2024_04_09_99b1df652a5f3c1dff03g

PHYS 2LA: Lab 1
Acceleration Due to Gravity Precise
PHYS 2LA：实验室1重力加速度精确

Objectives 目标

This lab introduces fundamental concepts involved in physics experimentation like measurement, mathematical analysis, and graphical analysis. You will put these concepts in action to measure the acceleration due to gravity acting on an object in free-fall. Read all the steps in each part before you start. Work in your assigned groups and maintain a collaborative and communicative team.
本实验介绍了物理实验中涉及的基本概念，如测量，数学分析和图形分析。您将把这些概念付诸实践，以测量由于重力作用在自由落体中的物体上而产生的加速度。在开始之前阅读每个部分的所有步骤。在你指定的小组中工作，保持一个协作和沟通的团队。

Of the 8 learning objectives listed at the beginning of the Student Information Guide, you should expect to work on the following during today's lab.
在《学生信息指南》开头列出的8个学习目标中，您应该在今天的实验中完成以下内容。

A. Number 1. Create an appropriate graph based on collected data. Be able interpret information from that graph.
A.一号。根据收集的数据创建适当的图表。从图表中解读信息。

B. Number 5. Use calculus, scalars, vectors, and pictorial representations in order to solve problems.
B。5号运用微积分、标量、向量和图示来解决问题。

C. Number 7. Explain how an abstract model relates to physical phenomena, including identifying the limitations of a model.
C.七号。解释抽象模型如何与物理现象相关联，包括识别模型的局限性。

Introduction 介绍

If an object is dropped near the Earth's surface, we claim that it will fall with a constant acceleration due to the Earth's gravity,

. You will experimentally test this claim in today's lab.
如果一个物体落在地球表面附近，我们声称它将由于地球的引力而以恒定的加速度下落，

。您将在今天的实验中通过实验验证这一说法。

The motion of an object in free fall is one-dimensional motion in the y-direction with constant acceleration. In general, an object undergoing free fall follows the kinematic equation:
自由落体中的物体的运动是在y方向上具有恒定加速度的一维运动。通常，经历自由落体的物体遵循运动学方程：

where

is the displacement of the object in time,

, and

is the initial falling speed of the object, and

is the acceleration of that object in free fall

. If the
其中，

是物体在时间上的位移，

，

是物体的初始下落速度，

是物体在自由下落时的加速度

。如果
object is dropped from standstill

, we can update Eq. 1 :
如果物体从静止

下降，我们可以更新Eq.一曰：

We can now rearrange this to calculate the acceleration due to gravity,

, from the initial height when the object was released and the time of free fall:
我们现在可以重新排列它，从物体被释放时的初始高度和自由落体的时间计算重力加速度

：

Developing good laboratory habits:
养成良好的实验室习惯：

One of the primary objectives in our physics labs is to familiarize you with rigorous scientific methodology that includes setting up experiments, collecting and analyzing data, and deriving conclusions compatible with a given theoretical background and hypothesis. As a general rule:
我们物理实验室的主要目标之一是让您熟悉严格的科学方法，包括设置实验，收集和分析数据，并得出与给定理论背景和假设兼容的结论。一般来说：

Fill every data column and calculate the answer before moving on to the next column.
填写每个数据列并计算答案，然后再进入下一列。
Let everyone in the group participate in the data taking - distributing the procedure among different people will increase precision.
让组中的每个人都参与数据采集-将过程分配给不同的人将提高精度。
Make sure that the result is compatible with your physical hypothesis, or if it isn't, make sure that you can explain why it isn't.
确保结果与你的物理假设相一致，或者如果不一致，确保你能解释为什么不一致。
Do not finish any experiment before you are convinced that your overall analysis and conclusions make sense.
在你确信你的整体分析和结论是有意义的之前，不要完成任何实验。

