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0.82 | A cubic inch is a measure of volume that is equal to that of a cube measuring 1 inch (2.5 cm) on each side. An object's volume in cubic inches is, thus, the same as that of a certain number of these hypothetical cubes. There are a number of ways to calculate an object's volume in cubic inches, but in the simplest cases, as with 3-dimensional rectangular prisms (boxes), the volume is simply
**length × width × depth** when all measurements are in inches. | 立方英寸是体积单位，1立方英寸（约为16.387立方厘米）就是一个边长为1英寸（2.54厘米）的立方体的体积。所以，一个立体图形的体积数就是它所能分成的立方体的个数。计算一个物体的体积有很多方法，但是对于最基础的长方体来说，它的体积公式就是长× 宽× 高，本文中所有单位都为英寸。 |
0.804 | - If you know (and are wiling to admit) your math isn't that great, check your answer using a calculator or another person. Just make sure you get a person who knows what they're doing and that you push the right buttons. Thanks Helpful 0 Not Helpful 1
- Cubic inches measure volume, how much "stuff" fits inside something. Thanks Helpful 0 Not Helpful 0
- Make sure to use a ruler or tape measure for measuring accuracy, especially if you're doing something important, like engineering something. Thanks Helpful 0 Not Helpful 0 | - 如果你觉得自己的计算能力不好，你可以用计算器算一遍，或者让别人算一下。不过，要确保你找到人数学很好，或者使用计算器时按键正确。
- 立方英寸是体积单位，描述了一个物体中能“填充”多少东西。
- 为了测量准确，一定要使用直尺或者卷尺，特别是要求计算准确的情况下，比如工程中。 |
0.815 | - For ship displacement, you can carry this process further to figure out how low the ship has to sit in the water. The ship will sit sufficiently low in the water such that the weight of water displaced by the volume of the ship that has pushed down into the water equals the weight of the ship. | - 对于船只的排水量，你可以进一步弄清楚船在水中能下沉到多低。当船只沉得足够低时，船体体积排出的水的质量与船只的重量相等。 |
0.893 | How to Calculate Force: 6 Steps (with Pictures) | 如何计算力: 6 步骤（包含图片） |
0.948 | 4 Ways to Calculate Frequency | 4种方法来计算频率 |
0.891 | Frequency, also called wave frequency, is a measurement of the total number of vibrations or oscillations made within a certain amount of time. There are a few different ways to calculate frequency based on the information you have available to you. Keep reading to learn some of the most common and useful versions. | 频率，又称为波频，是单位时间内震动或震荡的次数。根据已知信息的不同，计算频率的方法也不同。阅读本文，学习几种常见而且有用的频率计算方法吧。 |
0.814 | Frequency from Time or Period | 通过时间或周期求频率 |
0.88 | Learn the formula.
Frequency and the time taken to finish a single wave oscillation are inversely proportional. As such, the formula for calculating frequency when given the time taken to complete a wave cycle is written as: **f = 1 / T**
- In this formula,
*f* represents frequency and *T* represents the time period or amount of time required to complete a single wave oscillation.
- Example A: The time for a certain wave to complete a single oscillation is 0.32 seconds. What is the frequency of this wave?
- Example B: In 0.57 seconds, a certain wave can complete 15 oscillations. What is the frequency of this wave? | 公式。频率和完成一次振动所需的时间互为倒数。所以，已知完成一次振动需要的时间，求频率所用的公式：f = 1 / T 公式中，f代表频率，T代表周期或完成一次振动所需的时间。 例A：一道波完成一次振动需要0.
32秒，求波的频率。 例B：在0.57秒内，一道波振动15次，求波的频率。 |
0.871 | Divide the number of oscillations by the time period.
Usually, you will be told how long it takes to complete a single oscillation, in which case, you would just divide the number **1** by the time period,**T**. If given a time period for numerous oscillations, however, you will need to divide the number of oscillations by the overall time period required to complete them.
- Example A: f = 1 / T = 1 / 0.32 = 3.125
- Example B: f = 1 / T = 15 / 0.57 = 26.316 | 用振动数除以时间。通常，题目中会告诉你完成一次振动需要的时间，你只需要用1除以时间T就可以了。如果已知完成多次振动需要的时间，那么你需要用对应的次数除以时间。 例A：f = 1 / T = 1 / 0.
32 = 3.125 例B： f = 1 / T = 15 / 0.57 = 26.316 |
0.869 | Write your answer.
This calculation should tell you the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency. Example A: The frequency of this wave is 3.125 Hz. Example B: The frequency of this wave is 26.316 Hz. | 写出答案。完成上一步之后，就得到了波的频率。不要忘了加上频率的单位，Hz。 例A：波的频率是3.
125 Hz。 例B：波的频率是26.316 Hz。 |
0.809 | Learn the formula.
When told the angular frequency of a wave but not the standard frequency of that same wave, the formula to calculate the standard frequency is written as: **f = ω / (2π)**
- In this formula,
*f* represents the frequency of the wave and *ω* represents the angular frequency. As with any mathematical problem, *π* stands for pi, a mathematical constant.
- Example: A particular wave rotates with an angular frequency of 7.17 radians per second. What is the frequency of that wave? | 公式。已知波的角频率，求波的频率的公式是：f = ω / (2π) 公式中，f代表频率，ω代表角频率。在数学中，π都是一个常数。 例：一道波以每秒7.
17度的角频率振动，求波的频率。 |
0.829 | Multiply pi by two.
In order to find the denominator of the equation, you need to double the value of pi, 3.14. Example: 2 * π = 2 * 3.14 = 6.28 | 用π乘以2。公式的分母，是π的两倍。 例：2 * π = 2 * 3.
14 = 6.28 |
0.907 | Divide the angular frequency by the double of pi.
Divide the angular frequency of the wave, given in radians per second, by 6.28, the doubled value of pi.Example: f = ω / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14 | 用角频率除以π的两倍。用波的角频率，除以6.
28，即π值的两倍。 例：f = ω / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14 |
0.84 | Write your answer.
This final bit of calculation should indicate what the frequency of the wave is. Write your answer in Hertz, Hz, the unit for frequency. Example: The frequency of this wave is 1.14 Hz. | 写出答案。完成上一步之后，就得到了波的频率。不要忘了加上频率的单位，Hz。 例：波的频率是1.
14 Hz。 |
0.876 | 4 Ways to Calculate GPA | 3种方法来计算GPA |
0.855 | - Universities often provide special tests for those who cannot calculate a GPA of any currency due to length of time between high school and college admittance. Inquire at you college of interest for more details. Thanks Helpful 5 Not Helpful 0
- Note that although most schools will only calculate out to 1 decimal point, others may calculate to 2 decimal points. With 2 decimal points, an A- is 3.67, a B+ 3.33; with 1 decimal point an A- is 3.7, a B+ 3.3. Ask your school if you are unsure which way they calculate the grades.
- Many colleges and universities offer online GPA calculating tools, which calculate your GPA for you after you plug in grades, credit hours, and other additional information. Thanks Helpful 3 Not Helpful 2 | - 对于因高中和大学入学的时间间隔而无法通过通用的计分方式计算GPA的学生，很多大学都会为他们提供特别的测试。请向你的学校咨询详情。
- 很多美国的高中学校对荣誉或先修(AP)课程给予额外的学分。在这类系统中，为A到C-之间的成绩加1分，但不对D或F加分。
- 某些大学也会考虑学期GPA（SGPA）和累积GPA（CGPA）。
- 某些学校将按学分比例给定成绩。.
- 注意，某些学校会将计算结果保留2位小数，另一些学校则只保留1位小数。对于2位小数的计分制度，则A-为3.67，B+为3.33; 对于1位小数的计分制度，则A-为3.7，B+为3.3。如果你不清楚你的学校采用哪种制度，请尝试使用两种方法进行计算并看看它们的差别。 |
0.921 | The half-life of a substance undergoing decay is the time it takes for the amount of the substance to decrease by half. It was originally used to describe the decay of radioactive elements like uranium or plutonium, but it can be used for any substance which undergoes decay along a set, or exponential, rate. You can calculate the half-life of any substance, given the rate of decay, which is the initial quantity of the substance and the quantity remaining after a measured period of time. | 物质的半衰期是物质的量减少一半所花费的时间。它最初是用来描述放射性元素如铀或钚的衰减，但它可以被用于任何发生衰减的物质，衰减指数或汇率。下面是如何计算任何物质的半衰期，给定的衰减率，这是初始的物质的量和一段时间后测得的剩余数量。 |
0.819 | How to Calculate Horsepower: 12 Steps (with Pictures) | 如何计算马力: 12 步骤 |
0.93 | Horsepower is a unit of measurement that calculates power. It was originally coined by a Scottish engineer to compare the power of steam engines with the power of horses. This article will show you how to calculate the horsepower of your cars engine, an electric motor, and your own body. | 马力是一种功率计量单位。它最初是由一位苏格兰工程师所提出，用来比较蒸汽机功率与马的力量。本文将向你介绍如何计算汽车发动机、电动机甚至你自己的马力。 |
0.84 | Calculating Your Own Horsepower | 计算你自己的马力 |
0.824 | Weigh yourself.
