Understanding the Principle of Conservation of Linear Momentum

Principle of Conservation of Linear Momentum

PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM

There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.

Let us prove the law of conservation of linear momentum with the following illustration:

Figure 1.7 Conservation of linear momentum

Proof:

Let two bodies A and B having masses m₁ and m₂ move with initial velocity u₁ and u₂ in a straight line. Let the velocity of the first body be higher than that of the second body. i.e., u₁>u₂ . During an interval of time t second, they tend to have a collision. After the impact, both of them move along the same straight line with a velocity v₁ and v₂ respectively.

Force on body B due to A,

F_B= m₂ (v₂–u₂)/t

Force on body A due to B,

F_A = m₁ (v₁–u₁)/t

By Newton’s III law of motion,

Action force = Reaction force

F_A    =         –F_B

m₁ (v₁-u₁)/t  =       –m₂ (v₂-u₂)/t

m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂ ------ (1.9)

The above equation confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.

Hence the law of conservation linear momentum is proved.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail. 10th Science : Chapter 1 : Laws of Motion : Principle of Conservation of Linear Momentum.

Understanding Newton's Third Law of Motion: Action and Reaction

Newton’s Third Law of Motion

Newton's Third Law Explained

NEWTON’S THIRD LAW OF MOTION

Newton’s third law states that ‘for every action, there is an equal and opposite reaction. They always act on two different bodies’.

If a body A applies a force F_A on a body B, then the body B reacts with force F_B on the body A, which is equal to F_A in magnitude, but opposite in direction. F_B = –F_A

Examples:

• When birds fly they push the air downwards with their wings (Action) and the air pushes the bird upwards (Reaction).
• When a person swims he pushes the water using the hands backwards (Action), and the water pushes the swimmer in the forward direction (Reaction).
• When you fire a bullet, the gun recoils backward and the bullet is moving forward (Action) and the gun equalises this forward action by moving backward (Reaction).

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

10th Science : Chapter 1 : Laws of Motion : Newton’s Third Law of Motion |

Introduction to Laws of Motion | Chapter 1 | 10th Science

10th Science : Chapter 1 : Laws of Motion | Introduction

LAWS OF MOTION

INTRODUCTION

Human beings are so curious about things around them. Things around us are related to one another. Some bodies are at rest and some are in motion. Rest and motion are interrelated terms.

In the previous classes you have learnt about various types of motion such as linear motion, circular motion, oscillatory motion, and so on. So far, you have discussed the motion of bodies in terms of their displacement, velocity, and acceleration. In this unit, let us investigate the cause of motion.

When a body is at rest, starts moving, a question that arises in our mind is ‘what causes the body to move?’ Similarly, when a moving object comes to rest, you would like to know what brings it to rest? If a moving object speeds up or slows down or changes its direction. what speeds up or slows down the body? What changes the direction of motion?

One answer for all the above questions is ‘Force’. In a common man’s understanding of motion, a body needs a ‘push’ or ‘pull’ to move, or bring to rest or change its velocity. Hence, this ‘push’ or ‘pull’ is called as ‘force’.

Let us define force in a more scientific manner using the three laws proposed by Sir Isaac Newton. These laws help you to understand the motion of a body and also to predict the future course of its motion, if you know the forces acting on it. Before Newton formulated his three laws of motion, a different perception about the force and motion of bodies prevailed. Let us first look at these ideas and then eventually learn about Newton’s laws in this unit.

Mechanics

Mechanics is the branch of physics that deals with the effect of force on bodies. It is divided into two branches, namely, statics and dynamics.

• Statics:

  It deals with the bodies, which are at rest under the action of forces.

• Dynamics:

  It is the study of moving bodies under the action of forces. Dynamics is further divided as follows.

  • Kinematics:

    It deals with the motion of bodies without considering the cause of motion.

  • Kinetics:

    It deals with the motion of bodies considering the cause of motion.

A mechanic unscrew a nut by applying a force of 140 N with a spanner of length 40 cm. What should be the length of the spanner if a force of 40 N is applied to unscrew the same nut? - Science

The Physics of a Spanner: Understanding Torque

Ever wondered why it's easier to loosen a stubborn nut with a longer wrench? The answer isn't magic; it's physics! Specifically, it's a fundamental concept called torque, or the moment of force.

Torque is the measure of the force that can cause an object to rotate around an axis. Think of it as a "turning" or "twisting" force. It’s at play in many of our daily activities, from pushing open a door (you push farthest from the hinges, right?) to pedaling a bicycle.

To see this principle in action, let's break down a classic physics problem.

The Problem

A mechanic unscrews a nut by applying a force of 140 Newtons (N) with a spanner that is 40 centimeters (cm) long.

Question: What should be the length of the spanner if a force of only 40 N is applied to unscrew the exact same nut?

The Science Behind the Solution

To loosen the nut, a specific amount of torque is required. This required torque is a constant. It doesn't change whether you use a short spanner with a lot of force or a long spanner with less force. The turning effect must be the same.

The formula for torque is simple:

$$Torque = Force \times \text{Perpendicular Distance from the pivot}$$

In our case, the "distance" is the length of the spanner. Let's call our first scenario (Case 1) and our second scenario (Case 2). The core principle is:

$$Torque_1 = Torque_2$$

Which means:

$$(Force_1 \times \text{Length}_1) = (Force_2 \times \text{Length}_2)$$

Solving the Problem Step-by-Step

Let's list what we know:

• Force 1 ($F_1$): 140 N
• Length 1 ($d_1$): 40 cm
• Force 2 ($F_2$): 40 N
• Length 2 ($d_2$): ? (This is what we need to find)

Now, we plug these values into our equation:

$$F_1 \times d_1 = F_2 \times d_2$$

$$140 \text{ N} \times 40 \text{ cm} = 40 \text{ N} \times d_2$$

To solve for $d_2$, we can rearrange the equation:

$$d_2 = \frac{(140 \text{ N} \times 40 \text{ cm})}{40 \text{ N}}$$

As you can see, the "40 N" on the top and bottom of the fraction cancel each other out.

$$d_2 = 140 \text{ cm}$$

Answer: The mechanic would need a spanner that is 140 cm long.

The Takeaway

This problem beautifully illustrates the inverse relationship between force and the length of the lever arm when torque is constant.

• Less force? You need a longer lever.
• Shorter lever? You need to apply more force.

So, the next time you're struggling with a tight bolt, remember your physics lesson and grab a longer wrench!