Therefore, a = -60 m/s2 [-ve sign indicates retardation]
Thus, the retarding Force, F = ma = 1 × 60 = 60N

### Line of Action of Force

The line along which a force is acting on an object is called the line of action of the force. The point where the force is acting on an object is called the point of application of the force. The force which opposes the relative motion between the surfaces of two objects in contact and acts along the surfaces is called the force of friction.

Experimentally Galileo has proven that objects in motion travel at steady speed while there is no force acting on them. He could note that when a sphere is rolling down an inclined plane, its speed increases because of the gravitational pull which is acting on it.

If all forces acting on an object are balanced the acting net force is zero. However, when all the forces acting on a body results in an unbalanced force, then the unbalanced force will accelerate the body, meaning that a net force acting on a body will either increase its velocity strength or alter its velocity direction. For instance, If several forces are act on a body and the body is observed to be at rest, then it can be assumed that the total force acting on the body is zero.

## 3.6 Friction and Rolling Friction

A friction is the resistance that one surface or object encounters when moving over another.

The resistance to movement that occurs when two objects are in contact.

For a moving solid body, there are two principal types of friction that act upon it, Rolling Friction and Sliding Friction.

The force resisting the motion of a rolling body on a surface is known as Rolling friction or Rolling resistance. Rolling of ball or wheel on the ground is an example of Rolling friction.

The other type of friction is Sliding friction. In this type of friction, there is a restriction on the body’s movement as only one side of the body is in contact with the surface.
Pushing a box across the table is an example of Sliding friction.
Rolling friction is considerably weaker than Sliding friction.

**Laws of Rolling Friction**

There are three laws of rolling friction:

1. With the increase in smoothness, the force of rolling friction decreases.

2. Rolling friction is expressed as a product of load and constant to the fractional power.

F = kLn

3. Rolling friction force is directly proportional to load and inversely proportional to radius of curvature.

F=μ×Wr

### Causes of Rolling Friction

When an object is rolled on a surface, certain things happen:
* The object is deformed at the point of contact with the surface.
* The surface is deformed at the point of contact with the object.
* Motion is created below the surface as a result of the above mentioned points.


Ref: https://tse2.mm.bing.net/th?id=OIP.ilshZj9--KbixkjwFBQ-qgAAAA&pid=Api&P=0&w=354&h=154

The primary cause of this friction is that the energy of deformation is greater than the energy of recovery. Also, there is an adhesive force between the two surfaces which needs to be overcome constantly.

The amount of friction is based on a variety of factors such as:

* The quality of the sliding body
* The quality of the surface
* Load
* Diameter of the rolling object
* Surface area of the body
* Coefficient of Rolling Friction

#### Rolling Friction Examples

A basketball rolled on the court will eventually come to a halt because of rolling friction.
A bike with a broad tire will burn more fuel because of the increased rolling friction.
A ball rolled on a field will go lesser distance than a ball rolled on a concrete floor because it will experience greater rolling friction on the former surface.