Find out how much you weigh in pounds. Write your weight down. If your scale uses kilograms, multiply this number by 2.2 to find your weight in pounds. | 测量体重。称一称自己的体重有多少磅。记下自己的体重。如果是以公斤为单位，那么把公斤数乘以2.
2就能换算成有多少磅。
找一段没有障碍物的楼梯。你得戴着秒表跑上这些楼梯，所以得找一段不常使用的楼梯。 |
0.825 | How to Calculate Impedance: 10 Steps (with Pictures) | 如何计算阻抗: 10 步骤 |
0.902 | Impedance is the opposition of a circuit to alternating current. It's measured in ohms. To calculate impedance, you must know the value of all resistors and the impedance of all inductors and capacitors, which offer varying amounts of opposition to the current depending on how the current is changing in strength, speed, and direction. You can calculate impedance using a simple mathematical formula. | 阻抗是电路对交流电的阻力。它的单位是欧姆。为了计算阻抗，你必须知道所有电阻的值以及所有电感和电容的阻抗，这些电阻和阻抗会根据电流在强度、速度和方向上的变化，产生不同大小的电流阻力。你可以用一个简单的数学公式来计算阻抗。 |
0.877 | Calculating Total Impedance | 计算总阻抗 |
0.911 | Add resistances in the same circuit.
Total impedance is simple if the circuit has several resistors, but no inductors or capacitors. First, measure the resistance across each resistor (or any component with resistance), or refer to the circuit diagram for the labeled resistance in ohms (Ω). Combine these according to how the components are connected:
- Resistors in series (connected end to end along one wire) can be added together. The total resistance R = R
1 + R 2 + R 3...
- Resistors in parallel (each on a different wire that connects to the same circuit) are added as their reciprocals. To find the total resistance R, solve the equation
R = R + 1 R + 2 R ... 3 | 将同一电路的电阻相加。如果电路有几个电阻，但是没有电感或电容，那么总阻抗的计算就非常简单。首先，测量每个电阻或每个含有电阻的元件的阻值，或者查阅电路图中以欧姆（Ω）为单位的标记电阻。根据电阻的连接方式计算总阻值： 串联，或者说在一根电线中首尾相连的电阻，总阻值等于各电阻阻值之和。总电阻值R = R1 + R2 + R3.
.. 并联，或者说连接在同一电路不同导线上的电阻，总阻值等于各电阻阻值倒数之和的倒数。要计算总阻值R，必须解方程R = R1 + R2 + R3 ... |
0.894 | - To find acceleration (the change in velocity over time), use the method in part one to get a derivative equation for your displacement function. Then, take another derivative, this time of your derivative equation. This will give you an equation for finding acceleration at a given time - all you have to do is plug in your value for time.
- The equation which relates Y (displacement) to X (time) might be really simple, like, for instance, Y= 6x + 3. In this case the slope is constant and it is not necessary to find a derivative to find the slope, which is, following the Y = mx + b basic model for linear graphs, 6.
- Displacement is like distance but it has a set direction, this makes displacement a vector and speed a scalar. Displacement can be negative while distance will only be positive. Thanks Helpful 29 Not Helpful 16 | - 位移类似距离，但是有一定方向，因此位移是矢量，速率是标量。当往反方向运动的时候，位移可以是负的。
- Y (位移)和 X (时间)的函数关系，可以很简单，如 Y= 6x + 3 ，这样斜率就是固定的，就不用求导了。 以Y = mx + b 的格式求导得到斜率为 6。
- 要找出加速度（速度随着时间的变化量），用方法一找出斜率式，即速度，然后对斜率式再求导，得到加速度和时间的关系式。代入时间即可求得加速度。 |
0.809 | How to Calculate Kinetic Energy: 9 Steps (with Pictures) | 如何计算动能: 5 步骤（包含图片） |
0.845 | Know the formula for calculating kinetic energy.
The formula for calculating kinetic energy (KE) is *KE = 0.5 x mv*. Here *m* stands for mass, the measure of how much matter is in an object, and *v* stands for the velocity of the object, or the rate at which the object changes its position.
- Your answer should always be stated in joules (J), which is the standard unit of measurement for kinetic energy. It is equivalent to 1 kg * m | 动能公式。动能（KE）的计算公式： KE = 0.
5 * mv 。m表示质量，即物体含有物质的量。v代表速度，即物体改变位置的快慢。 答案用焦耳表示。焦耳是动能的标准单位，1焦耳相当于 1 kg * (m/s) |
0.883 | A margin is a percentage based on sales and production that can be used to assess several aspects of business profitability. You can find out how to calculate the gross profit margin for your business using the method below. | 利润率是个基于销售量和产量的百分比，可以用来评估商业盈利的方方面面。你可以通过以下方法，找出如何计算总利润率的方法。 |
0.807 | 5 Ways to Calculate Mean, Standard Deviation, and Standard Error | 4种方法来计算均值、标准差和标准误差 |
0.911 | After collecting data, oftentimes the first thing you need to do is analyze it. This usually entails finding the mean, the standard deviation, and the standard error of the data. This article will show you how it's done. | 收集数据后，你要做的第一件事往往就是对它进行分析。这通常都免不了要计算均值、标准差和标准误差。本文将向你展示如何计算。 |
0.905 | - Calculations of the mean, standard deviation, and standard error are most useful for analysis of normally distributed data. One standard deviation about the central tendency covers approximately 68 percent of the data, 2 standard deviation 95 percent of the data, and 3 standard deviation 99.7 percent of the data. The standard error gets smaller (narrower spread) as the sample size increases.
- An easy to use online standard deviation calculator Thanks Helpful 0 Not Helpful 0 | - 均值、标准差和标准误差的计算对于分析正态分布的数据最有用。距离中心位置1个标准差的范围覆盖了约68%的数据，距离其2个标准差的范围覆盖了95%的数据，而3个标准差能覆盖99.7%的数据。随着样本大小的增加，标准误差会变小（分布范围变窄）。
- 易用在线标准差计算器 |
0.941 | Calculate the standard deviation.
This represents the spread of the population.
Standard deviation = σ = sq rt [(Σ((X-μ)^2))/(N)].
- For the example given, the standard deviation is sqrt[((12-62)^2 + (55-62)^2 + (74-62)^2 + (79-62)^2 + (90-62)^2)/(5)] = 27.4. (Note that if this was the sample standard deviation, you would divide by n-1, the sample size minus 1.) | 计算标准差。它表征总体的分布情况。 标准差 = σ = sqrt [(Σ((X-μ)^2))/(N)].
对以上给出的例子，标准差是 sqrt[((12-62)^2 + (55-62)^2 + (74-62)^2 + (79-62)^2 + (90-62)^2)/(5)] = 27.4。（注意，如果要求样本的标准差，则应除以n-1，即样本大小减1。 |
0.868 | The Standard Error of the Mean | 均值的标准误差 |
0.936 | Calculate the standard error (of the mean).
This represents how well the sample mean approximates the population mean. The larger the sample, the smaller the standard error, and the closer the sample mean approximates the population mean. Do this by dividing the standard deviation by the square root of N, the sample size.
Standard error = σ/sqrt(n)
- So for the example above, if this were a sampling of 5 students from a class of 50 and the 50 students had a standard deviation of 17 (σ = 21), the standard error = 17/sqrt(5) = 7.6. | 计算（均值的）标准误差。它表征的是样本均值与总体均值的近似度。样本越大，标准误差就越小，样本均值与总体均值也就越接近。将标准差除以样本大小N的平方根即可得出标准误差。标准误差 = σ/sqrt(n) 就以上的例子而言，如果从一个有50名学生的班级中抽取5个学生做样本，而50名学生的标准差为17 (σ = 21)，则标准误差即为 17/sqrt(5) = 7.