Software: 软件方面：

We will make use of a software interface called Capstone to collect, analyze, and manipulate data from experiments. The PASCO 850 interface is used to translate data from various sensors to the software. Throughout the introductory physics lab curriculum, you will use different features of the software, though the most commonly used will be the "graphs", "tables", "digits", and "calculator" features. Capstone has four main palettes, which are described on the following page:
我们将使用一个名为Capstone的软件界面来收集、分析和操作实验数据。PASCO 850接口用于将来自各种传感器的数据转换为软件。在整个介绍性物理实验室课程中，您将使用该软件的不同功能，尽管最常用的是“图形”，“表格”，“数字”和“计算器”功能。Capstone有四个主要的调色板，如下所述：

(1) Tools: Used to add and configure sensors and interfaces, edit data sets and properties, calibrate sensors, define calculations, and set up signal generators.
(1)工具：用于添加和配置传感器和接口、编辑数据集和属性、校准传感器、定义计算以及设置信号发生器。

(2) Controls: Used to start/stop data collection, set the data monitoring mode, set the sampling rate, delete data runs, and define start/stop conditions.
(2)对照组：用于启动/停止数据采集、设置数据监测模式、设置采样率、删除数据运行以及定义启动/停止条件。

(3) Displays: Used to add data displays such as data tables, graphs, and digital monitoring.
(3)显示：用于添加数据显示，如数据表、图形和数字监控。

(4) Central Display: Displays the data displays selected from the "Displays" palette
(4)中央显示：显示从“显示”选项板中选择的数据显示

Experimental Apparatus: 实验装置：

In the first part of the lab, you will use a two-meter stick and a motion sensor.
在本实验的第一部分中，您将使用一根两米长的棍子和一个运动传感器。

In the second part of the lab, the experimental apparatus you will use to measure

(shown at right) consists of:
在本实验的第二部分中，您将用于测量

的实验装置（如右图所示）包括：

A two-meter stick, 一根两米长的棍子
A steel ball, 一个钢球，
A ball release mechanism,
一种球释放机构，
And a receptor plate.
以及一个接收板。

This apparatus will allow you to precisely measure
这个仪器能让你精确测量

Release Plate takes for an object released from a known height to ground, hence allowing you to calculate

using Eq. 3 . the time it hit the
释放板用于从已知高度释放到地面的物体，因此允许您使用公式计算

。3 .当它撞上

Part I: Introduction to Capstone 1. Data Acquisition and Graphical Analysis
第一部分：Capstone 1的介绍。数据采集和图形分析

The purpose of this first section is to introduce you to data-input and graphical analysis in the Capstone software. You will generate functions of position versus time by moving along a line while trying to arrive at specific positions at specific times. The data will be acquired by a motion sensor that sends data through the 850 interface to the software.
第一部分的目的是向您介绍Capstone软件中的数据输入和图形分析。您将通过沿沿着移动并试图在特定时间到达特定位置来生成位置与时间的函数。数据将由运动传感器采集，该传感器通过850接口向软件发送数据。

1.1: Turn on the 850 interface and make sure the motion sensor is plugged into "Pasport Input 1" and the free fall adapter is plugged into "Digital Input 1". Open the Capstone template corresponding to this week's lab in the "

" folder on your computer's desktop. Position the motion sensor at the front edge of the lab table.
1.1：打开850接口，确保运动传感器插入“Pasport Input 1”，自由落体适配器插入“Digital Input 1”。在电脑桌面的“

“文件夹中打开与本周实验对应的Capstone模板。将运动传感器放置在实验台的前边缘。

1.2: In Capstone, click on the "Hardware Setup" menu under the tools palette. An image of the 850 interface should appear. You will see next to "Pasport Input 1" the icon for the motion sensor (") (you will also see next to "Digital Input 1" the icon for the free fall adapter ( the second part of the lab). Click Hardware Setup again to close the menu.
1.2：在Capstone中，点击工具面板下的“硬件设置”菜单。应出现850接口的图像。您将在“Pasport Input 1”旁边看到运动传感器的图标（“）（您还将在“Digital Input 1”旁边看到自由落体适配器的图标（本实验的第二部分））。再次单击硬件设置关闭菜单。

