In the formula F = ma, when the acceleration a is negative, is f also negative?

In the formula F = ma, when the acceleration a is negative, is f also negative?

In the formula F = ma, when the acceleration a is negative, f is also negative, but the negative sign here means that the direction of resultant force is opposite to that of velocity. We should understand the meaning of the negative sign

Why is the acceleration and the direction of force the same? Newton's second law: F = ma? What is the deeper mechanism behind it?

You need to know how acceleration comes from. Acceleration exists only when an object is subjected to external force, that is, the existing force has acceleration. In other words, the existence of acceleration depends on the existence of force

Why is f = ma in Newton's second law?
High school compulsory one says f = KMA, K is 1, so f = ma. But why k = 1? Why not equal to 2, 3, 4, 5

If the unit of force is n and the unit of acceleration is n / m, it is obvious that k = 1. If the unit of force is not n and the unit of acceleration is n / m, maybe K is not equal to 1. The magnitude of K is determined by the unit of F / MA, and the expression of Newton's second law will not change, always f = KMA

Is the voltage of alternating current power supply 6V the RMS of power supply voltage? Is the withstand voltage of capacitor the RMS or the peak voltage?

The voltage of alternating current power supply is 6V, which means the effective value of power supply voltage. Correct, the withstand voltage value of capacitor is instantaneous value, which should be greater than the peak value of voltage, because the breakdown is only instantaneous

The effective value of the instantaneous voltage is obtained

u=U1sinwt+U2coswt
=U1sinwt+U2sin(wt+1/π)
That is, U2 is 190 degrees ahead of U2
The effective value of the voltage U = √ (U1 ^ 2 + U2 ^ 2) △ 2
Answer: the effective value of the voltage U = √ (U1 ^ 2 + U2 ^ 2) △ 2

Using approximate formula to find the value of base e of natural logarithm
e=1+1!+1/2!+…… +1 / N! Until 1 /! Is less than the - 5th power of 10,

#include
using namespace std;
void main()
{int a;
long s=1;
double e=1.0;
for(a=1;;a++)
{s*=a;
if(1.0/s>1e-5){e+=1.0/s;}else break;}
cout

The source of natural logarithm

Here, e is the symbol of a number, and what we are going to talk about is the story of E. This is a bit curious. If it can be said to be a book, this number should have a great origin, at least it should be very famous. However, after searching, the most important number that most people can think of, except for the well-known 0 and 1, is probably the π related to the circle, In high school mathematics, we all learned the concept of logarithm and used the logarithm table. The logarithm table in the textbook is based on 10, which is called common logarithm The logarithm of base number is called natural logarithm. This e is the protagonist of our story. I wonder if it causes you more doubts? In the decimal system, is it more natural to use such a strange number as the base than to use 10? What's more curious is that such a strange number looks like this, What's the story? I'm afraid all inclusive e-readers have been thinking that calculating interest alone should not be enough to tell a whole book. Of course, no, interest is only a very small part. Surprisingly, this number closely related to calculating compound interest is actually related to many problems in different branches of mathematics, In fact, there are many other possibilities. Although the questions are different, the answers all point to the number E. for example, one of the famous questions is to find the area under the hyperbola y = 1 / X. what's the relationship between hyperbola and calculating compound interest? No matter you look horizontally, vertically, sitting and lying, you can't think of a reason, right? But the area is calculated, But it is closely related to E. I just gave an example, which is mentioned more in this book. It has to be mentioned from ancient times. At least half a century before the invention of calculus, this number was mentioned, so although it often appeared in calculus, it was not born with calculus. So under what circumstances did it appear? A possible explanation is, This number is related to the calculation of interest. We all know what compound interest is, that is, interest can also be added to the principal to regenerate interest. But the sum of principal and interest depends on the interest period. For a year, interest can be calculated only once a year, once every half a year, once a quarter, once a month, or even once a day. Of course, the shorter the interest period is, Some people wonder what will happen if the interest period is shortened indefinitely, such as once a minute, or even every second, or every instant (theoretically). Will the sum of capital and interest increase indefinitely? The answer is no, its value will stabilize and approach a limit, And the number e appears in the limit value (of course, it was not named e at that time). So in today's mathematical language, e can be defined as a limit value, but at that time, there was no concept of limit at all, so the value of e should be observed, not obtained by rigorous proof, Bernoulli's achievements (not only in the field of Mathematics) are as thick as a book. However, there is another thing that this family is good at, It's a fight. If the family doesn't fight enough, they also fight with the people outside (it can be said that it's the same inside and outside). Even when the father and his son won a grand prize together, the father is still very dissatisfied. He thinks it should be his own. He is so angry that he drives his son out of the house, This father should be ashamed. The "influence" of E is not limited to mathematics. In nature, the arrangement of sunflower seeds and the pattern on parrot shell all present the shape of helix, and the equation of helix is defined by e. the construction of scale also uses E. if a chain is fixed at both ends and hung loosely, its shape is expressed by mathematical formula, It's also necessary to use e. it's amazing that these problems, which can't be solved by calculating interest rate or hyperbolic area, are all related to E. in fact, mathematics is not so difficult! Everyone of us has read a lot of mathematics in the process of growing up, but in many people's minds, mathematics seems to be a boring or even terrible subject. Especially in the University of calculus, there are definitions, theorems and formulas everywhere, One of the reasons why we are afraid of a subject is that we have a sense of distance. The things in calculus seem to come out of nowhere, have no sense of it, and have nothing to do with me, What kind of person is the inventor? This sense of distance should be reduced or even disappeared, and calculus will no longer be a "stranger". Try to imagine that for 20 years, people have been doing the same kind of tedious calculations every day. This kind of boring day is not acceptable to ordinary people. But Napier survived, And his hard work was rewarded - logarithm was warmly welcomed by many European and even Chinese scientists. Even Napier was praised from all over the world. Among the first people to use logarithm, including the famous astronomer Kepler, he used logarithm to simplify the complicated calculation of planetary orbits, It's too embarrassing to say that it's a story. In fact, when the author discusses mathematics, he intersperses many interesting related stories. For example, do you know who invented the first logarithmic table? It's John Napier. Haven't you heard of it? This is normal, I didn't know him until I read this book. The important thing is the next question. Do you know how much time Napier spent building the whole logarithm table? Please note that this happened at the end of the 16th century and the beginning of the 17th century. Let alone computers and computers, there are no calculation tools at all. All calculations can only be done slowly one by one with paper and pen, So Napier spent 20 years building his logarithm table. It's incredible!

How to prove that the two definitions of natural logarithm e are equivalent?
The reciprocal of E = 1 + the reciprocal of 2 + +The limit of the reciprocal of n
and
The limit of E = (reciprocal of 1 + x) ^ x
Why are these two forms the same and how to prove them?
There are no high quality textbooks
C (I, x) x ^ (- I) is obviously different from 1 / I

Let me tell you: e = LIM (1 + 1 / N) ^ n --- (n → + ∞) this is the definition of E. let me tell you why e = 1 / 0! + 1 / 1! + 1 / 2! + 1 / 3! +. 1 / N! Let an = (1 + 1 / N) ^ n = 1 ^ n + n * 1 / N + (1 / 2!) * (1-1 / N) + (1 / 3!) * (1-1 / N) (1-2 / N) +... + (1 / N!) *

Why take e as the base of natural logarithm

In exponential function, only e ^ x is the original function after derivation

How to calculate the base e of natural logarithm?

e=1+1+1/2+1/3!+1/4!+…
e=lim(x→∞) (1+ 1/x)^x