6。 |
0.894 | How to Calculate Mean Deviation About Mean (for Ungrouped Data) | 如何计算平均值的平均偏差（对于未分组的数据） |
0.926 | In working with data, there are several different ways to measure how closely grouped your data values are. The most common is the mean. Most people learn early in school to calculate the mean by finding the sum of a group of data values and then dividing by the number of values in the set. A more advanced calculation is the mean deviation about the mean. This calculation tells you how close to the mean your values are. Finding this consists of finding the mean for a data set, finding the difference of each data point from that mean, and then taking the mean of those differences. | 在处理数据时，有几种不同的方法可以衡量数据值分组的紧密程度，其中最常见的就是平均值。大多数人在学校里很早就学会了用一组数据值的和除以个数来计算平均值。一种更高级的计算方法是关于平均值的平均偏差。这个计算结果可以让你知道值有多接近平均值。计算平均偏差包括求出一个数据集的平均值，算出每个数据点与平均值的差值，然后再取这些差值的平均值。 |
0.82 | How to Calculate Molar Absorptivity: 8 Steps (with Pictures) | 如何计算摩尔吸光系数: 8 步骤 |
0.906 | Molar absorptivity, also known as the molar extinction coefficient, is a measure of how well a chemical species absorbs a given wavelength of light. It allows you to make comparisons about the probability of electrons transition between levels for different compounds without taking into account differences in concentration or solution length during measurements. | 摩尔吸光系数也被称为摩尔消光系数，是用来衡量化学物质吸收特定波长光线的能力的一个指标。使用摩尔吸光系数，你可以在不考虑测量过程中浓度或溶液长度差异的情况下，比较电子在不同化合物的能级间发生跃迁的概率。 |
0.839 | - While most relative atomic masses are known to a precision of 1 part in 10 thousand (4 decimal places), in most laboratory work, molar masses are normally quoted to 2 decimal places and fewer for particularly large masses. Thus, in the laboratory, the molar mass for hydrogen chloride would be given as 36.46 grams per mole and that of glucose as 180.14 grams per mole. | - 尽管大多数已知的相对原子质量都可以精确到万分之一克（小数点后四位），但在大多数实验室工作中，摩尔质量一般精确到小数点后两位即可。如果质量非常大还会精确到更高的位数。所以，在实验室中，氯化氢的摩尔质量写作36.46g/mol，葡萄糖为180.14g/mol。 |
0.807 | Find the relative atomic mass of each element in the compound.
Using the periodic table, locate the relative atomic mass for each element. It is the number located beneath the symbol for the element.
- The relative atomic masses of the elements in hydrochloric acid are: hydrogen, 1.007 g/mol and chlorine, 35.453 g/mol.
- The relative atomic masses of the elements in glucose are: carbon, 12.0107 g/mol; hydrogen, 1.007 g/mol; and oxygen, 15.9994 g/mol. | 计算化合物中各元素的摩尔质量。用元素的原子质量乘以化合物中元素原子的数量，可以求出这个化合物中每个元素的相对含量。 在氯化氢（HCl）中，每摩尔氢元素的质量是1.
007克，而每摩尔氯元素的质量是35.453克。 在葡萄糖（C6H12O6）中，每种元素的摩尔质量如下：碳，12.0107 x 6 = 72.0642 g/mol；氢，1.007 x 12 = 12.084 g/mol；氧，15.9994 x 6 = 95.9964 g/mol。 |
0.885 | How to Calculate P Value: 7 Steps (with Pictures) | 如何计算P值: 4 步骤（包含图片） |
0.825 | - A scientific calculator will make the computation far easier. You can also find calculators online. Thanks Helpful 75 Not Helpful 42
- You can calculate p-value using several computer programs, including commonly-used spreadsheet software, and more specialized statistical software. Thanks Helpful 64 Not Helpful 41 | - 用个科学计算器可以让计算过程快得多。在网上也可以找到计算器。
- 可以用各种软件计算P值。包括一般使用的制表软件或更专业的统计软件等等。 |
1 | ||
0.871 | In mathematics, the concept of percent change is used to describe the relationship between an old value and new value. Specifically, the percent change expresses the difference between the old and new values as a percentage of the old value. Use the equation
**((**, in which *V* - 2 *V*) / 1 *V*) × 100 1 *V* represents an old or initial value and 1 *V* represents the new or current value. If the number is positive, it indicates a percent increase and if it’s negative, it indicates a percent decrease. You can also use a modified formula to determine percent decrease rather than working with negative numbers.
2 | 在数学中，百分比变化是用来描述旧的数值或数量与新的数值或数量之间关系的概念。百分比变化值专门用来将新值与旧值之间的差值表述成旧值百分比的形式。通常来说， V1代表旧值或初始值，V2代表新值或现值。通过等式((V2-V1)/V1) × 100表示百分比变化。注意这里的数量被表述成百分比的形式。从下面的第一步开始了解这一过程的分解步骤。 |
0.814 | How to Calculate Percent Yield in Chemistry: 15 Steps | 如何计算化学中的产率: 9 步骤 |
0.858 | In chemistry, the
**theoretical yield** is the maximum amount of product a chemical reaction could create based on chemical equations. In reality, most reactions are not perfectly efficient. If you perform the experiment, you'll end up with a smaller amount, the **actual yield**. To express the efficiency of a reaction, you can calculate the **percent yield** using this formula: *%yield = (actual yield/theoretical yield) x 100*. A percent yield of 90% means the reaction was 90% efficient, and 10% of the materials were wasted (they failed to react, or their products were not captured). | 在化学中，反应产量是指通过化学反应所产出的产品的数额。理论产量是指在完美平衡的反应中所能产出的最大的产品量，但实际产量往往会低于理论产量。为体现反应效率，可以使用下面的公式来计算产率：%产率=（实际产量/理论产量）x 100。 |
0.876 | 5 Ways to Calculate Pi | 5种方法来计算圆周率 Pi |
0.807 | - Calculating pi can be fun and challenging, but doing so too deeply has diminishing returns. Astrophysicists say they only need to use pi to 39 decimal places in order to do cosmological calculations that are accurate to the size of an atom. Thanks Helpful 1 Not Helpful 0 | - 计算 Pi 的值是一个有趣的难题，但如投入太多时间精力进去则得不偿失。天文物理学家表示，为了进行原子大小的天文物理学计算，他们只需使用带有 39 位小数的圆周率 Pi 值即可。 |
0.837 | Calculating Pi Using an Infinite Series | 使用无穷级数来计算 Pi值 |
0.862 | Use the Gregory-Leibniz series.
Mathematicians have found several different mathematical series that, if carried out infinitely, will accurately calculate pi to a great number of decimal places. Some of these are so complex they require supercomputers to process them. One of the simplest, however, is the Gregory-Leibniz series.
- **π=(4/1)-(4/3)+(4/5)-(4/7)+(4/9)-(4/11)+(4/13)-(4/15) ⋯**
- Take 4 and subtract 4 divided by 3. Then add 4 divided by 5. Then subtract 4 divided by 7. Continue alternating between adding and subtracting fractions with a numerator of 4 and a denominator of each subsequent odd number. The more times you do this, the closer you will get to pi. | 使用格雷戈里 - 莱布尼茨无穷级数。
数学家们发现了若干个数学级数，如果实施无穷多次运算，就能精确计算出 Pi 小数点后面的多位数字。其中部分无穷级数非常复杂，需要超级计算机才能运算处理。但是有一个最简单的无穷级数，即格雷戈里-莱布尼茨级数。尽管计算较费时间，但每一次迭代的结果都会更接近 Pi 的精确值，迭代 500,000 次后可准确计算出 Pi 的 10 位小数。
- **π = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...**
- 首先用 4 减去 4 除以 3，然后加上4除以5，然后减去4除以7。反复变换使用加减法，后面的小数是用4作分子，用连续的奇数作分母。计算的次数越多，则结果越接近 Pi。 |
0.893 | Try the Nilakantha series.
This is another infinite series to calculate pi that is fairly easy to understand. While somewhat more complicated, it converges on pi much quicker than the Leibniz formula.
- **π=3+4/(2·3·4)-4/(4·5·6)+4/(6·7·8)-4/(8·9·10)+4/(10·11·12)-4/(12·13·14) ⋯**
- For this formula, take three and start alternating between adding and subtracting fractions with numerators of 4 and denominators that are the product of three consecutive integers which increase with every new iteration. Each subsequent fraction begins its set of integers with the highest one used in the previous fraction. Carry this out even a few times and the results get fairly close to pi. | 使用 Nilakantha 级数。
这是可用于计算 Pi 的另一个无穷级数，非常容易理解。尽管结构较复杂，但它的计算机结果可比莱布尼茨公式更快地接近 Pi。
- **π = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11*12) - (4/(12*13*14) ...**
- 在该公式中，从 3 开始，依次交递加减以 4 为分子、三个连续整数乘积为分母的分数，每次迭代时三个连续整数中的最小整数是上次迭代时三个整数中的最大整数。反复计算几次，结果与 Pi 非常接近。 |
0.864 | Try this experiment to calculate pi by throwing hotdogs.
Pi, it turns out, also has a place in an interesting thought experiment called Buffon's Needle Problem,elongated objects will land either between or crossing a series of parallel lines on the floor. It turns out that if the distance between the lines is the same as the length of the tossed objects, the number of times the objects land across the lines out of a large number of throws can be used to calculate pi. Check out the above wikiHow article link for a fun breakdown of this experiment using thrown food.
