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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1
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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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193
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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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43
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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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1
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84
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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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185
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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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1
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94
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What is $V$ in $a$=$V$$dv$/$dx$? [duplicate]
$a$=instantaneous acceleration
$V$=instantaneous velocity
$x$=position
$dx$=small Chang in position
$a$=$dv$/$dt$
multiplying numerator and denominator by $dx$,we get
$a$=$dv$.$dx$/$dx$.$dt$
now we ...
- 161
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88
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Equilibrium of a body with potential energy as a function of position
We know that if the potential energy of a body, say $U(x)$ of a body is known as a function of its x-coordinate, for equilibrium, $$\frac{dU(x)}{dx} = 0$$ Also, several sources suggest that for the ...
- 301
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66
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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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30
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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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237
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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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Conservation Principle
We are introduced to Principle of Conservation of Linear Momentum via the Newton's Second Law
$$\vec{F_{net}}=\frac{d\vec{p}}{dt}$$
It states when net external force equals zero then $\vec{p}=$...
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4
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2k
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Help me understand the derivation of the kinetic energy formula please
In my physics textbook, kinetic energy is defined as $W$Net $=$ $\int m\frac {dv}{dt}$ $dx$ This makes sense to me just fine. The book goes on to rearrange the integral to say the following:
$W$Net $=...
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2
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268
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Circular motion equivalent in three dimensions [closed]
Are there equations or even a concept of circular motion/tangential acceleration/centripetal acceleration in three dimensions? Maybe something called "spherical acceleration"? or am I just ...
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Is the acceleration vector half of the gradient of velocity squared?
Consider the differentiation of speed squared with respect to time:
$$\frac{d(v^2)}{dt}=\frac{d(\mathbf v\cdot\mathbf v)}{dt}$$
$$=2\mathbf v\cdot\frac{d\mathbf v}{dt}$$
$$=2\mathbf v\cdot\mathbf a$$
$...
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6
answers
116
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Deriving Work-Kinetic Energy Theorem
I am currently reading Physics for Scientists and Engineers (Ninth Edition) by Serway and Jewett and in Chapter 7.5, a derivation of the work-kinetic energy theorem was shown.
To give context, ...
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2D rotation dynamics/control systems as a complex number
I have a dynamic system (it's a rocket in a 2D plane), that I'd like to model the orientation of using complex numbers to remove the need for trig functions in my ode.
I'm having trouble defining the ...
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Why does solving the differential equation for circular motion lead to an illogical result?
In uniform circular motion, acceleration is expressed by the equation
$$a = \frac{v^2}{r}. $$
But this is a differential equation and solving it gets the result $$v = -\frac{r}{c+t}.$$
This doesn’t ...
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2
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291
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Finding angular frequency via integration of Newton's Second Law for a physical pendulum
For context: I am a student enrolled in AP Physics C with prior knowledge from AP Calculus AB and AP Physics 1.
We just collected data for a lab to determine an experimental value for g. The setup ...
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523
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Acceleration as a function of displacement
I am given a question such that a 0.280kg object has a displacement (in meters) of $x=5t^3-8t^2-30t$. I need to find the average net power input from the interval of $t=2.0s$ to $t=4.0s$.
I know the ...
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12
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Issue with work vs force for calculating spring constant [duplicate]
Lets say I have a spring with spring constant k. I put a 10kg weight on the spring and it compresses the spring one meter before stopping. We know that at this point the downwards force is equal to ...
3
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5
answers
2k
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Guidelines to calculate moment of inertia
The moment of inertia is defined as
$$I = \int r^2 dm$$
but I am not sure how to proceed with solving the above integral. All examples I have seen seem to be done with different strategies. They ...
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178
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How do we show that the work done by a variable force (in one dimension) is the area under the $F$ vs. $x$ curve?
In my physics textbook, to show that work is the area under the $F$ vs. $x$ curve, the author first writes the relation $dw = F dx$. This part makes sense to me. From there, the author writes, $$W = \...
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Tidal forces mathematics
Let's calculate the difference in force, $\Delta F$, experienced by
the rocks. Because $\Delta r$ is very small compared to $r$,
$$\Delta F = F_{\text{out}} - F_{\text{in}} \approx\frac{dF}{dr}\Delta ...
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126
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Work-Energy Principle Derivation
I am currently in Mechanics I and both my professor and my book have derived the work principle in this way and I even asked about its derivation during class, but it has me puzzled.
I don't ...
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2
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83
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Kinematics confusion regarding sign of integration
I was solving some problems regarding non-inertial frames, and Newtonian mechanics in general, when I faced a major doubt regarding one of the seemingly simple topics, and I'd appreciate it if someone ...
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