6 Most SAQ’s of Laws of Motion Chapter in Inter 1st Year Physics (TS/AP)

4 Marks

SAQ-1 : State Newton’s second law of motion. Hence, derive the equation of motion F=ma.

Introduction

Newton’s Second Law of Motion is a fundamental principle in physics that relates force, mass, and acceleration. This law states that the force applied to an object is directly proportional to the rate of change of its momentum. We will use this law to derive the equation of motion F=ma and then apply it to find the mass of a body acted upon by a specific force, leading to a certain velocity over time.

Derivation of Newton’s Second Law

1. Initial Momentum: p_i​ = mu, where m is the mass and u is the initial velocity.
2. Final Momentum: p_f​ = mv, where v is the final velocity.
3. Change in Momentum: $$\Delta p = p_f – p_i = m(v – u)$$.
4. Time Interval: Δt, given as 20 seconds in the problem.
5. Rate of Change of Momentum: $$\frac{\Delta p}{\Delta t} = \frac{m(v – u)}{\Delta t}$$.
6. Applying Newton’s Second Law: $$F = \frac{dp}{dt}$$
   Therefore, $$F = \frac{m(v – u)}{\Delta t}$$

Applying the Law to Determine Mass

1. Given Force: $$\vec{F} = 2\vec{i} + \vec{j} – \vec{k}$$ newtons.
2. Final Velocity: $$\vec{v} = 4\vec{i} + 2\vec{j} – 2\vec{k}$$ m/s.
3. Initial Velocity: $$\vec{u} = 0$$ (as the body is initially at rest).
4. Time Taken: Δt=20 seconds.

Calculating Mass

1. Equating force components with the corresponding components of $$\frac{m(v – u)}{\Delta t}​$$
2. X-direction: $$2 = \frac{m(4 – 0)}{20}$$
3. Y-direction: $$1 = \frac{m(2 – 0)}{20}$$
4. Z-direction: $$-1 = \frac{m(-2 – 0)}{20}$$
5. Solve for m in each equation to find the common value, representing the mass of the body.

Summary

By applying Newton’s Second Law of Motion and the given force, initial and final velocities, we can determine the mass of the body. The calculation involves breaking down the force into its components and equating them with the components of the change in momentum over time. This approach is fundamental in solving problems involving force, mass, and motion in physics.

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SAQ-2 : Mention the methods used to decrease friction.

Introduction

Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. It can be advantageous in certain situations, but often, it is desirable to reduce friction. There are several methods to achieve this reduction, making it easier to move objects or improve the efficiency of machines. This discussion explores various ways to reduce friction and its practical applications.

1. Using Lubricants: Friction increases when surfaces have rough contact points. Lubricants, such as oils or greases, are substances used to reduce friction by filling the gaps and pores between contacting surfaces. The lubricant forms a thin film that separates the surfaces and allows them to slide more smoothly over each other, decreasing friction significantly. Practical Application: Lubricating the engine parts in vehicles reduces friction and wear, enhancing engine efficiency and prolonging the engine’s life.
2. Polishing Surfaces: Polishing involves making the surfaces smoother and more even. Smoother surfaces have fewer irregularities, resulting in reduced friction when in contact with each other. By removing the roughness, the surfaces can slide or roll more easily, leading to lower friction. Practical Application: Polishing the axles of bicycles or skateboards reduces friction, allowing the wheels to rotate smoothly.
3. Using Ball Bearings: Ball bearings are rolling elements used to reduce friction in rotating machinery. They consist of small metal balls held within a ring or cage. The rolling motion of the balls between the inner and outer races minimizes contact area and friction, making it more efficient than sliding friction. Practical Application: Ball bearings are commonly used in various machines, such as wheels in vehicles, industrial machinery, and skateboards, to reduce friction and enhance smooth movement.
4. Streamlining: Streamlining is a design technique used to reduce air resistance or fluid friction experienced by objects moving through air or liquids. By shaping the object to minimize its contact area with the surrounding medium, friction is reduced, allowing for more efficient movement. Practical Application: The design of modern cars, airplanes, and rockets incorporates streamlining to reduce air resistance, improve fuel efficiency, and increase speed.