- Scientists and mathematicians have not figured out a way to calculate pi exactly, since they have not been able to find a material so thin that it will work to find exact calculations. | 以扔香肠的方式，通过做实验来计算 Pi。
Pi 在一个名为“蒲丰投针问题”的思维实验中也占有一席之地。该实验旨在计算出一组随机抛掷的相同长条物体落在地面一系列平行线之间和落在平行线之上的概率。实验表明，如果平行线之间的距离与抛掷物体的长度相等，则在多次抛扔时物体落在平行线之上的次数除以试验次数可用于计算 Pi 的值。要了解如何用抛掷食物的方法进行该趣味实验的详细信息，请查阅相关 WikiHow 文章。
- 科学家和数学家并未想出一种精确计算Pi值的方法，因为他们没办法找到一种足够细的东西来满足精确计算所需。 |
0.859 | How to Calculate Population Density: 10 Steps (with Pictures) | 如何计算人口密度: 10 步骤 |
0.916 | Population density tells you how crowded an area is, on average. It can help you figure out the resources that a certain area requires, and it can help you compare areas. You'll need to gather data about the area and population size, then plug the numbers into the population density formula:
**Population Density = Number of People / Land Area**. | 人口密度表示一个地区的人口平均拥挤程度。它有助于你了解某个特定地区所需的资源，并对不同的地区加以比较。你需要收集有关面积和人口规模的数据，然后把这些数字代入人口密度公式：人口密度=人口数量/土地面积。 |
0.845 | - Compare the data you found to other reports on population density. If the population density you found differs from the data listed, investigate possible errors or trends in population density over time. Thanks Helpful 2 Not Helpful 0
- Use the same formula to figure out the population density of animals, such as livestock. Thanks Helpful 1 Not Helpful 1 | - 将找到的数据和其他人口密度报告进行对比。如果你发现的人口密度与列出的数据不同，研究人口密度随着时间的推移可能出现的错误或趋势。
- 用同样的公式计算出动物（如家畜）的种群密度。 |
0.824 | 4 Ways to Calculate Probability | 3种方法来计算概率 |
0.922 | Chances are (pun intended) you've encountered probability by now, but what exactly is probability, and how do you calculate it? Probability is the likelihood of a specific event happening, like winning the lottery or rolling a 6 on a die. Finding probability is easy using the probability formula (the number of favorable outcomes divided by the total number of outcomes). In this article, we'll walk you through exactly how to use the probability formula step by step, plus show you some examples of the probability formula in action. | 可能你经常听说概率，但究竟什么是概率，该如何计算它呢？概率是指发生某一特定事件的可能性，比如中彩票或用骰子掷出6点。借助公式（有利结果数除以结果总数）就能轻松求出概率。这篇文章将一步步地教你如何正确使用概率公式，同时介绍一些概率公式的实际应用案例。 |
0.929 | - Mathematicians typically use the term “relative probability” to refer to the chances of an event happening. They insert the word "relative" since no outcome is 100% guaranteed. For example, if you flip a coin 100 times, you
**probably**
won't get exactly 50 heads and 50 tails. Relative probability takes this caveat into account.
- You may need to know that that in sports betting and bookmaking, odds are expressed as “odds against,” which means that the odds of an event happening are written first, and the odds of an event not happening come second. Although it can be confusing, it's important to know this if you’re planning to bet on a sporting event.
- The most common ways of writing down probabilities include putting them as fractions, as decimals, as percentages, or on a 1–10 scale. Thanks Helpful 8 Not Helpful 5 | - 你可能得弄清楚，在体育博彩和赌博行业中，发生比会被表述为“赔率”，这意味着事件的发生可能性会写在前面，而不发生的可能性会写在后面。虽然这可能令人感到困惑，但要是你打算参与体育博彩之类的活动，了解这一点很重要。
- 最常见的写法包括把概率写成分数、小数、百分比，或者写成1-10的比例。
- 数学家通常会用“相对概率”一词来表示事件发生的几率。他们之所以要加上“相对”一词，是因为没有任何结果100%保证会出现。比方说，投掷100次硬币，你很可能并不会正好掷出50次正面和50次反面。相对概率就考虑到了这一点。
- 事件的概率必须始终是一个非负数。如果得出的概率是负数，那就是某个环节算错了。 |
0.852 | Consider the effect of prior events when calculating probability for dependent events.
If the occurrence of 1 event alters the probability of a second event occurring, you are measuring the probability of *dependent events.* For example, if you choose 2 cards out of a deck of 52 cards, when you choose the first card, that affects what cards are available when you choose the second card. To calculate the probability for the second of two dependent events, you’ll need to subtract 1 from the possible number of outcomes when calculating the probability of the second event.
- **Example 1**: Consider the event: *Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs?* The likelihood that the first card is a club is 13/52, or 1/4. (There are 13 clubs in every deck of cards.)
- Now, the likelihood that the second card is a club is 12/51, since 1 club will have already been removed. This is because what you do the first time affects the second. If you draw a 3 of clubs and don't put it back, there will be one less club and one less card in the deck (51 instead of 52).
- **Example 2**: *A jar contains 4 blue marbles, 5 red marbles, and 11 white marbles. If 3 marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white?*
- The probability that the first marble is red is 5/20, or 1/4. The probability of the second marble being blue is 4/19, since we have 1 less marble, but not 1 less
*blue* marble. And the probability that the third marble is white is 11/18, because we’ve already chosen 2 marbles. | 把每个独立事件的概率彼此相乘。
无论处理的是独立事件还是相关事件，也无论处理的总共是2个、3个还是10个结果，你都可以通过将各个事件的单独概率彼此相乘来计算出总概率。这样，你就能得到多个事件相继发生的概率。因此，对于上面 *用6个面的骰子连续掷出两次5的概率是多少？*的例子，两个独立事件的概率分别是1/6。那么概率就是1/6 x 1/6 = 1/36。你也可以把它表示为0.027或2.7%。
- **例子1**：从一副扑克牌中随机抽两张牌，而两张都是梅花的概率有多大？ *第一个事件发生的概率是13/52。第二个事件发生的概率是12/51。最后，两张都是梅花的概率为13/52 x 12/51 = 12/204 = 1/17。你也可以把它表示为0.058或5.8%。*
- **例子2**： *一个罐子里有4颗蓝色弹珠、5颗红色弹珠和11颗白色弹珠。如果从罐子里随机抽出3颗弹珠，第一颗弹珠是红色的，第二颗弹珠是蓝色的，第三颗是白色的概率是多少？*第一个事件的概率是5/20。第二个事件的概率是4/19。而第三个事件的概率是11/18。那么总的概率就是5/20 x 4/19 x 11/18 = 44/1368 = 0.032。你也可以把它表示为3.2%。 |
0.902 | How to Calculate Range: 4 Steps (with Pictures) | 如何计算组距: 4 步骤（包含图片） |
0.864 | In statistics,
*range* represents the difference between the highest value of a data set and the lowest value of a data set. The range shows how spread out the values in a series are. If the range is a high number, then the values in the series are spread far apart; if the range is a small number, then the values in the series are close to each other. If you want to know how to calculate range, just follow these steps. | 在统计学中，组距表示一组数据中最大值与最小值之间的差。组距反映的是一系列数值的分散程度。如果组距较大，说明该系列数据的值较分散；如果组距较小，说明该系列数据的各个值比较接近。想知道如何计算组距吗？请按以下步骤操作。 |
0.902 | - The median value of any statistical data set represents the "middle" of the data set in terms of the data distribution, not its range. So although you might be tempted to assume that the median of a given data set is the range divided by 2--or halfway between the extremes of the range--that usually isn't the case. To find the correct median, you must list the data elements in order, then locate the element in the middle of the list. That element is the median. For example, if you have a list of 29 elements, the 15th element will be equidistant from both the top and bottom of the ordered list, so the 15th element is the median, no matter how its value relates to the range.
- You can also interpret "range" in algebraic terms, but first you have to grasp the concept of an algebraic function, or a set of operations on any given number. Since the function's operations can be performed on any number, even an unknown number, that number is represented by a letter variable, usually "x." The domain is the set of all possible input values you can substitute for that unknown number. The range of a function, then, is the set of all possible results you can get after inputting one of the domain values, and performing all the operations defined by the function. Unfortunately, there's no single way to calculate a function's range. Sometimes graphing the function or calculating several values will demonstrate a clear pattern. You can also use your knowledge of the function's domain to eliminate possible output values, or narrow down the data set that indicates the range. | - 一组统计数字的中位数是数组在数据分布意义上的“中间”值，而不是其组距。因此，尽管您可能会假定给定数组的中位数是组距来除以 2（或者说组距中两个极值差距的一半），但通常情况下事实并非如此。要计算正确的中位数，必须按顺序排列所有数字，然后找到处于列表中间位置的那个数字，此即中位数。例如，如果一组数有 29 个数字，则第 15 个元素与有序列表的顶部和底部的距离相等，因此第 15 个元素即中位数，这个数字的值与组距无关。
- “组距”的概念还可以用代数语言来解释，但首先您要掌握代数函数的概念，即对任意给定数字实施的一组运算。由于可以对任意数字（即使是未知数）实施函数所规定的运算，因此用一个字母变量（通常是 X）来表示该数字。变量的定义域是可以用来替代该未知数的所有可能输入值的集合。函数的值域（“组距”），则是将定义域中的数值输入函数，并执行函数规定的所有运算后获得的所有可能结果的集合。遗憾的是，没有单一的方法来计算函数的值域。有时，绘制函数的图像或计算若干个值可以演示较清晰的规律。您还可以利用有关函数定义域的知识来排除可能的结果值，或者缩小值域的数据范围。 |
0.867 | How to Calculate Ratios: 9 Steps (with Pictures) | 如何计算比率: 7 步骤（包含图片） |
0.817 | Ratios are mathematical expressions that compare two or more numbers. They can compare absolute quantities and amounts
*or* can be used to compare portions of a larger whole. Ratios can be calculated and written in several different ways, but the principles guiding the use of ratios are universal to all. | 比率是比较两个或多个数的数学表达式。比率可以比较绝对数量，或者可以被用于比较较大整体中的各部分。比率可以用几种不同的方式书写和计算，但是比率使用的指导原则是统一的。参考下面的步骤1，开始学习怎样计算和表达比率吧。 |
0.901 | Need to know how to calculate series resistance, parallel resistance, and a combined series and parallel network? If you don't want to fry your circuit board, you do! This article will show you how in just a few easy steps. Before reading this, please understand that resistors do not actually have an "inside" and an "outside" to them. The use of "in" and "out" is merely a figure of speech to help novices understand the wiring concepts. | 你是否需要知道如何计算串联电阻、并联电阻和串并混合电路的电阻？如果不想把电路烧了，那你的确需要知道！本文将向你展示如何仅用几个简单的步骤就完成计算。阅读以前要说明，电阻其实并没有“内”、“外”之分，文中提到的“内”和“外”只是一种表述方式，帮助新手理解连接的概念。 |
0.847 | - Remember, when resistors are in parallel, there are many different means to an end, so the total resistance will be smaller than each pathway. When resistors are in series, the current will have to travel through each resistor, so the individual resistors will add to give the total resistance for the series.
