### 打点纸带的剪拼分析

《课本》p33：3-4

《金榜》p22：8

《导》    p32：6

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straight line motion                        直线运动

speed up                        加速

slow down                        减速

object                        物体

recording timer                        计时器

spark recording timer                        电火花计时器

ticker tape timer                        打点计时器

paper tape                        纸带

ticker tape                        打点纸带

dot                        点子、点

obtain                        获取、获得

mark                        标注

evidence                        证据

table                        表格

measure(-ment)                        测量

record                        记录

analyze                        分析

cut                        裁剪

paste                        粘贴

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time interval                        时间间隔

scale                        标量

vector                        矢量

magnitude                        大小

direction                        方向

displacement                        位移

distance                        距离、路程

speed                        速率

velocity                        速度

instant velocity                        瞬时速度

average velocity                        平均速度

acceleration                        加速度

equation                        公式、方程

time                        乘

divide by                        除以

square                        平方

evaluate                        计算

calculate                         计算

design                        设计

material                        仪器、器材

procedure                        过程

uniform motion                        匀速运动

cart                        小车

mass                        砝码

inclined ramp                        斜面、斜坡

variable                        变量

independent variable                        自变量

dependent variable                        因变量

graph                        图像

a graph of distance versus time

位移-时间图像

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graph paper                        坐标纸

origin                        坐标原点

axis                        坐标轴

vertical axis                        纵轴

horizontal axis                        横轴

slope                        斜率

best-fit                        拟合

values                        值

Mark off the tape in groups of five dots.

每五个点一组标注纸带

section                        段

width                        宽度

length                        长度

the distance traveled                        通过的距离

constant                        不变的(数),常数

one tenth of a second                        十分之一秒

InvestigationDetermining an Average Speed

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A ticker tape timer is the most commonly used technology for recording distances at regular time intervals for objects moving in a straight line. As the object attached to the end of the paper tape moves, it pulls the tape through the timer. As the tape moves through the timer, dots are recorded at constant time intervals.

The purpose of this investigation is to determine the average speed of an object by using a ticker tape timer, and to evaluate the experimental design, materials, and procedure.

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Question

What is the average speed of the object in uniform motion?

Design

Attach a cart to the ticker tape and let it run down a smooth, slightly inclined ramp at a constant speed. Calculate the slope of a graph of distance versus time to determine the average speed of the cart.

controlled variables: cart, ramp

independent variable: time elapsed

dependent variable: total distance travelled

(a) Prepare a table, similar to Table 1, in which to record your evidence.

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 Table 1: Motion of a Cart Dot Total time (ms) Total distance (mm) 1 0 0 2     3

Materials

• ticker tape timer

• roll of tape

• cart

• about 1–2 m smooth board

• small wood blocks or books

• adhesive tape

• (optional) stand and clamps for timer and/or tape roll

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Procedure

<!--[if !supportLists]-->1.        <!--[endif]-->Place the cart at one end of the board and adjust the height of the board until the cart just starts to move.

<!--[if !supportLists]-->2.        <!--[endif]-->Set up the ticker tape timer at the upper end of the ramp and either hold or clamp it in place.

<!--[if !supportLists]-->3.        <!--[endif]-->Attach the end of the tape to the cart with a piece of adhesive tape.

<!--[if !supportLists]-->4.        <!--[endif]-->Do a trial run to make sure that the tape runs smoothly through the timer when the cart is released, and that the cart’s speed is about constant.

<!--[if !supportLists]-->5.        <!--[endif]-->Return the cart to the top of the track, turn on the timer and then immediately release the cart.

<!--[if !supportLists]-->6.        <!--[endif]-->Turn off the timer and stop the cart when it reaches the end of the ramp.

<!--[if !supportLists]-->7.        <!--[endif]-->Cut the tape near the timer and remove the tape from the cart.

<!--[if !supportLists]-->8.        <!--[endif]-->Record the timer setting in milliseconds.

(b) Starting at the dot where the dots begin to be about equal distances apart, measure the total distance travelled (from the beginning) for each subsequent dot. It may be that only every second or sixth dot is used, as directed by your teacher. Measure the total distance to the nearest half millimeter.

(c) Enter the values of the time and distance measurements into your table. Use about 10 distance measurements. Clean up the laboratory station and dispose of, or recycle, any waste.

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Analysis and Evaluation

(d) Draw a total distance versus total elapsed time graph of the evidence gathered.

(e) Calculate the slope of the best-fit straight line to determine the average speed of the cart in meters per second.

(f) Evaluate the design, procedure, and materials.

(g) Write a formal lab report for this investigation.

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Understanding Concepts

1. The design used in this investigation tried to compensate for the effect of friction. Briefly explain how this was done.

2. Did your cart travel at a constant speed in this investigation? How do you know?

3. Suppose your cart hit a small imperfection such as a knot or groove in the board and you did not notice this when you were doing this investigation. How might this appear on your ticker tape? Describe and explain the appearance of the dots on the tape.

4. Suggest an experimental design for this investigation that would answer the same question using different equipment.

Exploring

5. Repeat the investigation with the ramp at a different angle. Predict how your results will be affected. Carry out the investigation to test your prediction.

Challenge

Compare the timing device used in this investigation with those available to Galileo. In what ways can timing devices be compared?

