chapter 2 luc va chuyen dong revised

Learning outcomeThe student should be able to:• Identify that a force is a vector quantity and thus hasboth magnitude and direction and also components.• Given two or more forces acting

TẬP ĐOÀN DẦU KHÍ VIỆT NAM

TRƯỜNG ĐẠI HỌC DẦU KHÍ VIỆT NAM

PVU

Lecturer : Assoc Prof Pham Hong Quang Email : quangph@pvu.edu.vn

General Physics I

The Laws of Motion

2.1 The Concept of Force 2.2 Newton’s First Law and Inertial Frames 2.3 Newton’s Second Law

2.4 Newton’s Third Law 2.5 Some Applications of Newton’s Laws 2.6 Forces of Friction

2.7 Momentum and Impulse

Chapter 2: The Laws of Motion

Learning outcome

The student should be able to:

• Identify that a force is a vector quantity and thus has

both magnitude and direction and also components.

• Given two or more forces acting on the same particle,

add the forces as vectors to get the net force.

• Identify Newton’s first and second laws of motion.

• Identify inertial reference frames.

• Sketch a free-body diagram for an object, showing the

object as a particle and drawing the forces acting on it as

vectors with their tails anchored on the particle.

• Apply the relationship (Newton’s second law) between

the net force on an object, the mass of the object, and the

acceleration produced by the net force.

• Identify that only external forces on an object can cause

the object to accelerate.

Learning outcome

• Determine the magnitude and direction of the normal

force on an object when the object is pressed or pulled

onto a surface.

•Identify that the force parallel to the surface is a frictional

force that appears when the object slides or attempts to

slide along the surface.

•Identify Newton’s third law of motion and third-law force pairs.

•For an object that moves vertically or on a horizontal or

inclined plane, apply Newton’s second law to a free-body

diagram of the object.

Learning outcome

•For an arrangement where a system of several objects moves rigidly together, draw a free-body diagram and apply Newton’s second law for the individual objects and also for the system

taken as a composite object.

•Identify that impulse is a vector quantity and thus has both

magnitude and direction and also components.

•Apply the relationship between impulse and momentum

change.

•Apply the relationship between impulse, average force,

and the time interval taken by the impulse.

2.1 The Concept of Force

Force

Forces are what cause any change in the velocity of an object

Newton’s definition:

A force is that which causes

an acceleration

2.1 The Concept of Force

•Contact forces involve

physical contact between

two objects

Examples a, b, c

•Non contact force, for

example Field forces act

through empty space

No physical contact is

required

2.1 The Concept of Force

2.1 The Concept of Force

Vector Nature of Forces

The forces are applied

perpendicularly to each other

The resultant (or net) force is

the hypotenuse

Forces are vectors, so you

must use the rules for vector

addition to find the net force

acting on an object

2.2 Newton’s First Law and Inertial Frames

•“If an object does not interact with other objects, it is

possible to identify a reference frame in which the object

has zero acceleration”

This is also called the law of inertia

We call this an inertial frame of reference

Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame

2.2 Newton’s First Law and Inertial Frames

Newton’s First Law – Alternative Statement

•In the absence of external forces, when viewed from an

inertial reference frame, an object at rest remains at rest

and an object in motion continues in motion with a

constant velocity

Newton’s First Law describes what happens in the

absence of a force

Also tells us that when no force acts on an object, the

acceleration of the object is zero

•A non-inertial reference frame is a frame of reference that is

undergoing acceleration with respect to an inertial frame

•The laws of motion in non-inertial frames do not take the

simple form they do in inertial frames, and the laws vary from frame to frame depending on the acceleration

•To explain the motion of bodies entirely within the viewpoint

of non-inertial reference frames, fictitious forces (also called

inertial forces) must be introduced to account for the observed motion, such as the Coriolis force or the centrifugal force, as derived from the acceleration of the non-inertial frame.

2.2 Newton’s First Law and Inertial Frames

2.2 Newton’s First Law and Inertial Frames

Which of the following is NOT an inertial

reference frame (where Newton’s Laws are invalid)?