- The equivalent resistance (Req) is always smaller than the smallest contributor for a parallel circuit; it is always greater than the greatest contributor for a series circuit. Thanks Helpful 1 Not Helpful 0
- Calculate the resistance using the ohms law or the power law: Thanks Helpful 0 Not Helpful 0 | - 并联电路的等效电阻（Req）总是小于所有并联电阻中最小的；串联电路的等效电阻总是大于所有串联电阻中最大的。
- 记住，当多个电阻并行连接时，有多条通路可导通电流，因此总阻抗小于每条通路的阻抗。而当电阻串联时，电流需要通过每个电阻才能流通，因此单个电阻的加和才是串联总电阻。 |
0.911 | What it is.
Series resistance is simply connecting the "out" side of one resistor to the "in" side of another in a circuit. Each additional resistor placed in a circuit adds to the total resistance of that circuit.
- The formula for calculating a total of
*n* number of resistors wired in series is:
R
eq = R 1 + R 2 + .... R n
That is, all the series resistor values are simply added. For example, consider finding the equivalent resistance in the image below
- In this example,
R
1 = 100 Ω and R 2 = 300Ω are wired in series. R eq = 100 Ω + 300 Ω = 400 Ω | 何为串联电阻。串联电阻就是把一个电阻的“外端”连接到电路中另一个电阻的“内端”。每增加一个电阻，电路的总阻抗都会增加。 以串行方式连接的 n 个电阻的计算公式是：Req = R1 + R2 + .
... Rn 即所有串联电阻阻值相加。举例说明，想想如何计算图中所示电路的等价阻值 在这个例子中， R1 = 100 Ω 和 R2 = 300Ω 相互串联。Req = 100 Ω + 300 Ω = 400 Ω |
0.936 | What it is.
Parallel resistance is when the "in" side of 2 or more resistors are connected, and the "out" side of those resistors are connected.
- The equation for combining
*n* resistors in parallel is:
R
eq = 1/{(1/R 1)+(1/R 2)+(1/R 3)..+(1/R n)}
- Here is an example, given R
1 = 20 Ω, R 2 = 30 Ω, and R 3 = 30 Ω.
- The total equivalent resistance for all 3 resistors in parallel is:
R
eq = 1/{(1/20)+(1/30)+(1/30)}
= 1/{(3/60)+(2/60)+(2/60)}
= 1/(7/60)=60/7 Ω = approximately 8.57 Ω. | 何为并联电阻。
当两个或多个电阻的“内端”彼此相连，“外端”也彼此相连时，即为并联电阻
- 以并行方式连接的
*n* 个电阻的计算公式是：
R
eq = 1/{(1/R 1)+(1/R 2)+(1/R 3)..+(1/R n)}
- 这里举例说明，已知R
1 = 20 Ω，R 2 = 30 Ω且R 3 = 30 Ω。
- 这3个电阻并联后的总阻值相当于：
R
eq = 1/{(1/20)+(1/30)+(1/30)}
= 1/{(3/60)+(2/60)+(2/60)}
= 1/(7/60)=60/7 Ω = 约 8.57 Ω。 |
0.954 | What it is.
A combined network is any combination of series and parallel circuits wired together.
- We see the resistors R
1 and R 2 are connected in series. So their equivalent resistance (let us denote it by R s) is:
R
s = R 1 + R 2 = 100 Ω + 300 Ω = 400 Ω.
- Next, we see the resistors R
3 and R 4 are connected in parallel. So their equivalent resistance (let us denote it by R p1) is:
R
p1 = 1/{(1/20)+(1/20)} = 1/(2/20)= 20/2 = 10 Ω
- Then we see the resistors R
5 and R 6 are also connected in parallel. So their equivalent resistance (let us denote it by R p2) is:
R
p2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω
- So now we have a circuit with the resistors R
s, R p1, R p2 and R 7 connected in series. These can now simply be added to get the equivalent resistance R 7 of the network given to us originally.
R
eq = 400 Ω + 20Ω + 8 Ω = 428 Ω. | 何为串并混合电路。
混合电路就是串联电路和并联电路以任何方式的连接组合。
- 可以看到，电阻R
1和R 2是串联的。因此其等价阻值（我们用R s来表示它）就是：
R
s = R 1 + R 2 = 100 Ω + 300 Ω = 400 Ω。
- 接下来，我们看到电阻R
3和R 4是并行连接的。因此其等价阻值（我们用R p1来表示它）就是：
R
p1 = 1/{(1/20)+(1/20)} = 1/(2/20)= 20/2 = 10 Ω
- 然后，我们看到电阻R
5和R 6也是并联的。因此其等价阻值（我们用R p2来表示它）就是：
R
p2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω
- 那么现在我们就有了一个由电阻R
s、R p1、R p2和R 7串联而成的电路。只需将其相加，即可得到原始电路的等效电阻R 7。
R
eq = 400 Ω + 20Ω + 8 Ω = 428 Ω. |
0.884 | How to Calculate Specific Heat: 6 Steps (with Pictures) | 如何计算比热: 6 步骤（包含图片） |
0.887 | Specific heat is the amount of energy required to raise one gram of a pure substance by one degree Centigrade. The specific heat of a substance is dependent on both its molecular structure and its phase. The discovery of specific heat sparked the studies of thermodynamics, the study of energy conversion involving heat and the work of a system. Specific heat and thermodynamics are used extensively in chemistry, nuclear engineering, and aerodynamics, as well as in everyday life in the radiator and cooling system of a car. If you want to know how to calculate specific heat, just follow these steps. | 比热是一克某纯净物质升高一摄氏度所需要的能量，受物体分子结构和相的影响。比热的重大发现加速了热力学的研究，以及含热能和系统功的能量转化过程的研究。比热和热力学在化学中、核工程中和空气动力学中应用甚广，在日常生活中，如汽车散热器、空调系统中都有应用到。如果想知道如何计算比热，按照下列步骤来做。 |
0.838 | 3 Ways to Calculate Square Meters | 3种方法来计算平方米面积 |
0.919 | - Say "five square meters" instead of "five meters squared." These are technically both correct, but the second one is often misinterpreted to mean the area of a square five meters long and five meters wide (which actually has an area of 25 square meters, or 5 x 5).
- If you're not sure whether you calculated correctly, check that your answer is in the right ballpark with these measurements:
- An American football field is about 5,400 square meters.
- An association football (soccer) field ranges from 4,000 to 11,000 square meters.
- A king-size mattress is about 5 square meters. | - 用“five square meters（5平方米）”来代替“five meters squared”。严格来说，这两个都是正确的，但是第二个经常被误解为一个边长5米的正方形的面积（实际上面积是25平方米，或5×5）。
- 如果你不确定计算是否正确，对照下列测量值，检查结果是否在正确的范围内： 一个美式足球场大约有5400平方米。 一个足球场的面积从4000平方米到11000平方米不等。 一个特大号床垫大约5平方米。 |
0.927 | Converting from Other Units | 从其他单位转换 |
0.89 | Multiply square feet by 0.093.
Measure the length and width in feet and multiply them together to get a result in square feet. Since 1 square foot = 0.093 square meters, multiply your result by 0.093 to get the answer in square meters instead.
- For greater precision, multiply by 0.092903 instead. | 平方英尺乘以0.
093。用英尺来测量长度和宽度，然后把它们相乘得到平方英尺。因为1平方英尺= 0.093平方米，所以把结果乘以0.093就能得到单位为平方米的面积。要想更精确，乘以0.092903。 |
0.912 | Multiply square yards by 0.