1.3: In the template you have a table already created for you. Enter the data in the table below on your computer. To do this, click at the top of one of the columns in the Capstone tables. Under "Create New", select "User-Entered Data". This will allow you to type in your data set by hand. Title the first column "Time Elapsed" with units (s) and the second column "Position Traveled" with units (m). Create the table as shown below:
1.3：在模板中，您已经创建了一个表。在您的计算机上输入下表中的数据。要执行此操作，请单击Capstone表中某列的顶部。在“新建”下，选择“用户输入的数据”。这将允许您手动输入数据集。第一列标题为“经过的时间”，单位为（s），第二列标题为“经过的位置”，单位为（m）。创建表格，如下所示：

Title	Match Graph
Time Elapsed (s)	Position Traveled (m)
0.00	2.00
1.00	1.40
2.00	1.00
4.00	1.00
5.00	1.60
6.00	2.00
8.00	1.00

1.4: Now plot the data from your table in the "Match Graph" at the bottom left of the screen. To do this, click on the vertical axis and select "Position Traveled

" under the "User-Entered Data" heading. Then assign "Time Elapsed (s)" to the horizontal axis.
1.4：现在在屏幕左下方的“匹配图”中绘制表格中的数据。为此，单击垂直轴并选择“用户输入的数据”标题下的“行程位置

“。然后将“Time Elapsed（s）”分配给水平轴。

1.5: Lay the two-meter stick on the floor in front of the motion sensor with the zero end of the scale approximately under the face of the motion sensor. Orient the stick so that the motion sensor is facing along the stick.
1.5：将两米长的杆放在运动传感器前面的地板上，使刻度的零端大约位于运动传感器表面下方。调整斗杆的方向，使运动传感器沿着斗杆朝向。

1.6: Adjust the position of the measuring stick with the following procedure:
1.6：按以下步骤调整测量杆的位置：

On the controls palette, click on "Recording Conditions" (
在控制面板上，单击“记录条件”（
Set the start condition type to "Time Based" and enter in for the time delay. Set the stop condition to "Time Based" and enter for the record time. When you're finished, click OK.
将启动条件类型设置为“基于时间”，并在中输入时间延迟。将停止条件设置为“基于时间”，并输入作为记录时间。完成后，单击“确定”。
Set the motion sensor's sampling rate to . Click on the Record button (O) at the bottom of the screen. The motion sensor will start to emit a clicking sound.
将运动传感器的采样率设置为。点击屏幕底部的录制按钮（O）。运动传感器将开始发出咔哒声。
Stand in front of the motion sensor.
站在运动传感器前面。
Observe the trace on the graph "Motion Sensor Data," which will begin tracing across the graph after a three-second count on the timer. While the trace moves across the graph, move toward or away from the motion sensor so that the trace reaches a vertical coordinate of 1.0 meter. The trace will automatically stop after eight seconds.
观察“运动传感器数据”图上的轨迹，计时器计时三秒后，该轨迹将开始在整个图上进行跟踪。当轨迹在图形上移动时，朝向或远离运动传感器移动，使轨迹达到1.0米的垂直坐标。跟踪将在8秒后自动停止。
Remain standing where you are.
站在原地别动。
Have your partner slide the stick towards or away from the motion sensor so that the 1.0-meter mark is under the front of your body.
让你的伙伴将棍子滑向或滑离运动传感器，使1.0米的标记位于你身体的前部。
Tape the stick in place with masking tape.
用胶带把棍子固定好。

1.7: Examine the match graph and determine the position coordinate of the graph for a time of zero seconds.
1.7：检查匹配图并确定图的零秒时间的位置坐标。

1.8: Click on the record button. A three-second countdown will commence, followed by eight seconds of measurement by the motion sensor. While the motion sensor is operating, it will emit a clicking sound.
1.8：点击记录按钮。将开始三秒倒计时，然后由运动传感器进行八秒的测量。当运动传感器工作时，它会发出咔哒声。