1) A train moving at constant velocity 100m/s;

2.2 Newton’s First Law and Inertial Frames

About Mass

•Mass is that property of an object that specifies how

much resistance an object exhibits to changes in its

velocity

•Mass is an inherent property of an object

•Mass is independent of the object’s surroundings

•Mass is independent of the method used to measure it

•Mass is a scalar quantity

•The SI unit of mass is kg

2.2 Newton’s First Law and Inertial Frames

Mass vs Weight

Mass and weight are two different quantitiesWeight is equal to the magnitude of the gravitational force exerted on the object

Weight will vary with locationExample:

wearth = 19.6 N; wmoon ~ 3.3 N

mearth = 2 kg; mmoon = 2 kg

2.3 Newton’s Second Law

“When viewed from an inertial reference frame, the

acceleration of an object is directly proportional to the net

force acting on it and inversely proportional to its mass”

Force is the cause of change in motion, as measured by the acceleration

Algebraically,

m m

2.3 Newton’s Second Law

2.3 Newton’s Second Law

Gravitational Mass vs Inertial Mass

In Newton’s Laws, the mass is the inertial mass and

measures the resistance to a change in the object’s

motion

In the gravitational force, the mass measures the

gravitational attraction between the object and the

Earth

Experiments show that gravitational mass and inertial

mass have the same value

2.3 Newton’s Second Law

2.4 Newton’s Third Law

“If two objects interact, the force exerted by object 1

on object 2 is equal in magnitude and opposite in

direction to the force exerted by object 2 on object 1

Forces always occur in pairs

A single isolated force cannot exist

The action force is equal in magnitude to the reaction force and opposite in direction

(table on monitor) is the

reaction of the force the

monitor exerts on the

table.

Normal means perpendicular, in this case

monitor) force is equal

in magnitude and

opposite in direction to

2.4 Newton’s Third Law

2.5 Some Applications of Newton’s Laws

Free Body Diagram

The most important step in solving

problems involving Newton’s Laws is to

draw the free body diagram:

In a free body diagram, you want the

forces acting on a particular object

Be sure to include only the forces

acting on the object of interest

Include any field forces acting on the

object

Neglect reaction forces

2.5 Some Applications of Newton’s Laws

Particles in Equilibrium

• If the acceleration of an object that can be modeled as

a particle is zero, the object is said to be in equilibrium

The model is the particle in equilibrium model

• Mathematically, the net force acting on the object is

2.5 Some Applications of Newton’s Laws

A lamp suspended

A lamp is suspended from a

chain of negligible mass

The forces acting on the lamp

are the downward force of

gravity the upward tension in

2.5 Some Applications of Newton’s Laws

Find the tension in the three cables

(a) A traffic light weighing 125 N suspended by cables (b)

Free-body diagram for the traffic light (c) Free-body diagram

2.5 Some Applications of Newton’s Laws

2.5 Some Applications of Newton’s Laws

Particles Under a Net Force

•If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it

Model is particle under a net force model

•Draw a free-body diagram

•Apply Newton’s Second Law in component form

2.5 Some Applications of Newton’s Laws

Newton’s Second Law,

•Forces acting on the crate:

A tension, acting through

the rope, is the magnitude

of force

The gravitational force,

The normal force, ,

exerted by the floor

2.5 Some Applications of Newton’s Laws

Newton’s Second Law, cont.

•Apply Newton’s Second Law in component form:

•Solve for the unknown(s)

•If the tension is constant, then a is constant and the

kinematic equations can be used to more fully describe

the motion of the crate

2.5 Some Applications of Newton’s Laws

Multiple Objects,

Conceptualize

•When two or more objects

are connected or in

contact, Newton’s laws

may be applied to the

system as a whole and/or

to each individual object

•Whichever you use to

solve the problem, the

other approach can be

used as a check

-T1 FP= 100 000N

T

Consider the horizontal motion only

2.5 Some Applications of Newton’s Laws

Net force on the tug

2.5 Some Applications of Newton’s Laws

Atwood’s machine

An Atwood’s machine is two masses connected by a strong light string that are hung over an ideal pulley (light and frictionless)

The masses have identical velocity and acceleration magnitudes at every instant

If we define up on the left and down on the right as positive directions, then the masses have identical velocities and accelerations period

2.5 Some Applications of Newton’s Laws

Atwood’s machine, cont.

) ( m1 m2

F a

m m

g m g

m a

h 

2.5 Some Applications of Newton’s Laws

2.7 Some Applications of Newton’s Laws

Note About the Normal

Force

The normal force is not always

equal to the gravitational force

of the object

For example, in this case

may also be less than

0 and

2.5 Some Applications of Newton’s Laws

Inclined Planes

•Forces acting on the object:

The normal force acts perpendicular

to the plane

The gravitational force acts straight

down

•Choose the coordinate system with

x along the incline and y

perpendicular to the incline

•Replace the force of gravity with its

2.5 Some Applications of Newton’s Laws

Problem-Solving Hints Newton’s Laws

2.5 Some Applications of Newton’s Laws

Problem-Solving Hints Newton’s Laws, cont

•Analyze

Draw free-body diagrams for each object

Include only forces acting on the object

Find components along the coordinate axes

Be sure units are consistent

Apply the appropriate equation(s) in component form

Solve for the unknown(s)

