Freefall

An object that is acted upon by a force which is constant in magnitude and direction will be accelerated with constant acceleration in the direction of the force. This is expressed by the relationship

一个受到大小和方向都保持不变的力作用的物体，将获得与该力方向相同的恒定加速度。这可以用关系式表示为

where F represents force, a is the acceleration, and m is the mass of the object.

其中F表示力，a是加速度，m是物体的质量。

Aristotle and other ancient philosophers reasoned (mistakenly) that the heavier a body is, the faster it should fall. Galileo is credited with discovering that the force of gravity is the cause of weight and that all bodies, regardless of their mass, are accelerated by the force of gravity at the same rate. That is, the ratio

亚里士多德和其他古代哲学家认为（错误地）物体越重，下落得越快。伽利略被归功于发现重力是重量的原因，并且所有物体，无论其质量如何，都以相同的加速度被重力加速。也就是说，加速度的比值

对所有物体来说，加速度是相同的，称为重力加速度“g”。“

Strictly speaking, free-fall experiments must be conducted in a vacuum so that the force of air resistance does not affect the results. For relatively small, smooth objects of considerable density, however, the error introduced by conducting such experiments in the atmosphere is quite small.

严格来说，自由落体实验必须在真空中进行，以避免空气阻力对结果的影响。然而，对于相对较小且表面光滑、密度较大的物体，在大气中进行此类实验所引入的误差相当小。

For the description of the motion of an object, the variables distance, velocity, acceleration and time are involved. One way to describe the motion of an object is with the relationship

描述物体的运动需要涉及距离、速度、加速度和时间等变量。描述物体运动的一种方法是通过以下关系来实现

where s is the distance traveled in time t and vavg is the average velocity for the time interval t.

其中s是时间t内行驶的距离，vavg是时间间隔t内的平均速度。

If the object accelerates uniformly as a result of the application of a constant force such as gravity, the acceleration can be found as the rate of change of the velocities over successive intervals of time. If equal time intervals t are used then the acceleration can be expressed as

如果物体由于恒定力（如重力）的作用而均匀加速，那么加速度可以表示为速度在连续时间间隔内的变化率。如果使用相等的时间间隔t，则加速度可以表示为

where v2 and v1 are the average velocities over any two successive time intervals t. In this experiment the acceleration of gravity, g, will be determined directly from the motion of a freely falling object using equations 3 and 4.

其中v2和v1是任意两个连续时间间隔内的平均速度。在本实验中，将通过自由下落物体的运动，直接利用方程3和4确定重力加速度g。

The free-fall apparatus has an electromagnet to hold the object until the record of its fall is to be made. When the switch to the coils of the electromagnet is opened, the magnet can no longer hold the object, and it falls freely into a cup below. A sparking device of known frequency (60 Hz) passes each spark from an outer wire through a conducting metal ring on the object, through a waxed recording tape, and on to a second wire to complete the circuit. The passage of the spark through the waxed tape leaves a small mark or spot on the tape, marking the position of the falling object. With 60 sparks per second, the space between successive marks represents the distance that the object has fallen in 1/60 second. Since the object is accelerating, the distance between marks should increase.

自由落体装置中有一个电磁体，用于在记录其下落之前固定物体。当电磁体线圈的开关打开时，磁体将无法再固定物体，物体便自由下落至下方的杯中。一个已知频率（60赫兹）的火花装置通过外导线将火花传递过物体上的导电金属环，穿过蜡制记录带，然后传到第二根导线以完成电路。火花通过蜡制带的传递会在带上有小标记或斑点，标记下落物体的位置。由于每秒有60次火花，相邻标记之间的距离代表物体在1/60秒内下落的距离。由于物体在加速，标记之间的距离应逐渐增加。

You will be provided with a tape from the free-fall apparatus. (A demonstration will be conducted so that you can see how the tape was made.)

您将获得一段从自由落体装置中获取的胶带。（将进行演示，以便您看到胶带是如何制作的。）

将胶带的两端用贴纸胶带固定在桌面上。

2. Look at the dots on the tape and note the way the distance between dots increases. You should be able to detect a "misfire" of the apparatus if a dot is missing or if there is an extra mark. If a dot is missing, you need to take that into account in entering your data into the calculation program described below.

