Chapter 3 Force and Newton’s Chapter 3 Force and Newton’s lawslaws

Issac Newton (1642 － 1727 ）

Galileo Galilei (1564 － 1642 ）

Section 3-1 Classical mechanicsSection 3-1 Classical mechanics• The approach to the dynamics we consider here is generally called classical mechanics.

• In this chapter, we will study in detail the bases of classical mechanics: Newton’s three laws.

• Classical mechanics was found not to describe well the motions in certain realms.• For ordinary objects, classical mechanics is important and very useful.

Section 3-2 Newton’s first lawSection 3-2 Newton’s first law

Newton’s first law :Newton’s first law :

Every body continues in its state of Every body continues in its state of rest or uniformrest or uniform motionmotion in a straight line, unless it is compelled to in a straight line, unless it is compelled to change that state by forces impressed on it. change that state by forces impressed on it.

What can What can causecause the motion of a body? the motion of a body?

Take the apple’s freely falling motion as an exampleTake the apple’s freely falling motion as an exampleForceForce

What will be the states of the body if there is no any interactions between it and its What will be the states of the body if there is no any interactions between it and its environment?environment?

(an isolated system)(an isolated system)

At restAt rest or or 1D uniform motion1D uniform motion

1. 1. Newton’s first law tells us:Newton’s first law tells us:

Consider a body on which no net force acts.Consider a body on which no net force acts.

1) If the body is at rest, it will remain at rest1) If the body is at rest, it will remain at rest ；；

2) If the body is moving with constant velocity, it wil2) If the body is moving with constant velocity, it will continue to do so, no force is needed to keep it ml continue to do so, no force is needed to keep it moving.oving.

2. The 2. The correctnesscorrectness of Newton’s laws is dependent on the of Newton’s laws is dependent on the reference framesreference frames!!

See an example in See an example in

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3. Inertial frames(3. Inertial frames( 惯性参考系惯性参考系 ):):

No net force or No accelerationNo net force or No acceleration

• The reference frames to which Newton’s law The reference frames to which Newton’s law applies (applies ( 适用适用 ) are called “) are called “inertial framesinertial frames”.”.

• The tendency of a body to remain The tendency of a body to remain at rest or inat rest or in uniform linear motionuniform linear motion is called “ is called “inertiainertia”. ”.

• Can we find inertial frames in the nature?Can we find inertial frames in the nature?

地心系 , 地球赤道加速度 a=3.4x10-2m/s2

日心系 , 地球公转轨道加速度 a=6x10-3m/s2

银河系 , 太阳向心加速度 a=3x10-10m/s2

• Newton’s first law is often called Newton’s first law is often called the law of inertiathe law of inertia..

• A frame that keeps rest or uniform linear motion,A frame that keeps rest or uniform linear motion,relative to any inertial frames, relative to any inertial frames, is an inertial frameis an inertial frame..

See 动画库动画库 // 力学夹力学夹 /2-01/2-01 德行与惯性德行与惯性 .exe.exe

Section 3-3 ForceSection 3-3 Force

The The forceforce is determined through the is determined through the measure of measure of accelerationacceleration the body gets under the body gets under the force.the force.

Newton’s first law tell us that Newton’s first law tell us that forceforce causes causes the change in the motion states (~ ). the change in the motion states (~ ). aF

v

For a fixed body, a larger force applied to For a fixed body, a larger force applied to the body will generate a larger acceleration the body will generate a larger acceleration for the body. for the body.

Section 3-4 MassSection 3-4 Mass

It is much easy to It is much easy to accelerateaccelerate a bicyclea bicycle than than a cara car by pushing it. by pushing it.

Clearly Clearly same forcesame force produces produces differentdifferent accelerationacceleration when applied to when applied to different different bodies.bodies.

What makes the difference???What makes the difference??? Mass

In experiments, it is easy to prove that the In experiments, it is easy to prove that the magnitude of the magnitude of the accelerationacceleration is is proportionalproportional to to that of the that of the forceforce applied to a given body. applied to a given body.

This ratio is called the mass of the bodyThis ratio is called the mass of the body. Thus . Thus

m=F/a m=F/a

or or F=maF=ma

Mass :The property of a body that determines The property of a body that determines its resistance to a change in it’s motion.its resistance to a change in it’s motion.

