All Questions
14
questions
0
votes
3
answers
185
views
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. ...
- 37
0
votes
2
answers
88
views
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
0
votes
2
answers
52
views
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 ...
- 3,340
4
votes
4
answers
2k
views
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 $=...
0
votes
6
answers
116
views
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, ...
- 43
0
votes
0
answers
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 ...
0
votes
1
answer
120
views
Why can we multiply by $dt/dt$ to change variable of integration? Please look at equation 5-20 [closed]
I am struggling to understand why can we just multiply by $dt/dt$. I was thinking it was just a change of variables, but I cannot come up how that works. Can someone explain why we are allowed to do ...
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1
vote
3
answers
65
views
Position Dependence in Equation of Motion
Our lecturer gives study material which contained that Newton's second law could be written as:
$$ \begin{aligned} F &= m \ddot{x} \\ &= m \frac{d \dot{x}}{dt} \\ &= m \frac{dx}{dx} \frac{...
- 13
-2
votes
1
answer
222
views
If kinetic energy is mass times the integral of velocity, isn't it just a product of mass times distance? [closed]
I'm still learning Calculus at the moment and I'm currently on integration. The moment I realized the "$1/2$" and square value in $v^2$ are just products of integration, can't one just use ...
- 1
0
votes
3
answers
305
views
Issue with deriving the work-energy theorem
I'm a little confused regarding the way Total work = Change in kinetic energy is derived using calculus. My issue can be seen at 3:26 of this video: https://youtu.be/2dqO4sy4Njg?t=3m20s
Why can the ...
3
votes
4
answers
1k
views
Can a proof of the work-energy theorem be made, that doesn't use Leibniz notation to cancel differentials?
I've been doing some reading, and even though many people say different things, i think i'm pretty confident in saying that we can't treat differentials as fractions. In some scenarios it works out (...
- 305
0
votes
1
answer
1k
views
Infinitesimal work
I am a newbie in Physics (Senior on highschool) and our teacher wrote in a proof
$$\dfrac{dK}{dt}=\dfrac{dW}{dt},$$
where $K$ is the Kinetic energy of a body and $W$ is the Work.
So now that I am ...
- 103
4
votes
3
answers
2k
views
"Rigorous" derivation of kinetic energy
I've always wondered where the formula of (non-relativistic) kinetic energy we learn at high school comes from. This is the "derivation" I came up with:
$\Delta W:=\int_{r_0}^{r_1}drF=m\int_{r_0}^{r_1}...
- 1,002
0
votes
2
answers
221
views
Differentiating displacement with respect to speed in order to obtain time
I have this problem where I am trying to calculate $d(t)$ and $v(t)$ of a mass m on a spring, dropped from a displacement $A$, without using anything else than Hooke's law and energy calculations. ...
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