观察胶带上的点，注意点之间的距离是如何增加的。如果你发现某个点缺失或多出一个标记，你应该能够检测到装置的“故障”。如果有一个点缺失，你需要在下面描述的计算程序中输入数据时加以考虑。

3. Find a dot for a starting point by dropping down at least a centimeter from the first marks so that the falling object will have cleared the magnetic field influence. Label this dot zero (0) and measure the distance from this zero point to each successive dot, measuring as many as possible (at least a dozen). Please note that the distance to be measured is the total distance to each dot from the starting point (zero) and not the distance from the preceding dot. This procedure improves the accuracy of the set of measurements. These distance measurements are critical since they are multiplied by a large number in calculating the acceleration. Measure the distances to the nearest millimeter and then estimate to the nearest tenth of a millimeter. Place the meter stick on its edge so that the scale is next to the paper tape and look perpendicular to the meter stick when taking your reading. You may wish to tape the meter stick down to make sure it doesn't move between measurements.

3. 从第一个标记向下至少移出一厘米处标一个点作为起点，使下落的物体能够离开磁场区域。将此点标记为零（0），并测量该零点到每个后续点的距离，尽可能多地测量（至少十二个）。请注意，需要测量的是从起点（零点）到每个点的总距离，而不是到前一个点的距离。此过程提高了测量结果的准确性。这些距离测量至关重要，因为在计算加速度时会乘以一个较大的数值。测量距离时，应精确到毫米，并估算到毫米的十分位。将米尺放在边缘，使刻度贴近纸带，并在测量时正视米尺。可能需要将米尺固定，以确保测量过程中米尺不移动。

4. A Spreadsheet is an excellent tool for repetitive calculations and the plotting of data. A template titled FreefallTemplate has been set up, and you can find it under the Apple menu (extreme top left of screen). Open that template and record your measured positions in it. The template should appear similar to the illustration below. Record your position data in the column titled "Distance". The Time columns are set up to reflect the 1/60 second interval of the spark timer. The zeros in the Avg. velocity and Acceleration columns are actually the result of formulas which depend upon the distance data which you will enter.

4. 电子表格是进行重复计算和数据绘图的优秀工具。已设置了一个名为FreefallTemplate的模板，您可以在苹果菜单（屏幕极左上角）下找到它。打开该模板并在此记录您的测量位置。该模板应与下图类似。将您的位置数据记录在标题为"距离"的列中。时间列已设置为反映火花计时器的1/60秒间隔。平均速度和加速度列中的零实际上是由于依赖您将输入的距离数据的公式所致。

5. Make a plot of your Distance vs Time by clicking and holding down the mouse button in the upper left box of the first Time column a nd then dragging the mouse diagonally to select a rectangle including your time and distance data. Then release the mouse button and take the mouse up to click on the icon which looks like a magic wand over a bar graph. Then use the mouse to draw a rectangle out beside yur data table where you want the graph to appear. Follow the prompts to create a line graph of your positon data with the first column used as values for the horizontal axis.

5. 通过在第一列时间框的左上角单击并按住鼠标按钮，然后向斜方向拖动鼠标以选择一个包含你的时间和距离数据的矩形区域，然后释放鼠标按钮并将鼠标移至看起来像魔法棒 over 条形图的图标上。然后用鼠标在数据表旁边画一个矩形，以确定图表出现的位置。按照提示创建一个以第一列作为横轴值的线图。

The slope of the distance vs time graph represents the rate of change of distance, which is the velocity.

6. Repeat the process above to plot your Avg. Velocity vs Time. What does this graph tell you?

重复上述过程，绘制平均速度与时间的关系图。这个图告诉你什么？

7. The values calculated for acceleration are meaningful only as far down as you have position data. Position the mouse on the first acceleration value below the level of your position data and click and hold down the mouse button. Drag the mouse down to the bottom of the column of numbers and release the mouse button to highlight these numbers. Choose Blank from the Edit menu to blank out those values. Then the calculation below should show the average acceleration in cm/s^2. (You can plot these acceleration values if you wish, but they generally swing pretty wildly because any position measurement errors are greatly magnified in the acceleration calculation.)

计算出的加速度值只有在你有位置数据的情况下才有意义。将鼠标移到你位置数据以下的第一个加速度值上，按住鼠标按钮不放。将鼠标向下拖动到数字列的底部，然后释放鼠标按钮以选中这些数值。从编辑菜单中选择'空白'，以清除这些值。然后下面的计算应显示平均加速度（单位为cm/s²）。（如果你想的话，可以绘制这些加速度值，但它们通常波动很大，因为任何位置测量误差在加速度计算中都会被大大放大。）

Graphs of position and velocity represent one good way to analyze motion, and the analysis of straight line, constant acceleration motion such as freefall provides an instructive example.

位置和速度的图象是分析运动的一个良好方法，而直线匀加速运动（如自由落体）的分析提供了一个有教育意义的例子。

Uniformly Accelerated Motion

The Freely Falling Object