# Solve Hard Integral: Find v Function

• jaumzaum
In summary: So you should have the speed of the vehicle at that point, and the angle of the vehicle relative to a line that goes from the center of the circle to the point of contact with the circle. That's what I'd think anyway. I think you're getting confused by the \alpha term, and I'm not really sure what that is supposed to refer to.In summary, the conversation is about a physics problem involving determining the velocity function of a car traveling in a loop trajectory with friction. The problem was initially posted in a physics forum, but no one was able to provide a solution. The equation of motion provided by the OP seemed to be incorrect and needed to be corrected in order to solve the problem. The OP is
jaumzaum
I've tried to ask this on the physics section but nobody know how to do it

$a = g(sen\alpha - cos\alpha u) -(\frac{v² u}{R})$
$V = \sqrt{Vo² + \int 2a.ds}$

$\alpha = \frac{s}{R}$

Then, find the function v

What is the question and where is your attempt? I'm new here, but I don't think I'm out of line by saying that this is a "help" community and not a "do" community... If you just want the answer to your problem, plug it into wolfram... If you want some "help", state specifically what you've attempted and where you're stuck...

Cheers!

Ken

Last edited:
jaumzaum said:
I've tried to ask this on the physics section but nobody know how to do it

$a = g(sen\alpha - cos\alpha u) -(\frac{v² u}{R})$
$V = \sqrt{Vo² + \int 2a.ds}$

$\alpha = \frac{s}{R}$

Then, find the function v

I cannot figure out your question. What is $sen\alpha$? Do you mean $\sin \alpha$ or $\sin(\alpha)$? Is $cos\alpha u$ supposed to be $\cos(\alpha u)$, or is it $u \cos \alpha$? I will assume you want to integrate 2a with respect to s, where
$$a = g \displaystyle \sin\left(\frac{s}{R}\right) - g \cos\left(\frac{u s}{R}\right) - \frac{uv^2}{R}.$$
That is an easy, elementary integral of the type you saw in Calculus 101 (assuming, or course, that v and u do not involve s in some unstated way).

RGV

$a = g(sin(\alpha) - cos(\alpha ) u) -(\frac{v² u}{R})$
$V = \sqrt{Vo² + \int 2a.ds}$

$\alpha = \frac{s}{R}$Its a problem to determinate the velocity function of a car that is
describing a loop trajectory with friction
a is momentary acceleration, \alpha is the momentary angle that the
car is in the loop, u is the friction coefficient, v is the momentary
velocity, vo is initial v and s is the distance already traveled, R is
the radius of the loop

What is the question and where is your attempt? I'm new here, but I don't think I'm out of line by saying that this is a "help" community and not a "do" community... If you just want the answer to your problem, plug it into wolfram... If you want some "help", state specifically what you've attempted and where you're stuck...

Cheers!

Ken

I know it's a help community, but in the hole problem, I balked just here, I reay don't now what to do. I have wolfram mathemat ica here and I already tried to solve this integral, but I don't know the function that does that. Besides, it's a problem for trainning in the Ipho, the original problem had no friction, so I solved it easily, but then I tried to solve same problem with "friction" (that btw, I created) and I've gotten in this integral. I don't know actually if this type of integral is needed for the test, but I want to know how to solve it, the problem is that I've never solved a integral that is in function of 3 things. V is in function of a and s, a is in function os v and s

That is an easy, elementary integral of the type you saw in Calculus 101 (assuming, or course, that v and u do not involve s in some unstated way).

I'm sorry, I'm a high school student, I 've not learned integral with teachers, I actually did that by the internet. Brazil don't have teachers that teach this in the secondary school (I hoped it had), but you actually have to learn everything alone, then if you are selected to the IphO, you have some "classes" that is more " question solvng classes" and nobody explain things like solving an integral or other math things, they suppose you already know all those things, they only teach the physics stuff.

Could you tell me at least what to search for?

[]'s
John

jaumzaum said:
I've tried to ask this on the physics section but nobody know how to do it

$$a = g(\sin\alpha - (\cos\alpha)u) -\left(\frac{v^2 u}{R}\right)$$
$$V = \sqrt{Vo^2 + \int 2a.ds}$$

$$\alpha = \frac{s}{R}$$

Then, find the function v
I've edited the above quoted post to make it a bit more readable.

The above looks somewhat different than the original post in the physics section.

Fc=N+g.cos alpha

$$A(\alpha ) = g.\sin\alpha - (v^2/R + g.\cos \alpha)u$$

$$V = \sqrt{Vo^2 + \int a.ds}$$

Last edited by a moderator:
To be honest, and I may have the wrong idea of the problem you're describing, it seems like your equation of motion is wrong. You'll have tangential and radial components for the acceleration. Radial should be more or less what you have, the v2/r term, but tangential should be something like $\frac{dv(\theta)}{dt}$ which must be evaluated using the chain rule.

## 1. How do I know when to use integration by parts?

Integration by parts is typically used when the integral involves a product of two functions, and one of the functions has a known derivative. This method can also be used to simplify integrals that involve trigonometric functions, logarithms, or inverse trigonometric functions.

## 2. What is the first step in solving a hard integral?

The first step in solving a hard integral is to identify what type of integral it is. This can include techniques such as integration by substitution, integration by parts, or using trigonometric identities. Once you have identified the type of integral, you can then use the appropriate method to solve it.

## 3. How do I know if my answer to the integral is correct?

After solving the integral, you can check your answer by differentiating it. If the derivative matches the integrand, then your answer is correct. You can also use online integral calculators or ask for help from a math tutor to verify your answer.

## 4. Can I use a calculator to solve a hard integral?

While a calculator can be helpful for checking your answer, it is not recommended to solely rely on a calculator to solve a hard integral. It is important to understand the underlying concepts and techniques in order to correctly solve the integral.

## 5. Are there any tips for solving hard integrals?

One helpful tip for solving hard integrals is to look for ways to simplify the integral before attempting to solve it. This can include factoring, using trigonometric identities, or using algebraic manipulation. It is also important to practice and familiarize yourself with different types of integrals and their corresponding techniques.

Replies
3
Views
1K
Replies
21
Views
1K
Replies
10
Views
1K
Replies
3
Views
779
Replies
1
Views
851
Replies
22
Views
2K
Replies
3
Views
834
Replies
12
Views
1K
Replies
4
Views
654
Replies
2
Views
1K