1.9: During the three-second countdown, stand in front of the motion sensor at the initial position of the match graph, which you determined in step 1.7.
1.9：在三秒倒计时期间，站在运动传感器前面的匹配图的初始位置（您在步骤1.7中确定）。

1.10: During the eight seconds of measurement, have your partner give you instructions to move towards or away from the motion sensor so that the trace moving across the graph matches the colored graph as nearly as possible. It may be helpful to rehearse your movements before taking data.
1.10：在8秒钟的测量过程中，让你的搭档给予指示，让你靠近或远离运动传感器，以便在图表上移动的轨迹尽可能与彩色图表匹配。在获取数据之前，排练一下你的动作可能会有所帮助。

What do the flat lines on the position versus time graphs represent?
位置-时间图上的平线代表什么？
What do diagonal lines connecting the flat lines represent? What do their slopes represent (i.e. a steeper slope versus a more gradual slope)?
连接平线的对角线代表什么？它们的斜率代表什么（即较陡的斜率与较平缓的斜率）？

1.11: Repeat steps 1.8-1.10 until a reasonably good match is obtained for the match graph on the bottom left. Ask your TA to check your match.
1.11：重复步骤1.8-1.10，直到为左下角的匹配图获得相当好的匹配。让你的TA检查你的比赛。

In your notebook, briefly summarize the activity from this section: Explain what skills you learned and why they might be useful in the study of experimental physics. Also discuss the difference between your theoretical data (the information you inserted into the table) and your measured data (the trace you generated using the motion sensor).
在你的笔记本上，简要总结本节的活动：解释你学到了什么技能，为什么它们在实验物理学的研究中可能有用。同时讨论理论数据（插入表格的信息）和测量数据（使用运动传感器生成的轨迹）之间的差异。

Part II: Determination of
第二部分：的确定

Equipment Setup 设备设置

2.1: In Capstone, select the second tab at the top of your screen titled "Time of Fall Measurements". You should see a page with a table and a "Digits display" on the left and a graph on the right.
2.1：在Capstone中，选择屏幕顶部的第二个选项卡，标题为“坠落时间测量”。您应该看到一个页面，左侧有一个表格和一个“数字显示”，右侧有一个图表。

2.2: From the "Controls" palette, change the recording mode from "Continuous Mode" to "Keep Mode". The "Controls" palette should now look like the image below. With Capstone now ready, it is time to setup the apparatus.
2.2：从“控制”选项板中，将录制模式从“连续模式”更改为“保持模式”。“控件”调色板现在应该看起来像下面的图像。随着Capstone现在准备就绪，是时候设置设备了。

NOTE: "Keep Mode" will allow you to preview the measured value before it is stored into the data table. If you want to keep the value, click

to record the
注：“保持模式”将允许您在将测量值存储到数据表中之前预览测量值。如果要保留该值，请单击

以记录

data. If you do not want to keep the value, do not hit stop. Simply redo the sample run.
数据如果你不想保留价值，不要点击停止。只需重新运行样品。

2.3: On the experimental apparatus (refer to the figure on p. 3), press the dowel pin until the release plate/contact screw separation is slightly less than the diameter of the ball. Insert the ball between the contact screw and the release plate then tighten the thumbscrew to secure the steel ball. It should fit just tightly enough to prevent it from falling, but not so tight that the release plate is damaged. Move the clamp holding the release plate along the meter stick, such that the bottom of the ball is at a height of

.
2.3：在实验装置上（参见第3页的图），按压定位销，直到释放板/接触螺钉的间距略小于球的直径。将钢球插入接触螺钉和释放板之间，然后拧紧指旋螺钉以固定钢球。它应该安装得足够紧，以防止它下降，但不要太紧，释放板损坏。沿仪表杆沿着移动固定释放板的夹具，使球的底部处于

的高度。

2.4: To release the ball, loosen the thumbscrew. Make sure that the ball strikes the center of the receptor pad. Re-position the receptor pad as necessary. Repeat steps 2.3 and 2.4 as needed to ensure the ball strikes the center of the receptor pad.
2.4：松开指旋螺钉，即可释放球头。确保球撞击接收器垫的中心。根据需要重新定位接收器垫。根据需要重复步骤2.3和2.4，以确保球撞击接收器垫的中心。

