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## Solving Problems in Mechanics

- Inertia – Definition, Types, Sample Questions
- Newton’s First Law of Motion – Law of Inertia
- Impulse – Definition, Formula, Applications
- Linear Momentum of a System of Particles

## Newton’s Second Law of Motion

- Laws of Conservation of Momentum
- What is Equilibrium? – Definition, Types, Laws, Effects
- What is Friction?
- Types of Friction – Definition, Static, Kinetic, Rolling and Fluid Friction
- Factors Affecting Friction
- Motion Along a Rough Inclined Plane
- Problems on Friction Formula
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- Last Updated : 18 Jan, 2023

## Newton’s First Law of Motion

Applications of Newton’s First Law of Motion:

- An object is thrown in outer space moves with zero acceleration in the same direction until unless any other external object hit it with some force.
- A book lying on the table remains at rest as long as no net force acts on it.
- A marathon runner continues to run several meters beyond the finish line due to the inertia.

where, dp is the change in the momentum wrt change in time dt.

Applications of Newton’s Second Law of Motion:

- It is easier to push an empty cart in a supermarket than to push a loaded cart. More mass requires more power for acceleration.
- An object falling down from a certain height, undergoes an increase in acceleration because of the gravitational force applied.

Applications of Newton’s Third Law of Motion:

- When we pull an elastic band, it automatically returns to its original position. The action (applied force) is stored as energy and is released as a reaction with an equal and opposite force.
- When a rocket is fired, the force of the burning gases coming out (action) exerts an equal and opposite force on the rocket (reaction) and it moves upward.

In practical, the particle does not change its state of rest or of uniform motion along a straight line unless it is forced to do this. This tendency of particle to do not change its state of rest or state of uniform motion along a straight line, unless that state is changed by an external force is called as inertia.

where μ is the coefficient of friction and N is the normal force.

- While walking friction between the ground and shoes prevent us from slipping.
- Without friction, motion cannot be covered by belts from motor to machine.

Example of free body diagram (FBD)

## Sample Questions

According to Newton’s first law of motion, object in a motion tends to stay in a motion unless until any external force is not acting. As there is no air friction acting on a object (mobile phone) to slow down the object in the horizontal direction after it drops from the train and acceleration due to gravity would only affect in the vertical direction. So, horizontal speed of the mobile phone just before hitting ground would be approximately 100 km/hr.

According to Newton’s first law of motion,every body continues to be in its state of rest or of uniform motion in a straight line until unless any external force is not acting. If the net external force on a body is zero, its acceleration is zero.Hence force needed is also zero. Therefore 0 N net force required to keep ball moving with constant velocity of 40 m/s.

Newton’s first law of motion states that object remains in a motion until unless any external force is not acting on a object.In a space there is vacuum and there is no external air resistance.Hence, spaceship will travel at constant velocity of 1200 m/s with zero acceleration. Since, m= mass of spaceship = 2000 kg a= acceleration of spaceship = 0 ∑F = m×a = 2000 × 0 = 0 N Hence, net force is acting on a spaceship is 0 N.

Question 4: What is meant by static and kinetic friction?

Resistance encountered by a body in static condition while tending to move under the action of an external force is called static friction. In static friction, the frictional force resists force that is applied to an object, and the object remains at rest until the force of static friction is overcome.It is denoted as μ s . The resistance encountered by sliding body on a surface is known as kinetic friction. Kinetic friction is denoted as μ k . Kinetic friction is defined as a force that acts between moving surfaces. A body moving on the surface experiences a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.

Given that, Mass of a car = M c = 200 kg Acceleration of a car = a c =5 m/s 2 Using formula F = M c × a = 200 × 5 = 1000 N Therefore, the net Force is 1000 N.

Given that, Initial velocity of the ball = 12 m/s Final velocity of the ball = 20 m/s Mass of the ball = 0.10kg Change in momentum = final momentum – initial momentum = m×v2 – m×v1 = 0.10×20 – (-0.10×12) (ball again is in the direction from the batsman to the bowler) = 3.2 N.s Therefore, the change in momentum is 3.2 N.s.

