All Questions
Tagged with calculus newtonian-mechanics
119
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What is the actual meaning of $dx$ in $W=-F.dx $, in work in thermodynamics?
what I want to ask is that the $dx$ in that formula is the displacement of piston or the displacement of the center of mass of the gas. also is there any situation where this clarity is useful.
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103
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How to Find Trajectory of Particle?
Let’s say I have a particle, and I know all the forces acting on it at every position. (Let’s say the particle is in an electric/gravitational field to simplify the mathematics involved.) Now, is ...
3
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4
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Is is true to say $F(x) = ma(x)$?
Considering the equation $F(t) = ma(t)$, I'm trying to figure out if the following is also always true:
$$F(x(t)) = m\cdot a(x(t))$$
I.e.: $F$ as a function of $X$ (the position, which itself is a ...
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Why is time taken to go around the Sun to cover a small fixed angle proportional to the square of the distance?
I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar ...
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Energy Dissipated by Damper Infinitesimal Derivation
If we consider a damper (dashpot) element that exerts a force opposite the direction of motion proportional to the velocity, i.e. $$ \vec{F} = -c \vec{v}$$
Therefore, we can consider an infinitesimal ...
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Understanding the double integral solution to Newtons second law?
I was following this lecture on Newtons Laws.
https://youtu.be/2tHpgQmnH3A?si=Wbp36oBS_4b1HhIi
At 31:56 in the video, the board has a very general solution to Newton's second law.
However the second ...
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3
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What does it mean in terms of energy if power is increasing with time? [closed]
Recently I have been studying work and energy and in this chapter I encountered with the term power. In terms of work power is written as $dW/dt$. So I have a doubt that suppose power is increasing. ...
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What is $V$ in $a$=$V$$dv$/$dx$? [duplicate]
$a$=instantaneous acceleration
$V$=instantaneous velocity
$x$=position
$dx$=small Chang in position
$a$=$dv$/$dt$
multiplying numerator and denominator by $dx$,we get
$a$=$dv$.$dx$/$dx$.$dt$
now we ...
- 161
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Equilibrium of a body with potential energy as a function of position
We know that if the potential energy of a body, say $U(x)$ of a body is known as a function of its x-coordinate, for equilibrium, $$\frac{dU(x)}{dx} = 0$$ Also, several sources suggest that for the ...
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Can someone help me with differential equation please? [duplicate]
here is the topic of the problem:
You are given $2$ baseballs (consider them as perfect solid spheres) have equal properties with mass $m = 0,142kg$, radius $r_0 = 0.037m$ in the space and thay are $...
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The choice of the direction of the displacement vector when calculating potential energy of a system
Here, when referring to potential energy, I will take gravitational potential energy as an example. Consider the following diagram where two point masses $m_1$ and $m_2$ at a distance $r$ from each ...
-1
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2
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233
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(Physics 2, Waves) Why does $\tan(\theta) = dy/dx$? [closed]
In the following example:
At the very last step, how does the author get that $\tan(\theta) = dy/dx$? To which $dy$ and $dx$ is this referring to? It can't be the same $dx$ that is labelled in the ...
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52
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Work-Energy Theorem for a path that is not smooth
In the analysis of Newtonian Mechanics for a single particle, we come across the definition of work and also the Work-Kinetic Energy theorem:
For a single particle, the work done on a particle by a ...
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160
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How do I write the gradient in angular coordinates ($\theta_1$, $\theta_2$, $\theta_3$)?
I have to find $\tau$ by finding the gradient of $U(\theta_1, \theta_2, \theta_3)$, where my coordinates are $(\theta_1, \theta_2, \theta_3)$. I assume the gradient is not the simple Cartesian ...
2
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Why is the gravitational potential of a uniform disc not symmetric about its center?
Consider a uniform, infinitely thin disc of surface mass density $\sigma$ and radius $R$ placed in the $xy$-plane with its center as the origin.
The gravitational potential at a point on the axis of ...
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