NOTE: Make sure the receptor pad is level and aligned with the bottom of the two-meter stick. If the pad is placed completely under the stick, it may not register the strike of the ball.
注：确保接收器垫水平并与两米棒的底部对齐。如果球垫完全放在球杆下面，它可能无法记录球的撞击。

NOTE: When inserting the ball into the release mechanism, a bogus value of time appears in the digits display. Ignore this value; it will be automatically erased when a fall time measurement is complete.
注：当将球插入释放机制时，数字显示屏上会出现虚假的时间值。忽略此值;当下降时间测量完成时，此值将自动删除。

3. Data Collection 3.数据收集

3.1:

Tighten the thumbscrew and insert the ball between the contact screw and the release plate. Click "Preview" (O) to begin data collection. Release the ball by loosening the screw. When the ball hits the receptor pad, the time between when the ball leaves the contact screw to when it hits the release plate will be recorded on the digits display - this is the "Time of Fall".
3.1：

拧紧指旋螺钉，并将球插入接触螺钉和释放板之间。点击“预览”（O）开始数据收集。松开螺钉，释放滚珠。当球撞击接收器垫时，从球离开接触螺钉到球撞击释放板之间的时间将记录在数字显示器上-这是“坠落时间”。

3.2: For the first sample run, record the data in your notebook (eg. "Attempt 1:

). Does it make sense for the ball to have fallen from that distance in that amount of time? (eg.

is not a reasonable amount of time and that measurement would lead us to presume that our experiment is not measuring what we want it to measure). If you estimate
3.2：对于第一次样品运行，将数据记录在笔记本中（例如：“尝试1：

）。球在那么长的时间内从那么远的地方落下有意义吗？（例如：

不是一个合理的时间量，这种测量会导致我们假设我们的实验没有测量我们想要测量的东西）。如果你估计
that your measured time of fall is approximately near what it should be, you can move on to take meaningful data.
如果你测量到的坠落时间接近它应该是什么，你可以继续采取有意义的数据。

3.3: Repeat the measurement. When finished, click to stop data collection. Once you complete your measurement, record it in your notebook and copy the time into the table in Capstone.
3.3：重复测量。完成后，单击以停止数据收集。完成测量后，将其记录在笔记本上，并将时间复制到Capstone的表格中。

3.4: Repeat steps 3.1-3.3 to measure fall times from

, and

. Move the clamp holding the release plate along the two-meter stick, such that the bottom of the ball is at the chosen height.
3.4：重复步骤3.1-3.3，测量从

和

开始的跌落时间。将固定释放板的夹子沿着两米长的棍子移动，使球的底部处于选定的高度。

4. Data Analysis 4.数据分析

4.1: Using the time value you found for

, calculate

using Eq. 3. Do the same calculation for each of the six data points. Comment on the calculated values. How do they compare to

? Are the calculated values for

the same for each fall height? Explain why or why not. If they are different, which calculated value do you think is "most correct"? Why?
4.1：使用您为

找到的时间值，使用等式计算

3.对六个数据点中的每一个进行相同的计算。对计算值进行注释。如何与

比较？

的计算值对于每个坠落高度是否相同？解释为什么或为什么不。如果它们不同，您认为哪个计算值“最正确”？为什么？为什么？

4.2: Now that we've done so analytically, Let's analyze the data graphically. Add the

data to the vertical axis of the plot in Capstone and add the

data to the horizontal axis. This doesn't tell us much as it is now, but the power of graphical analysis is that we can compare measured data (like you have in your graph) to theoretical predictions for physical behavior (like Eq. 2).
4.2：既然我们已经完成了分析，让我们以图形方式分析数据。将

