as 物理讲义 · ①add and subtract coplanar vectors a b c equilibrium : resultant force = 0 ②...

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As 物理讲义

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Chapter 1-Physical qualities ＆ units

1 SI units

2 Derived units from Base SI units

eg1: [ ] [ ][ ]F m a

2N kgms

eg2: [ ] [ ][ ] [ ]W F s ma m

2 2J kgms m kgm

eg3: 3122][

]][[

][][

SAkgmAS

mkgms

SA

mma

tI

WV




3

3 Check whether a formula is correct

Base unit of [ ]A = Base unit of [ ]B

4 Prefix

5 Esitmate

quantities magnitude quantities magnitud

e

quantities magnitu

de

Distance from

Sun to Earth

1.510 11 m Distance

from London

to Paris

3.510 5 m Length of car 4m

Diameter of a

hair

510 4 m Diameter of

an atom

310 10 m Diameter of

a nucleus

410 15

The mass of

orange

100—150g The mass of

an adult

human

50—100kg The height

of a room

2—3m

The diameter

of a pencil

0.5—1.0cm The volume

of a small

0.5cm 3 The volume

of a human

head

410 3




4

bean

The speed of a

jumbo jet( 客

机)

220m/s The

temperature

of the human

body

310K The speed

of sound in

air

340m/s

The density of

Air

0.5—1.5kg/m 3 The mass of

a protractor

5—50g Frequency of

audible

sound wave

20—20K

HZ

6 Vector ＆ Scalar

Vector: has both magnitude and direction

Scalar: has only magnitude

①Add and subtract coplanar vectors

cba equilibrium : resultant force = 0

② Represent a vector as two perpendicular components.

1F rF Resultant force : 2 2

1 2rF F F

Horizontal component : 1 cosrF F

2F Vertical component : 2 sinrF F

③常见的 vector and scalar

vector scalar




5

Force

Displacement

Acceleration

Velocity

Momentum

Weight

Current

Voltage

Speed

Work

Energy

Power

Chapter 2 Measurement ＆ Uncertainty

1. Measurement equipment 测量仪器

会使用天平秒表螺旋测微仪游标卡尺温度计直尺

Eg:

micrometer screw 螺旋测微仪：

主尺 3.5mm，副尺 20*0.01mm=0.20mm，长度 3.5+0.20=3.70mm

vernier caliper 游标卡尺

主尺 0.5cm，副尺 1*0.01cm=0.01cm，长度 0.5+0.01=0.51cm

When used to measure diameter of a wire

(1) when the wire is not uniform, measure at different positions.

(2) when the cross-section of the wire is noncircular, measure along the wire.

2. Non-linear scals




6




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3. Error

(1) Systematic error ( affecting accurate )

Results in all readings being far from the “true value”.

·Zero error , Parallex error，Reaction time

·can be reduced / eliminated

(2) random error ( affecting precise)

Results in readings being scattered around the “true value”.

·Can be reduced by repeating and averaging.

Eg: (1) 测重力加速度的值，真实值是 9.81

Big system error

small random error

small system error

big random error

7.81 9.90

7.82 9.79

7.83 9.83

7.82 9.68

(2) 对于 readings 的 count rate 图




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A，small system error ，small random error （精确又准确）

B，small system error ，big random error （准确不精确）

C，big system error ，small random error （精确不准确）

D，big system error ，big random error （既不精确又不准确）

4. Uncertainty

（1）type of uncertainty

Eg : 15.2 0.1 cm

Absolute uncertainty : 0.1 cm

Fractional uncertainty : 0.1 / 15.2 = 0.007 cm

Percentage uncertainty : .0.1 / 15.2100% = 0.7%

measured value should be recorded under the uncertainty

Eg:15.26 0.24cm should be recorded as 15.3 0.2cm

（2） Caculation involving error---uncertainty




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① “+” / “-”

mCKBA CmBKA

② “×” / “÷”

qk

nm

ST

BAaP

S

Sq

T

Tk

B

B

nA

Am

P

P

1

5. Graph skills

（1）Graph of experiment

Eg：求加速度（ 21

2s at ）

y-intercept ： system error in distance

mesuring

points aroud：random error in experiment

（2）Calibration curves




10

虚线：Reading = true value

虚线以上，度数偏大，虚线以下，度数偏小




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Chapter 3 Forces

1. Type of forces

（1）Weight

W=mg （作用在重心上）

（i）Centre of gravity（centre of weight）

The point at which the whole weight is considered to act on.

（ii）Difference between mass and weight

Mass：Quantity of substance，scalar

Weight：Force due to gravity，vector

（2）Upthrust

Produced by pressure difference

2

1

2 1( )

u u

d d

u d u d

F P A gh A

F P A gh A

upthrust F F P A P A gh gh A




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（3）Frictional force

Direction :

Always opposite with the moving direction or the direction of moving in trends。

Magnitude :

When moving forward

f R F

: coefficient of frictional

R : normal reaction

（4）viscous force（Drag）

流体（liquid and air）中的摩擦力，与物体运动方向相反




13

2D kv ，速度越大，Drag 越大

Drag depend on several factors

* velocity *cross-sectional area

* roughness of surface *shape

一般，在液体中，Upthrust < Viscous force，在空气中 Viscous force <

Upthrust

2．Equilibrium of forces

(1) Resolve

在平行于接触面和垂直于接触面的方向将力分解

sin 30

cos30

f W

R W

(2) Vector triangle

将力平移在一起能构成一个 closed triangle




14

sin 30

cos30

f W

R W

3 .Turning Effect of Forces

(1) Moment

The product of force and perpendicular distance from the pivot to the

action line

of the force.

a. 1M F x b.

2 sinM F x F d

PS：当作用力经过支点时，力矩为 0

Eg：悬挂法找重心




15

（i）分析物体受到的力

* weight

* normal reaction at A： AR

* frictional force at A： AF

（ii）Take moment about A

AR 和 AF 均经过 A 点，关于 A 的 moment 为 0

物体静止时， 0rM ，重力一定经过 A 点，所以重心一定在 A 的正下方

(2) Torque

Couple： two parallel forces are same in magnitude and opposite in

direction

Torque：product of one of the forces and the perpendicular distance

between the

two forces.

Eg：




16

F s

3. Equilibrium 平衡状态

（1） Equilibrium of forces

The net forces acting on an object in any direction is zero

（2） Equilibrium of moments

The net moments/torques acting on an object about any point is zero

Eg：

（i）力的平衡

A BT T Mg mg (1)




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（ii）力矩的平衡

Take moment about A

1.5 3

1.8B

M Mg mg

M T

, 1.5 3 1.8BM M Mg mg T (2)

（iii）联立(1)(2)可求 ,A BT T

Ps：选择支点的原则：

不要选择已知力和所求力所经过的点作为支点

尽量选择未知的不需要求的力经过的点作为支点

求 TA，选：B 作为支点

1.8 1.2

0.3

1.8 1.2 0.3

A

A

M T mg

M Mg

T mg Mg

即可求出 TA


as 物理讲义 · ①add and subtract coplanar vectors a b c equilibrium : resultant force = 0 ②...

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