84. If you have the measurement in square yards, multiply by 0.84 to get the measurement in square meters.For greater precision, multiply by 0.83613 instead. | 平方码乘以0.
84。如果测量单位是平方码，乘以0.84可以得到平方米。要想更精确，那就乘以0.83613。 |
0.928 | Multiply acres by 4050.
One acre contains about 4050 square meters. If you want to be more precise, multiply by 4046.9 instead. | 英亩乘以4050。一英亩约为4050平方米。如果你想更精确，乘以4046.
9。 |
0.801 | Convert
** square miles to square kilometers instead.
** One square mile is much, much larger than a square meter, so typically it is converted into square kilometers instead. Multiply the square miles by 2.6 to find the area in square kilometers instead. (Or multiply by 2.59 instead to be more precise.)
- If you really want to convert to square meters, 1 square kilometer = 1,000,000 square meters. | 将平方英里转换为平方公里。一平方英里比一平方米要大得多，所以通常它会转化为平方公里。用平方英里乘以2.
6得到平方公里（或者乘以2.59更为精确）。如果你真的想换算成平方米，1平方公里= 1,000,000平方米。
把平方米转换成面积单位，而不是长度单位。平方米是测量面积或二维表面的单位。把它们与测量长度，或单向距离的单位进行比较没有任何意义。你可以在“平方米”和“平方英尺”之间转换，但不能在“平方米”和“英尺”之间转换。 不要使用本部分中的计算方法在长度单位之间进行转换。长度单位的转换需要使用 不同的数字。 |
0.866 | In physics, tension is the force exerted by a rope, string, cable, or similar object on one or more objects. Anything pulled, hung, supported, or swung from a rope, string, cable, etc. is subject to the force of tension.engineers and architects, who, to build safe buildings, must know whether the tension on a given rope or cable can withstand the strain caused by the weight of the object before yielding and breaking. See Step 1 to learn how to calculate tension in several physical systems. | 物理学中，拉力是由绳子、弦、线缆或类似的物体施加在一个或若干个物体上的力。任何被绳子、弦、线缆等拉拽、悬挂、支撑或挥动的物体，都是拉力的受力方。与其他所有力相同，拉力可以使物体加速或变形。计算拉力不仅对于物理系的学生很重要，也是工程师和建筑师的一项必备技能——为了建造安全的建筑，他们必须清楚绳子或线缆能否承受连接在上面的物体带来的拉力而不变形或损坏。这篇文章可以帮你了解如何计算几个物理系统中的拉力。 |
0.914 | Define the forces
** on either end of the strand.
** The tension in a given strand of string or rope is a result of the forces pulling on the rope from either end. As a reminder,**force = mass × acceleration**. Assuming the rope is stretched tightly, any change in acceleration or mass in objects the rope is supporting will cause a change in tension in the rope. Don't forget the constant acceleration due to gravity - even if a system is at rest, its components are subject to this force. We can think of a tension in a given rope as T = (m × g) + (m × a), where "g" is the acceleration due to gravity of any objects the rope is supporting and "a" is any other acceleration on any objects the rope is supporting.
- For the purposes of most physics problems, we assume
*ideal strings* - in other words, that our rope, cable, etc. is thin, massless, and can't be stretched or broken.
- As an example, let's consider a system where a weight hangs from a wooden beam via a single rope (see picture). Neither the weight nor the rope are moving - the entire system is at rest. Because of this, we know that, for the weight to be held in equilibrium, the tension force must equal the force of gravity on the weight. In other words, Tension (F
t) = Force of gravity (F g) = m × g.
- Assuming a 10 kg weight, then, the tension force is 10 kg × 9.8 m/s
**98 Newtons.** | 定义绳子任意一端的拉力。
一根给定的弦或绳中的拉力是作用在其任意一端的所有力作用的结果。我们给出“力=质量×加速度”这一定律。假设绳子是拉紧的，那么这根绳子所牵引的物体在加速度和质量上的任何改变都会造成绳中拉力的改变。不要忘记恒定的重力加速度：即使对于静止系统，它的每一部分也都会受到重力。我们可以将一根给定的绳子中的拉力表示为T = (m × g) + (m × a)，其中g为重力加速度，a是这根绳子所牵引的物体的其他加速度。
- 在多数物理问题中，我们都假设所用的绳子是理想的，即这些绳子足够细、没有质量，不能被拉伸或损坏。
- 这里举一个例子。我们考虑如图所示的一个物理系统：一个物体通过一根绳子悬挂在一根木梁上。物体和绳子都没有在运动，因此整个系统都是静止的。因此，为了使物体保持平衡，绳中的拉力必须等于物体所受的重力，即拉力F
t = 重力F g = m × g。
- 假设物体质量为10kg，那么拉力为10 kg × 9.8 m/s
**98 N** |
0.896 | Account for acceleration after defining the forces.
Gravity isn't the only force that can affect the tension in a rope - so can any force related to acceleration of an object the rope is attached to. If, for instance, a suspended object is being accelerated by a force on the rope or cable, the acceleration force (mass × acceleration) is added to the tension caused by the weight of the object.
- Let's say that, in our example of the 10 kg weight suspended by a rope, that, instead of being fixed to a wooden beam, the rope is actually being used to pull the weight upwards at an acceleration of 1 m/s
- F
t = F g + m × a
- F
t = 98 + 10 kg × 1 m/s
- F
t = **108 Newtons.** | 考虑加速度。 除重力以外，任何使系在绳上的物体产生加速度的力也都可以影响绳中的拉力。例如，如果一个悬挂着的物体因绳中的拉力而加速，那么除重力之外，这一“加速力”（质量 × 加速度）也应被考虑到拉力的计算中。 仍采用上面的例子，假设绳子不再被固定在木梁上，而是牵引物体以1m/sFt = Fg + m × a = 98 + 10 kg × 1 m/s108 N. |
0.912 | Account for rotational acceleration.
An object being rotated around a central point via a rope (like a pendulum) exerts strain on the rope caused by centripetal force. Centripetal force is the added tension force the rope exerts by "pulling" inward to keep an object moving in its arc and not in a straight line. The faster the object is moving, the greater the centripetal force. Centripetal force (F c) is equal to m × v
- Since the direction and magnitude of centripetal force changes as the object on the rope moves and changes speeds, so does the total tension in the rope, which always pulls parallel to the rope towards the central point. Remember also that the force of gravity is constantly acting on the object in a downward direction. So, if an object is being spun or swung vertically, total tension is
*greatest* at the bottom of the arc (for a pendulum, this is called the equilibrium point) when the object is moving fastest and *least* at the top of the arc when it is moving slowest.
- Let's say in our example problem that our object is no longer accelerating upwards but instead is swinging like a pendulum. We'll say that our rope is 1.5 meters (4.9 ft) long and that our weight is moving at 2 m/s when it passes through the bottom of its swing. If we want to calculate tension at the bottom of the arc when it's highest, we would first recognize that the tension due to gravity at this point is the same as when the weight was held motionless - 98 Newtons.To find the additional centripetal force, we would solve as follows:
- F
c = m × v
- F
c = 10 × 2
- F
c =10 × 2.67 = 26.7 Newtons.
- So, our the total tension would be 98 + 26.7 =
**124.7 Newtons.** | 考虑旋转加速度。
在绳子牵引下绕着圆心运动的物体（如钟摆）因为向心力而对绳子施加一定拉力。向心力是绳子对物体施加的额外的拉力，用于向内“拉”物体，以使物体沿圆弧而不是直线运动。物体运动越快，向心力就越大。向心力的计算公式是F c=mv
- 因为系在绳上的物体运动的同时向心力的大小和方向都在发生变化，所以绳中的拉力也会变化。其方向永远平行于绳指向圆心。同时恒定的竖直向下的重力一直作用在物体上。因此，如果物体在竖直平面内被旋转或摆动，那么绳中的拉力在轨迹的最低点（对于摆，这一点被称为平衡点）最大，此时运动速度也最大；在轨迹的最高点最小，此时运动速度也最小。
- 仍采用上面的例子，假设绳子1.5m长，物体在最低点的速度为2m/s，计算最低点处的拉力（亦即拉力的最大值）。我们注意到此时因重力产生的拉力与物体静止时相同：98N。计算因向心力产生的额外拉力：
- F
c = m × v
- 因此总拉力为98 + 26.7 =
**124.7 N**. |
0.924 | Understand that tension due to gravity changes throughout a swinging object's arc.
As noted above, both the direction and magnitude of centripetal force change as an object swings. However, though the force of gravity remains constant, the *tension resulting from gravity* also changes. When a swinging object *isn't* at the bottom of its arc (its equilibrium point), gravity is pulling directly downward, but tension is pulling up at an angle. Because of this, tension only has to counteract part of the force due to gravity, rather than its entirety.