Fa

The mass defined in Newton’s law is an inertial mass.

Suppose we apply a certain force to a Suppose we apply a certain force to a body having mass and observe an body having mass and observe an acceleration of . We then apply the same acceleration of . We then apply the same force to another body of mass ,observing force to another body of mass ,observing an acceleration . Thus an acceleration . Thus

or (3-3) or (3-3)

F

m1

a1

m2

a2

amam 2211

aa

mm

2

1

1

2

maam 1

2

12

One method to quantitatively determine the One method to quantitatively determine the mass of a body, (relative to others’)mass of a body, (relative to others’)

Section 3-5 Newton’s Section 3-5 Newton’s secondsecond law law

The mathematical statement of Newton’s The mathematical statement of Newton’s

second law of motion is second law of motion is

1.1. Here is the vector sum of all the Here is the vector sum of all the

forces acting on the body.forces acting on the body.

iF ma����������������������������

iF

2.2. Is the Is the firstfirst law not totally contained in law not totally contained in

second second law?law?

(3-4)(3-4)

No.

3.3. Equation (3-4) is a vector equation. We can Equation (3-4) is a vector equation. We can write it as three one-dimensional equation:write it as three one-dimensional equation:

Here (or , ) is the algebraic sum of the x Here (or , ) is the algebraic sum of the x (or, y, z) components of all the forces acting on (or, y, z) components of all the forces acting on m. m.

4.4. If we measure the mass in If we measure the mass in kgkg and the and the acceleration in ,Newton’s second law gives acceleration in ,Newton’s second law gives the force in the force in N.N.

ix xmaF iy y

maF iz zmaF

F x F y F z

2/11 smkgN

2/ sm

(3-5)(3-5)

Sample problems

1. A worker pushes a loaded sled, whose mass m is 240 kg for a distance d of 2.3 m over the surface of a frozen lake. The sled moves with negligible friction on the ice. The worker exerts a constant horizontal force of 130 N as she does so. If the sled starts from rest, what is its final velocity?

2. The worker in Sample Problem 1 wants to reverse the direction of the velocity of the sled in 4.5s. With what constant force must she push on the sled to do so?

3. An object is moving north. From only this information one can conclude:

(A) that there is a single force on the object directed north.

(B) that there is a net force on the object directed north.

(C) that there may be several forces on the object, but the largest must be directed north.

(D) nothing about the forces on the object.

with an increasing speed

(D) (B)

11 ）） Newton’s third law is: Newton’s third law is:

To every action there is an equal and opposite reactiTo every action there is an equal and opposite reaction.on. If the body If the body BB exerts a force on body exerts a force on body AA; expe; experiment shows that bodyriment shows that body A A exerts a force on bod exerts a force on body y BB. These forces are related by . These forces are related by

(3-6)(3-6)

Note: the actionthe action and and reaction forcesreaction forces always act on di always act on different bodiesfferent bodies..

Section 3-6 Newton’s third law Section 3-6 Newton’s third law

F AB

F BA

FF BAAB

mm

＇T

T

P

＇P

地球

22)Dynamical analysis using Newton’s laws)Dynamical analysis using Newton’s laws

In analyzing problems using Newton’s law, therIn analyzing problems using Newton’s law, there are several steps that we should follow:e are several steps that we should follow:

1.1. choose a suitable choose a suitable inertial reference frameinertial reference frame. .

2.2. For each object in the problem, For each object in the problem, draw a “free bdraw a “free body diagram”,ody diagram”, showing all of the forces acting on t showing all of the forces acting on that body.hat body.

3.3. For each body, For each body, find the vector sum of all the ffind the vector sum of all the forcesorces. In practice, this usually means separately a. In practice, this usually means separately adding the dding the x, y, zx, y, z components of the forces. Then u components of the forces. Then use Eqs (3-5) to find acceleration components se Eqs (3-5) to find acceleration components

Sample problems

1. A worker W is pushing a packing crate of mass m1=4.2 Kg. In front of the crate is a second crate of mass m2=1.4 Kg. Both crates slides across the floor without friction. The worker pushes on crate 1 with a force F1w=3.2 N. Find the accelerations of the crates and the force exerted by crate 1 on crate 2.

2. See 动画库动画库 // 力学夹力学夹 /2-02/2-02 牛顿定律例题 例牛顿定律例题 例 11