Summary

Friction reduction techniques play a crucial role in enhancing the efficiency of machines, improving energy consumption, and making various processes more manageable. By using lubricants, polishing surfaces, employing ball bearings, and streamlining designs, we can effectively reduce friction and enjoy smoother, more efficient operations in numerous practical applications.

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SAQ-3 : Define the terms momentum and impulse. State and explain the law of conservation of linear momentum. Give example.

Introduction

In the study of physics, momentum and impulse play crucial roles in understanding the motion of objects. Momentum, a vector quantity, is the product of an object’s mass and velocity. Impulse is defined as the product of force and time. The law of conservation of linear momentum states that in a closed system, the total momentum remains constant before and after a collision. This principle is foundational in physics, with applications in various scenarios. Here, we explore these concepts in detail.

1. Momentum (p): Momentum, denoted as p, is a vector quantity representing the product of an object’s mass (m) and velocity (v). Mathematically, it’s expressed as p=mv. The momentum of an object is directly proportional to its mass and velocity, meaning a larger mass or higher velocity results in greater momentum.
2. Impulse (J): Impulse, denoted as J, is the change in momentum of an object when a significant force (F) acts on it for a short time (t). It’s mathematically expressed as J=F×t. The impulse experienced by an object can lead to changes in its motion, like acceleration or deceleration.
3. Law of Conservation of Linear Momentum: This law is a fundamental principle in physics, asserting that the total momentum of a closed system is constant before and after a collision. It implies that the combined momentum of all interacting objects in a system remains unchanged, regardless of the number of collisions within the system.

Proof: Consider two bodies, A and B, with masses moving with initial momenta P_A​ and P_B​ respectively, before a collision. During the collision, they exchange momenta over a short time Δt. Let their final momenta be P_1A​ and P_1B​. According to Newton’s third law, the forces they exert on each other are equal and opposite. Using Newton’s second law, the change in momentum for A and B during the collision is:

• Change in momentum of A: $$F_{AB} \Delta t = P_{1A} – P_A​$$
• Change in momentum of B: $$F_{BA} \Delta t = P_{1B} – P_B​$$

Equating these changes, we get: $$P_A + P_B = P_{1A} + P_{1B}​$$

This equation demonstrates that the total momentum before the collision equals the total momentum after, confirming the law of conservation of linear momentum.

Examples

1. Explosion of a bomb: The momentum of the system is conserved even as fragments move in various directions.
2. Firing of a bullet from a gun: The bullet and recoiling gun’s momentum are conserved in opposite directions, resulting in no net momentum change for the system.

Summary

Understanding momentum, impulse, and the law of conservation of linear momentum is vital for analyzing and predicting the motion and behavior of objects during collisions. These concepts are widely applied across various fields, enhancing our understanding of the dynamics in physical systems.

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SAQ-4 : Explain the advantages and disadvantages of friction.

Introduction

Friction is a force that opposes the relative motion or the tendency towards motion between two surfaces in contact. It is a fundamental aspect of our daily lives, offering both advantages and disadvantages. Understanding these aspects of friction helps in various applications and situations.

Advantages of Friction

1. Walking on the Ground: Friction between the soles of our shoes and the ground is crucial for walking without slipping, providing the necessary grip and stability.
2. Writing: The friction between a pen or pencil and paper enables us to write and draw, offering control over the movement of writing instruments.
3. Braking in Vehicles: Essential for vehicle safety, friction between brake pads and wheels creates a retarding force that brings vehicles to a halt.
4. Heat Generation: In certain scenarios, like rubbing hands together, friction is beneficial for generating heat, especially in cold weather.
5. Asteroid Protection: Friction with the Earth’s atmosphere causes asteroids to burn up, acting as a natural defense and protecting the Earth from potential impacts.

Disadvantages of Friction

1. Heat Wastage: Friction in machinery and engines often leads to unwanted heat generation, causing energy wastage and reduced efficiency.
2. Increased Energy Requirement: Due to its opposing nature, friction requires more energy to overcome, leading to higher fuel consumption in machines and vehicles.
3. Noise Production: Friction between moving parts can produce noise, leading to discomfort and necessitating maintenance to reduce noise levels.
4. Forest Fires: Under certain conditions, friction between dry branches can generate enough heat to ignite fires, posing a risk in dry environments.
5. Maintenance and Cost: Overcoming friction requires additional efforts like greasing and oiling, along with regular maintenance to minimize wear and tear, incurring extra costs.