- Breaking gravitational force up into two vectors can help you visualize this concept. At any given point in the arc of a vertically swinging object, the rope forms an angle "θ" with the line through the equilibrium point and the central point of rotation. As the pendulum swings, gravitational force (m × g) can be broken up into two vectors - mgsin(θ) acting tangent to the arc in the direction of the equilibrium point and mgcos(θ) acting parallel to the tension force in the opposite direction. Tension only has to counter mgcos(θ) - the force pulling against it - not the entire gravitational force (except at the equilibrium point, when these are equal).
- Let's say that when our pendulum forms an angle of 15 degrees with the vertical, it's moving 1.5 m/s. We would find tension by solving as follows:
- Tension due to gravity (T
g) = 98cos(15) = 98(0.96) = 94.08 Newtons
- Centripetal force (F
c) = 10 × 1.5
- Total tension = T
g + F c = 94.08 + 15 = **109.08 Newtons.** | 理解因重力产生的加速度在物体摆动过程中会变化。
前面已经指出，向心力的大小和方向在物体摆动过程中都会变化。尽管物体的重力恒定不变，但因重力产生的拉力则会不断改变。当摆动中的物体不处在轨迹最低点（平衡点）时，重力的方向竖直向下，拉力则沿一定角度向上。因此，拉力只需要抵消掉重力的一部分，而不是全部。
- 将重力分解为两个分量可以帮助我们更直观的理解这一点。在竖直平面内摆动的物体的运动轨迹上的任意一点，设绳与竖直方向（圆心与平衡点连线所在的直线方向）的夹角为θ。物体摆动时，重力mg可以分解为两个分力：沿轨迹切线指向平衡点的mgsin(θ)和沿拉力相反方向的mgcos(θ).拉力只需要抵消与它方向相反的mgcos(θ)部分，而不是整个重力。当然平衡点处除外，此时mgcos(θ)=mg.
- 仍采用上面的例子，假设绳与竖直方向的夹角为15度时物体的速度为1.5m/s，我们计算绳中的拉力：
- 由重力导致的拉力 T
g = 98cos(15) = 98(0.96) = 94.08 N
- 向心力 F
c = 10 × 1.5
- 总拉力 = T
g + F c = 94.08 + 15 = **109.08 N**. |
0.911 | Account for friction.
Any object being pulled by a rope that experiences a "drag" force from friction against another object (or fluid) transfers this force to the tension in the rope. Force from friction between two objects is calculated as it would be in any other situation - via the following equation: Force due to friction (usually written F r) = (mu)N, where mu is the friction coefficient between the two objects and N is the normal force between the two objects, or the force with which they are pressing into each other. Note that static friction - the friction that results when trying to put a stationary object into motion - is different than kinetic friction - the friction that results when trying to keep a moving object in motion.
- Let's say that our 10 kg weight is no longer being swung but is now being dragged horizontally along the ground by our rope. Let's say that the ground has a kinetic friction coefficient of 0.5 and that our weight is moving at a constant velocity but that we want to accelerate it at 1 m/s
- Normal force (N) = 10 kg × 9.8 (acceleration from gravity) = 98 N
- Force from kinetic friction (F
r) = 0.5 × 98 N = 49 Newtons
- Force from acceleration (F
a) = 10 kg × 1 m/s
- Total tension = F
r + F a = 49 + 10 = **59 Newtons.** | 考虑摩擦力。
系在绳上的物体如果受到另一个物体（或流体）的摩擦阻力，则会把这个力“传递”给绳中的拉力。两个物体间摩擦力的计算与其他情况下相同：摩擦力F r = μ × N，其中μ为两个物体间的摩擦系数，N为垂直于两物体接触面的压力。这里需要注意静摩擦力与动摩擦力的区别：前者是外力试图使静止状态的物体运动而物体没有运动时产生的摩擦力，后者是运动中的物体产生的摩擦力。这里的运动指的都是两物体间的相对运动。
- 仍采用上面的例子，假设10kg的物体不再摆动，而是被绳子沿水平方向牵引着在地面上运动，物体与地面之间的动摩擦系数为0.5。物体正在匀速运动，但我们希望它以1m/s
- 物体与地面间的压力N = 10 kg × 9.8 m/s
- 动摩擦力F
r = 0.5 × 98 N = 49 N
- 因加速导致的拉力F
a = 10 kg × 1 m/s
- 总拉力= F
r + F a = 49 + 10 = **59 N**. |
0.803 | Calculating Tensions On Multiple Strands | 多股绳中拉力的计算 |
0.886 | Lift parallel vertical loads using a pulley.
Pulleys are simple machines consisting of a suspended disk that allows the tension force in a rope to change direction. In a simple pulley configuration, the rope or cable runs from a suspended weight up to the pulley, then down to another, creating 2 lengths of rope or cable strands. However, the tension in both sections of rope is equal, even if both ends of the rope are being pulled by forces of different magnitudes. For a system of two masses hanging from a vertical pulley, tension equals 2g(m 1)(m 2)/(m 2+m 1), where "g" is the acceleration of gravity, "m 1" is the mass of object 1, and "m 2" is the mass of object 2.
- Note that, usually, physics problems assume
*ideal pulleys* - massless, frictionless pulleys that can't break, deform, or become separated from the ceiling, rope, etc. that supports them.
- Let's say we have two weights hanging vertically from a pulley in parallel strands. Weight 1 has a mass of 10 kg, while weight 2 has a mass of 5 kg. In this case, we would find tension as follows:
- T = 2g(m
1)(m 2)/(m 2+m 1)
- T = 2(9.8)(10)(5)/(5 + 10)
- T = 19.6(50)/(15)
- T = 980/15
- T =
**65.33 Newtons.**
- Note that, because one weight is heavier than the other, all other things being equal, this system will begin to accelerate, with the 10 kg moving downward and the 5 kg weight moving upward. | 用两股绳平行的滑轮抬升重物。
滑轮是一种简单机械，它用一个悬挂着的轮子来改变绳中拉力的方向。在一个简单的滑轮系统中，系在一个重物m 1上的绳子绕过滑轮系到另一个重物m 2上，这样这个系统中就包含了两股绳子。绳子两部分中的拉力大小是相同的，即使绳子两端所受的拉力大小不同。若该系统处于竖直平面内，则拉力的大小为2g(m 1)(m 2)/(m 1+m 2)，其中g为重力加速度，m 1，m 2分别为两物体的质量。
- 物理问题中，我们通常假设滑轮是理想的：没有质量，光滑，不会变形、损坏或与固定它的天花板和绳子等分离。
- 假设这样的一个滑轮系统中两个重物质量分别为m
1=10kg和m 2=5kg。则绳中拉力为
- T = 2g(m
1)(m 2)/(m 2+m 1) = 2(9.8)(10)(5)/(5 + 10) = **65.33 N**
- 需要注意，由于两个重物质量不同而其他初始条件都相同，这个系统将开始加速运动，10kg的重物向下而5kg的向上。 |
0.884 | Use multiple strands to support a hanging object.
Finally, let's consider an object hanging from a "Y-shaped" system of ropes - two ropes are attached to the ceiling, which meet at a central point from which a weight hangs by a third rope. The tension in the third rope is obvious - it's simply tension resulting from the gravitational force, or m(g). The tensions in the other two ropes are different and must add up to equal the gravitational force in the upward vertical direction and to equal zero in either horizontal direction, assuming the system is at rest. The tension in the ropes is affected both by the mass of the hanging weight and by the angle at which each rope meets the ceiling.
- Let's say in our Y-shaped system that the bottom weight has a mass of 10 kg and that the two upper ropes meet the ceiling at 30 degrees and 60 degrees respectively. If we want to find the tension in each of the upper ropes, we'll need to consider each tension's vertical and horizontal components. Nonetheless, in this example, the two ropes happens to be perpendicular to each other, making it easy for us to calculate according to the definitions of trigonometric functions as follows:
- The ratio between T
1 or T 2 and T = m(g) is equal to the sine of the angle between each supporting rope and the ceiling. For T 1, sin(30) = 0.5, while for T 2, sin(60) = 0.87
- Multiply the tension in the lower rope (T = mg) by the sine of each angle to find T
1 and T 2.