Straight Line Motion with a Stomper

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Objectives:
After this experience, the student should
1.  be able to define average speed (distance traveled/time)
2.  be able to graph distance vs time and velocity vs time
3.  be able to find the velocity from the distance time graph (slope)
4.  be able to find the acceleration from the velocity time graph (slope)
5. recognize constant velocity, constant acceleration and changing        acceleration from the shape of the distance-time and velocity-time graphs

Materials needed:
(for each group)
Stopwatch, meter stick, Stomper (battery powered toy car), large washer or 100 g mass, tape, paper tape (ticker tape) and a recording (ticker tape) timer, Tricycle (optional).

Strategy:
Part I:  Begin with the Stomper.  Show it going in a straight line along the counter top.  Ask:  How fast is it going?  What do we need to know to find out?  (You need a distance traveled and a time.)  Give each group a Stomper, stopwatch and meter stick. They should determine the average speed of their Stomper. It should take 10 or 15 minutes for them to do several trials.
Part II:  How fast was the Stomper going as it moved along?  Was it going the same speed everywhere or did it speed up or slow down?  Point out:  The stopwatch is only good for substantial times, several seconds.  It will not help us answer this question.  Demonstrate the recording timer by pulling a meter or so of tape through it.  Explain why the time intervals are equal and ask why the spaces are not even.  (The spaces are small where the speed was small.)
Each group should do two runs with the Stomper pulling a length of ticker tape behind it.  Mark off each tape in groups of six dots.  (Each six is one tenth of a second.)  The first tape will become a distance-time graph.  Rip each six dot section and glue it to a piece of graph paper.  The first section goes on next to the origin.  The second section goes over one width of tape, but starts up, so that its bottom is next to the first tapes' top.  The third goes over one and its bottom lines up with the top of the second section, etc.  Thus the vertical axis is the distance traveled in cm. and the horizontal axis is the time in tenths of a second.  This graph will have a constant slope equal to the average speed found with the stopwatch.  Demonstrate how to find slope.
The second tape will become a velocity-time graph.  Each six dot section is the distance traveled per tenth of a second, so it is the average velocity for that tenth of a second.  For this graph the vertical axis is the velocity in cm per tenth of a second, while the horizontal axis is again the time in tenths of a second.  For this graph, each tape has its bottom on the horizontal axis.  The tapes go next to each other in order.  This graph will have a slope very close to zero because the speed is very close to being constant.  How did this velocity compare to the slope of the first graph?  How did it compare to the speed found with the stopwatch?

Be certain that you ask the students to describe each of these two graphs and to compare them to each other.

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`     This is probably as much as you can expect for one day.  I would then spend a day or so doing constant velocity problems to reinforce this concept. `
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`     Part III:  Constant Acceleration      Drop a mass.  (Catch it!)  Ask if this is constant velocity.  Ask how you can find out.  Using the recording timers, attach the tape to the mass and drop the mass over the side of the table.  (It pays to protect the floor with a book, or a newspaper.)  Run two tapes.  Mark every sixth dot and create a distance-time and a velocity-time graph.  Look at them!  The distance graph will not be a straight line this time.  It should look like a parabola, because the speed is increasing, the slope will increase.  The velocity graph will be a straight line, but will not be horizontal, because the speed is increasing at a constant rate. The slope of this line is the acceleration.  (The change in velocity/the time it took (dV/dt).)      Again, it is very important to ask what these graphs look like and to compare them to each other and to the graphs from Part II. `
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`     This is probably a second day's work.  It should be followed by problems with distance, velocity and constant acceleration. `
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`     Part IV:  Constantly Increasing Acceleration      Lay a chain on the counter top.  Push it over the edge one link at a time, until it goes by itself.  Ask what kind of motion this is.  Again, we can analyze this motion if we attach a tape to it.  Mark every sixth dot.  The distance time graph is optional, be sure to do a velocity time graph.  This will not be a straight line because the velocity increases at an increasing rate. (The acceleration (slope) increases at a constant rate, thus we get a parabola.)      It is once more imperative that you ask the students to describe the shape of the graph(s) and compare them to the previous graphs.`
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`Optional:  Have Tricycle races.  Have someone ride a tricycle pulling ticker tape.  The velocity-time graph is the most interesting.  Be sure to ask about the accelerations.  They will be positive and negative!`
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`Conclusions:   Velocity is the distance traveled/time it took (dD/dt)   Velocity is the slope of a distance-time graph   Acceleration is the change in velocity/time it took (dV/dt)   Acceleration is the slope of a velocity-time graph   Constant velocity gives straight line graphs for both d-t and v-t   Constant acceleration gives parabolas for d-t, but straight lines for v-t   Changing acceleration gives v-t graphs with changing slopes Performance Assessment:     Using TWO SPEED Racer (a friction car, about \$2.75 at "Toys R Us"): Show it to the students.  Placing it on a flat surface, where all of them can watch it, pull it back until you hear a click.  Let it go.  It will go in a straight line, and suddenly increase its speed.     Ask the students to sketch two graphs.  A Distance vs Time and a Velocity vs Time graph. Rubric: 5 pts  Graphs are correctly labeled on each axis. Distance-time graph shows as short straight line, sloping up followed by a steeper straight line; also sloping up. Velocity-time graph shows a short, horizontal line, followed by a higher horizontal line. 4 pts  Graphs not correctly labeled, but show the proper shapes. 3 pts  Graphs not correctly labeled, and only one of the graphs shows the proper shape. 2 pts  Graphs properly labeled, but neither graph is the proper shape. 0 pt   No labels, and wrong shapes. Multicultural Applications:     There are many applications of distance vs time in life including the Summer Olympics track competitions and the speed skating and cross country skiing in the Winter Olympics.`
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