Summary

Friction is a double-edged sword, offering benefits essential for daily activities and safety, but also posing challenges in energy efficiency, maintenance, and environmental hazards. A thorough understanding of friction’s effects enables us to enhance its positive impacts and minimize its negative consequences in various systems and processes.

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SAQ-5 : What are the shock absorbers used in motor cycles and cars?

The Working of Shock Absorbers and Impulse: Shock absorbers, also known as dampers, are mechanical or hydraulic devices installed in vehicles to absorb and dampen shock impulses. These shocks typically arise from uneven surfaces or sudden movements. The primary function of shock absorbers is to convert the kinetic energy of the shock into another form, usually heat, which is then dissipated.

1. Impulse and Its Formula: Impulse is a concept in physics defined as the change in linear momentum of an object when a force is applied over a certain time period. The formula for impulse is Δp=FΔt, where Δp represents the change in momentum, F is the applied force, and Δt is the time duration of the impact.
2. Minimizing Impact with Shock Absorbers: Shock absorbers are essential in vehicles for minimizing the impact of forces encountered on uneven roads or during sudden movements. These devices help in reducing the jerks and impulsive forces that a vehicle experiences.
3. Inversely Proportional Relationship: Based on the impulse formula Δp=FΔt, there is an inversely proportional relationship between the force of impact and the duration of impact. This means that an increase in one results in a decrease in the other, and vice versa.
4. Role of Shock Absorbers: Shock absorbers play a crucial role in increasing the time duration of impact (Δt). By doing so, they effectively reduce the impulsive force (F). This increase in the time of the jerk aids in dissipating the kinetic energy more gradually, thus minimizing damage to the vehicle and enhancing the ride comfort for the passengers.

Summary

The functionality of shock absorbers in vehicles is intimately tied to the principle of impulse. By extending the duration of impact, they effectively lessen the force of impact, leading to improved vehicle stability, reduced wear and tear, and enhanced passenger comfort. Understanding the concept of impulse is crucial in grasping how shock absorbers work and their importance in vehicle suspension systems.

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SAQ-6 : State the laws of rolling friction.

Introduction

Rolling friction is the resistance experienced when a body rolls over a surface. It differs from sliding friction, which occurs when two surfaces slide against each other. Rolling friction involves the interaction between the rolling object and the contact surface. The laws governing rolling friction are crucial for understanding and optimizing various practical applications.

1. The Nature of Rolling Friction: Rolling friction is generally lower than sliding friction. This is because the interaction in rolling friction occurs mainly at the point of contact, making it more efficient and requiring less energy to overcome compared to sliding friction.
2. Influence of Wheel Diameter: The rolling friction is inversely related to the diameter of the wheel or rolling object. Larger wheels, which cover more ground per revolution, experience reduced rolling friction. This makes larger wheels more suitable for applications like vehicles and machinery, where low rolling resistance is desirable.
3. Influence of Surface Properties: The nature of the surface over which the object rolls significantly affects rolling friction. Smoother surfaces lead to lower rolling resistance due to less deformation at the contact points and lower frictional forces.
4. Direction of Force and Motion: The direction of the applied force in relation to the motion of the rolling object influences rolling friction. A force applied in the direction of motion results in lower rolling friction, while a force opposing the motion can increase resistance through skidding or slipping.
5. Hysteresis Loss: Hysteresis loss refers to the energy dissipated as heat due to the deformation and recovery of the materials in the rolling object and the surface. This energy loss, which arises from the elastic properties of the materials, contributes to rolling friction.

Summary

Understanding the laws of rolling friction is essential in fields like transportation, industrial machinery, and sports equipment design. By considering factors such as wheel diameter, surface properties, the direction of force and motion, and hysteresis loss, engineers and designers can optimize the design of rolling systems to achieve maximum efficiency, reduce energy consumption, and improve overall performance.