数据添加到Capstone中图的垂直轴，并将

数据添加到水平轴。这并没有告诉我们太多，因为它是现在，但图形分析的力量是，我们可以比较测量数据（就像你在你的图）的理论预测的物理行为（如方程。2）。

First, identify a physical hypothesis to describe the trend between your controlled (fall-height) and measured data (time-of-fall). Write down the equation that describes this hypothesis and explain your choice.
首先，确定一个物理假设来描述你的控制数据（坠落高度）和测量数据（坠落时间）之间的趋势。写下描述这个假设的等式，并解释你的选择。
From this statement of your physical hypothesis, identify the mathematical model that can be used to represent it (you may wish to reference the listed models on p. 2 of the "Graphical Analysis Guide"). State what the parameters in the mathematical represent in your physical hypothesis stated in the first bullet point, and state what terms from your hypothesis correlate with the ' ' and ' ' terms in the mathematical model.
从你的物理假设的陈述中，确定可以用来表示它的数学模型（你可能希望参考“图形分析指南”第2页上列出的模型）。说明数学模型中的参数在第一个要点中所述的物理假设中代表什么，并说明假设中的哪些项与数学模型中的“ ”和“ ”项相关。
Click the arrow next to the curve fitting icon ). You will see a big list of mathematical models. The closest one to your mathematical model is "Quadratic: ", but this is not the same as the model needed to describe your physical hypothesis (Eq. 2). Explain why not.
单击曲线拟合图标旁边的箭头）。你会看到一个很大的数学模型列表。最接近你的数学模型的是“二次： ”，但这与描述你的物理假设所需的模型不同（等式11）。2）。解释为什么不。
From the curve fitting menu, select "User-Defined Fit" so that you can tell the software which mathematical model to fit to your data. Click the "Curve Fit Editor" on the left of the screen ( %). Enter the correct mathematical model next to " " - it should be " " - then click "Apply". Your data will be fit accordingly, and the software will tell you the value of your fitting parameter, A, that yields the best-fit curve.
从曲线拟合菜单中，选择“用户定义的拟合”，这样您就可以告诉软件要拟合数据的数学模型。点击屏幕左侧的“曲线拟合编辑器”（ %）。在“ “旁边输入正确的数学模型-应该是“ “-然后点击“应用”。您的数据将相应地拟合，软件将告诉您拟合参数A的值，该值将产生最佳拟合曲线。
Use the value of your fit parameter to calculate . Compare this value to the values you calculated in step 4.1. Do you think it's more or less accurate than your analytical value? Why?
使用拟合参数的值计算。将此值与步骤4.1中计算的值进行比较。你认为它比你的分析值更准确还是更不准确？为什么？为什么？

4.3: Make a sketch of your graph in your lab notebook. Your TA should be able to provide guidance on what is important to include.
4.3：在实验笔记本上画一个草图。你的助教应该能够提供指导，告诉你什么是重要的。

Thought Experiment: How do you think air resistance affected your measured value of

? If you used a ping pong ball, for example, how would this affect the fall-time? Would you expect the ping pong ball and the steel ball to land at the same time if they were both dropped from a height of

? What would happen if you dropped both balls from a height of

?
思想实验：你认为空气阻力如何影响你的测量值

？例如，如果你使用一个乒乓球，这会如何影响下降时间？如果乒乓球和钢球都从1#的高度掉下来，你认为它们会同时落地吗？如果你把两个球从

的高度掉下来会发生什么？

Finally, write a short summary of today's activities. In it, please discuss:
最后，对今天的活动做一个简短的总结。请在其中讨论：

What is the difference between physical values (measured values) and mathematical values (exact numbers)?
物理值（测量值）和数学值（精确数字）之间的区别是什么？
Briefly describe the experiments you performed to measure .
简要描述您为测量而进行的实验。
What is the difference between the values you found for analytically (step 4.1) vs. graphically (step 4.2)?
您通过分析（步骤4.1）和图形（步骤4.2）找到的值之间的差异是什么？
Why are your measured values for different than the that we always use in physics?
为什么你对的测量值与我们在物理学中一直使用的不同？

PHYS 2LA: Lab 1 Acceleration Due to Gravity Precise PHYS 2LA：实验室1重力加速度精确