2.6 Forces of Friction

•When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion

This is due to the interactions between the object and its environment

•This resistance is called the force of friction

μ is the coefficient of

friction

• These equations relate

the magnitudes of the

2.6 Forces of Friction

•The coefficient of friction depends on the surfaces in

contact

•The force of static friction is generally greater than

the force of kinetic friction

•The direction of the frictional force is opposite the

direction of motion and parallel to the surfaces in

contact

•The coefficients of friction are nearly independent of

2.6 Forces of Friction

Friction in Newton’s Laws Problems

•Friction is a force, so it simply is included in the

in Newton’s Laws

•The rules of friction allow you to determine the direction and magnitude of the force of friction

2.7 Momentum and ImpulseNewton’s Second Law can read

Momentum = mass ´ velocity:

“Derivative of the momentum of an object with respect

to the time interval during which the object changes its

velocity equals the net force acting on the object”

Momentum = Động lượng

a m

F   

dt

v m

d dt

v

d m

p   

2.7 Momentum and Impulse

dt F

p

d   

Integral from t1 to t2 we get:

“The change of momentum of an object during the

time from t 1 to t 2 equals the impulse acting on it during

that time”

Impulse = Xung lượng

pulse dt

F p

Increasing Momentum

Apply the greatest force possible for the longest time possible.2.7 Momentum and Impulse

Ft=mΔvv

2.7 Momentum and Impulse

Decreasing Momentum

If you want to stop something’s motion, you can apply a LOT of force over a short time,

Or, you can apply a little force over a longer time

2.7 Momentum and Impulse

Key words of the chapter

Force; Reference frame; Inertial Frames; Non-inertial

frames; Inertial forces; Normal force; Gravitational force;

Forces of Friction; Free-body diagrams; Momentum;

Impulse

• Force: a push or pull

• Mass: measures the difficulty in accelerating an object

• Newton’s first law: if the net force on an object is zero, its

velocity is constant

• Inertial frame of reference: one in which the first law holds

• Newton’s second law: F=m.a

• Free-body diagram: a sketch showing all the forces on an

object

• Newton’s third law: If object 1 exerts a force on object 2,

then object 2 exerts a force – on object 1

• Contact forces: an action-reaction pair of forces produced

by two objects in physical contact

• Forces are vectors

• On the surface of the Earth, W = mg

• Normal force: force exerted perpendicular to a surface by

that surface

• Normal force may be equal to, lesser than, or greater than the object’s weight

Check your understanding 1

When the frictionless system shown above is accelerated by an applied force of magnitude F the tension in the string between the blocks is

(A) 2F (B) F (C) 2/3 F (D) ½ F (E) 1/3 F

Ans E

Check your understanding 2

A ball falls straight down through the air under the influence of

gravity There is a retarding force F on the ball with magnitude

given by F = bv, where v is the speed of the ball and b is a

positive constant The magnitude of the acceleration, a of the

ball at any time is equal to which of the following?

(A) g – b (B) g – bv/m (C) g + bv/m (D) g/b (E) bv/m

Ans B

ΣF = ma; mg – bv = maF = ma; mg – bv = ma

Check your understanding 3

A block of weight W is pulled along a horizontal surface at constant

speed v by a force F, which acts at an angle of θ with the horizontal,

as shown above The normal force exerted on the block by the surface has magnitude

(A) W – F cos θ (B) W – F sin θ (C) W (D) W + F sin θ (E) W + F cos θ Ans B

Check your understanding 4

A block of mass 3m can move without friction on a horizontal

table This block is attached to another block of mass m by a

cord that passes over a frictionless pulley, as shown above If

the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?

(A) Zero (B) g/4 (C) g/3 (D) 2g/3 (E) g

Ans B ΣF = ma; mg – bv = maFexternal = a.mtotal

mg is the only force acting from outside the system of masses

so we have mg = (4m)a

Check your understanding 5

A baseball is thrown by a pitcher with a speed of 35 m/s The

batter swings and hits the ball The magnitude of

the force that the ball exerts on the bat is always

(A) zero as it is only the bat that exerts a force on the ball.

(B) equal to the gravitational force acting on the ball.

(C) larger than the force the bat exerts on the ball.

(D) smaller than the force the bat exerts on the ball.

(E) equal to the force that the bat exerts on the ball.

Ans E

Thank you!