- T
1 = .5 × m(g) = .5 × 10(9.8) = **49 Newtons.**
- T
2 = .87 × m(g) = .87 × 10(9.8) = **85.26 Newtons.** | 用多股绳悬挂物体。
最后，我们考虑被一组“Y”形绳子悬挂着的物体：两根绳子分别有一端被固定在天花板上，另一端连接在一起，从连接点引出第三条绳子悬挂着一个物体。显然，第三条绳子中的拉力是由物体的重力导致的，故该拉力等于mg。另外两根绳子中的拉力通常是不同的，其在竖直方向的合力应竖直向上，大小等于mg，水平方向合力应为0，以使系统保持静止。这两根绳子中的拉力大小既受到物体重量的影响，也与每根绳子与天花板的交角有关。
- 假设Y形绳子系统中悬挂的物体质量为10kg，两根绳子与天花板的交角分别为30度和60度。为了计算两根绳子中的拉力T1和T2，我们需要考虑每根绳子上拉力的竖直和水平分量。但在该例中，由于两根绳子恰好成直角，我们可以直接根据三角函数的定义进行计算。此时T1,T2与T=mg的比值分别等于两根绳子与天花板夹角的正弦(sin)值。因此我们有
- T
1 = 0.5 × m(g) = 0.5 × 10(9,8) = **49 N**
- T
2 = 0.87 × m(g) = 0.87 × 10(9,8) = **85.26 N** |
0.889 | 3 Ways to Calculate Terminal Velocity | 3种方法来计算终极速度 |
0.87 | Ever wonder why skydivers eventually reach a maximum speed when falling, even though the force of gravity in a vacuum will cause an object to continually accelerate? A falling object will reach a constant speed when there is a restraining force, such as drag from the air. The force applied by gravity near to a massive body is mostly constant, but forces like air resistance increase the faster the falling object goes. If allowed to free fall for long enough, a falling object will reach a speed where the force of the drag will become equal the force of gravity, and the two will cancel each other out, causing the object to fall at that same speed until it hits the ground. This is called terminal velocity. | 想知道跳伞运动员何时达到速度极限？即使在真空情况下，重力加速度可以让物体不断加速，如果有阻力（如空气阻力），则会达到一个最大速度值。重力大多情况下是恒定的，而空气阻力这样的力，会随着物体下落速度的加快而加大，最后会达到和重力平衡的状态。两者就会抵消，使得物体匀速下落坠落到地面。而这个最大速度就是终极速度。 |
0.85 | - Without an open parachute, a skydiver would strike the ground at about 130 mph (210 km/h). Thanks Helpful 0 Not Helpful 0
- Terminal velocity will actually change slightly during the free fall. Gravity goes up slightly as the object gets closer to the center of the earth, but the amount is negligible. Density of the medium will rise as the object gets down deeper into the medium. This is a much more noticeable effect. A skydiver will actually slow down as the fall proceeds because the atmosphere gets increasingly thick as altitude drops. | - 终级速度实际上会在自由落体运动中稍稍变动，这是因为随着物体接近地心，重力稍稍加大，不过这个增加量可以忽略。介质密度会随着物体下落而增加，这个变化就比较大了，需要计算进去。跳伞员越靠近地面实际上速度越小，因为随着高度的变低，空气密度会变大。
- 没有降落伞的话，跳伞员会以大约209km/h的速度撞击地面。 |
0.899 | **Use the terminal velocity formula, v = the square root of ((2*m*g)/(ρ*A*C)).
** Plug the following values into that formula to solve for v, terminal velocity.
- m = mass of the falling object
- g = the acceleration due to gravity. On Earth this is approximately 9.8 meters per second squared.
- ρ = the density of the fluid the object is falling through.
- A = the projected area of the object. This means the area of the object if you projected it onto a plane that was perpendicular to the direction the object is moving.
- C = the drag coefficient. This number depends on the shape of the object. The more streamlined the shape, the lower the coefficient. You can look up some approximate drag coefficients | 用终极速度公式：v=根号下((2*m*g)/(ρ*A*C))。将下列量代入，求得v，即终级速度： m = 下降物体质量 g = 重力加速度。地球上大约是9.
8 米每平方秒。 ρ = 物体下降的环境介质的密度。 A = 物体投影面积。表示和下落方向平行的物体在地面的投影。 C = 阻力系数。根据物体形状而不同。越是流线型的物体，系数越低。你可以在这里查查某个物体的阻力系数。 |
0.801 | 5 Ways to Calculate Total Resistance in Circuits | 4种方法来计算电路的总电阻 |
0.883 | There are two ways to hook together electrical components. Series circuits use components connected one after the other, while parallel circuits connect components along parallel branches. The way resistors are hooked up determines how they contribute to the total resistance of the circuit. | 连接电气元件的方式有两种。串联电路将元件一个接一个地连在一起，而并联电路则是沿并联支路连接元件。电阻连接的方式决定了它影响电路电阻值的方式。 |
0.895 | - The power value P used in these formulas refers to instantaneous power, or power at a specific moment in time. If the circuit uses AC power, the power is changing constantly. Electricians calculate the average power for AC circuits using the formula P
average
= VIcosθ, where cosθ is the power factor of the circuit.
- Power is measured in watts (W). Thanks Helpful 1 Not Helpful 0
- Voltage is measured in volts (V). Thanks Helpful 1 Not Helpful 0 | - 功率的单位是瓦特（W）。
- 电压的单位是伏特（V）。
- 电流的单位是安培（A）或毫安（mA）。1 mA = 1 ∗ 10 − 3 {\displaystyle 1*10^{-3}} A = 0.001 A。
- 这些公式中的功率值P指的是瞬时功率，即特定时刻的功率。如果电路使用的是交流电，则功率值会不断改变。电工会使用公式P平均 = VIcosθ来计算交流电路的平均功率，其中cosθ是电路的功率因数。 |
0.833 | Combination Circuit | 混合电路 |
0.888 | Break down your circuit into series sections and parallel sections.
A combination circuit has some components linked together in series (one after the other), and others in parallel (on different branches). Look for areas of your diagram that simplify to a single series or parallel section.
- For example, a circuit has a 1 Ω resistor and a 1.5 Ω resistor connected in series. After the second resistor, the circuit splits into two parallel branches, one with a 5 Ω resistor and the other with a 3 Ω resistor.
Circle the two parallel branches to separate them from the rest of the circuit. | 将电路分解成串联部分和并联部分。在混合电路中，部分元件一个接一个地以串联形式连接，而其他元件在不同的支路中以并联方式连接。找到电路图中的特定部分，将问题简化为单个串联部分或并联部分。圈出各部分来帮助自己跟踪它们。 例如，电路有一个1 Ω的电阻和一个1.
5 Ω的电阻串联，并在第二个电阻后分成两条并联的支路，一个阻值为5 Ω，另一个阻值为3 Ω。将两条并联支路圈出，使之与电路的其余部分分隔开来。 |
0.841 | Find the resistance of each parallel section.
Use the parallel resistance formula 1 R T = 1 R 1 + 1 R 2 + 1 R 3 + . . . 1 R n {\displaystyle {\frac {1}{R_{T}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+{\frac {1}{R_{3}}}+...{\frac {1}{R_{n}}}} to find the total resistance of a single parallel section of the circuit.The example circuit has two branches with resistance R1 = 5 Ω and R2 = 3 Ω. 1 R p a r a l l e l = 1 5 + 1 3 {\displaystyle {\frac {1}{R_{parallel}}}={\frac {1}{5}}+{\frac {1}{3}}} 1 R p a r a l l e l = 3 15 + 5 15 = 3 + 5 15 = 8 15 {\displaystyle {\frac {1}{R_{parallel}}}={\frac {3}{15}}+{\frac {5}{15}}={\frac {3+5}{15}}={\frac {8}{15}}} R p a r a l l e l = 15 8 = 1.875 {\displaystyle R_{parallel}={\frac {15}{8}}=1.875} Ω | 计算各并联部分的电阻。使用并联电阻公式1/RT = 1/R1 + 1/R2 + 1/R3 + .
..1/Rn计算电路单个并联部分的总电阻。 示例电路中有两条支路，阻值分别为R1 = 5 Ω和R2 = 3 Ω，1/Rparallel = 1/5 + 1/31/Rparallel = 3/15 + 5/15 = (3+5)/15 = 8/15Rparallel = 15/8 = 1.875Ω |
0.865 | Simplify your diagram.
Once you've found the total resistance of a parallel section, you can cross out that whole section on your diagram. Treat that area as a single wire with resistance equal to the value you found.
- In the example above, you can ignore the two branches and treat them as one resistor with resistance 1.875Ω. | 简化电路图。算出一个并联部分的总阻值后，你可以在电路图中整个删掉该部分。将该部分当做一根电线，它的阻值等于你之前计算所得的结果。 在以上示例中，你可以忽略两条支路，将之当做一个阻值为1.
875Ω的电阻。 |
0.807 | Add up resistances in series.
Once you've replaced each parallel section with a single resistance, your diagram should be a single loop: a series circuit. The total resistance of a series circuit is equal to the sum of all individual resistances, so just add them up to get your answer.
- The simplified diagram has a 1 Ω resistor, 1.5 Ω resistor, and the section with 1.875 Ω you just calculated. These are all connected in series, so Ω. | 将串联的各电阻阻值相加。将各并联部分替换为单个电阻后，电路图会变成一个只包含串联电路的单一回路。串联电路的总电阻等于所有单个电阻阻值之和，所以只用将它们相加就能得到答案。 简化后的电路图有一个1 Ω的电阻，一个1.
5 Ω的电阻，以及刚刚算出的、阻值为1.875 Ω的部分。它们都是串联连接，所以 R T = 1 + 1.5 + 1.875 = 4.375 {\displaystyle R_{T}=1+1.5+1.875=4.375} Ω。
使用欧姆定律来算出未知值。如果你不知道电路中某个元件的电阻，可以想方设法计算出来。如果知道该元件的电压V和电流I，那么你可以使用欧姆定律来计算它的电阻：R = V / I。 |
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