动力学系统

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PASCO

实验

Experiment 1

Dynamics Cart Accessory Track Set

实验一

动力学系统

Experiment 1

Acceleration and Harmonic Motion

实验

1

加速度和简谐振动

Equipment Needed:

-Dynamics Carts with Mass (ME-9430)

-Spring

-Base and Supported rod (ME-9355)

-Mass balance

-Acceleration sensor

-50 Newton force sensor

-Motion sensor

-Dynamic Cart Track with End stop

and Pivot clamp

Purpose

目的

目的是测量不同倾角的斜面上的弹簧和物

The

Purpose

is

to

measure

the

period

of

oscillation

of

a

spring

and

mass

system

on

an

体系统的振动周期，并验证牛顿第二定律，

incline

at

different

angles

and

compare

it

to

the

F=ma

。

< br>(

看图

1)

theoretical

value

and

verify

Newton’s

Second

Law, F=ma. (See Figure 1)

Theory

For

a

mass

attached

to

a

spring,

the

theoretical period of oscillation is given by

理论

对于弹簧上的物体，振动的理论周期为

T

?

2

?

m

k

T

?

2

?

m

k

m

是振动质量，

wh ere

T

is

the

time

for

one

complete

这里

T

是一个来回运动的时间，

back- and-forth

motion,

m

is

the

mass

that

is

k

是弹簧常数。

oscillating, and

k

is the spring constant.

.

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Figure

1

According to Hooke’s Law, the force exerted

根据虎克定律，弹簧产生的力与弹簧被压

by

the

spring

is

proportional

to

the

distance

the

缩或伸长的距离成正比，

F=kx,

这 里

k

是比例常

spring is compressed or stretched,

F=kx,

where

k

数。这样在实验上，可以通过施加不同的力让

is

the

proportionality

constant.

The

spring

弹簧压缩或伸长不同的距离来确定。作力—距< /p>

直线的斜率就等于

k

。

< br>根据牛顿第二定

constant

can

be

experimentally

determined

by

离的图，

applying

different

forces

to

stretch

the

spring

律

F=ma, F

是作用在物体

m

上的外力

< br>,a

是物体

different

distance.

When

the

force

is

plotted

的加速度。

versus distance, the slope of the res ulting straight

line is equal to

k

.

According to Newton’s Second Law,

F=ma

.

F

is

the net force acting on the object of mass

m

and

a

is the resulting acceleration of the object.

Procedure

Measurement to find the Theoretical period

①

Use

the

balance

to

find

the

mass

of

the

步骤

找到理论周期的测量

用天平称出小车和加速度传感器的质量，

cart

and

the

Acceleration

sensor,

Record

this

记下这个值

M

。

value M.

.

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②

Set

the

cart

on

the

track

and

attach

a

把小车放在导轨上，把弹簧的一端插入小

spring to one end of the cart by inserting the end

车的孔中，把弹簧和小车连在一起。然后把弹

of

the

spring

in

the

hole

provided

in

the

cart.

簧的另一端与导轨的末端连在一起。

Then attach the other end of the spring to the end

of the track.

③

Incline the track by raising the end of the

end

of

the

track

that

has

the

spring

attached.

As

the

end

of

the

track

is

raised

the

spring

will

stretched.

Keep

the

angle

of

inclination

of

the

track small enough so the spring is not stretched

more than half the length of the track. Record the

equilibrium position L

0

.

④

Computer Setup:

1.

Connect

the

Science

Workshop

interface

to the computer, turn on the interface, and turn on

the computer.

2.

Connect the force sensor’s DIN

plug into

Analog

Channel

A

of

the

interface,

the

motion

sensor’s digital plug into Channel 1 and 2.

3. Open the

Science Workshop

document, let

it be required working conditions.

lick

the

“REC”

button,

the

computer

starts

to

record data. Drag the cart to stretch the spring, in

the

graph

of

Force(N)

versus

position(m),the

slope

of

the

line

is

equal

to

the

effective

spring

constant, k.

Measuring the Experimental Period

⑥

Computer

Setup:

t

the

Science

Workshop

interface

to

the

computer,

turn

on

the

interface,

and

turn

on

the

computer.

t

the force sensor’s DIN plug into Analog Channel

A of the interface, the acceleration sens

or’s DIN

plug into Analog Channel B. 3. Open the

Science

Workshop

document,

let

it

be

required

working

.

抬高与弹簧相连 的导轨的末端，让导轨倾

斜。导轨的末端升高后，弹簧会伸长。让导轨

< br>的倾角足够小，这样，被拉长的弹簧的长度不

超过导轨长度的一半。记下平衡位置

L

0

。

计算机设置

把科学工作站接口连到计 算机上，打开接

口，打开计算机。

把 力传感器的模拟插头接到接口的

A

通

道 ，把运动传感器的数字插头接到通道

1

和

2

。

打开科学工作站文件，让它处 于所需的工

作状态。

点击

“REC”

按扭，计算机开始记录数据。

拖动小拉长弹簧，在力

-

位移的图中，斜率就是

弹簧常数

k