Given that, Mass of the bullet = M b = 10 gm = 0.010 kg Penetration of bullet before coming to rest = s = 4 cm = 0.04 m. Initial velocity of bullet = V i =400 m/s Final velocity of bullet = V f = 0 m/s Here, wooden block will exert force opposite in the direction of velocity,therefore this force causes deceleration. Hence a be the deceleration in this case (-a) By using kinematic equation, (V f ) 2 = (V i ) 2 + 2as ——(1) 0 = (400) 2 – 2 × a × 0.04 a = ( (400) 2 – 0 ) / 2 × 0.04 = 160000 / 0.08 = 2000000 The force on the bullet = M b × a = 0.01 × 2000000 = 20000 N

According to Newton’s third law motion,every action there is equal and opposite reaction.Hence the force exerted by the floor on the box will be the weight of box. Given that, Mass of box = M = 100 kg. weight of the box = M × g = 100 × 9.81 = 981 N The force exerted by the floor on the box = -981 N This Negative sign indicates that force applied by floor is in opposite direction of force applied by the box. Therefore, the Force applied by the floor is equal to 981 N.

Question 9: Define inertia of rest, motion , and direction?

A characteristic of matter that allows it to remain in its current condition of rest or uniform motion in a straight line until it is disrupted by an external force is called an inertia. Inertia of rest: The inability of a body to change its state of rest by itself is called inertia of rest Inertia of motion: The inability of a body to change its state of motion by itself is inertia of motion. Inertia of direction: The inability of a body to change its direction of motion by itself inertia of direction.

Given that, Upward force = 207 N Downward force = 180 N As they are accelerating in the upward direction then the net force- Net Force = ∑F = Upward force – Downward force = 207 -180 = 27 N To find total mass of the passengers, use the equation for force of gravity, F = m×g m = 180/10 m = 18 Kg To find net acceleration, use Newton’s second law of motion, F = m × a a = 27/18 a = 1.5 m/s 2 Therefore, they are accelerating in the upward direction at the rate of 1.5m/s 2 .

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## Major American Universities Ph.D. Qualifying Questions and Solutions - Physics

Problems and solutions on mechanics.

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Sample Chapter(s) Introduction (94 KB) Part I: Newtonian Mechanics (4,142 KB)

- This volume comprises 408 problems and is divided into three parts: I Newtonian Mechanics
- II Analytical Mechanics
- III Special Relativity

## FRONT MATTER

https://doi.org/10.1142/9789812384973_fmatter

## PART I NEWTONIAN MECHANICS

https://doi.org/10.1142/9789812384973_0001

- DYNAMICS OF A POINT MASS (1001–1108)
- DYNAMICS OF A SYSTEM OF POINT MASSES (1109–1144)
- DYNAMICS OF RIGID BODIES (1145–1223)
- DYNAMICS OF DEFORMABLE BODIES (1224–1272)

## PART II ANALYTICAL MECHANICS

https://doi.org/10.1142/9789812384973_0002

- LAGRANGE'S EQUATIONS (2001–2027)
- SMALL OSCILLATIONS (2028–2067)
- HAMILTON'S CANONICAL EQUATIONS (2068–2084)

## PART III SPECIAL RELATIVITY

https://doi.org/10.1142/9789812384973_0003

## BACK MATTER

https://doi.org/10.1142/9789812384973_bmatter

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## The Body Shapes of Extraterrestrials

## Waves and Rays in Elastic Continua

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## Non-Commutative Geometry

## Principles of Physics

## George Placzek

## Universality in Nonequilibrium Lattice Systems

## Statistical Physics

## Achieving the Rare

## A Bouquet of Dyson

## Physics of Buoyant Flows

## Newtonian Mechanics for Undergraduates

## Wavefronts and Rays as Characteristics and Asymptotics

## Microscopic and Macroscopic Simulation Techniques

## Ray and Wave Chaos in Ocean Acoustics

## Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory

## Annual Reviews of Computational Physics V

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2. How much gravitational potential energy is in a 20 kg mass when 0.6 meters above the ground?

## 3. How much gravitational potential energy does a 35 kg boulder have when 30 meters off the ground?

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I cancelled out the initial kinetic energy because:

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