All Questions
17
questions
26
votes
14
answers
4k
views
Explaining how we cannot account for changing acceleration questions without calculus
For context, I am a high school physics teacher.
I am teaching students about the basics of electromagnetic force between two point charges. The equation we use is $F=\frac{kq_1q_2}{r^2}$.
This gives ...
4
votes
2
answers
4k
views
friction of rope wrapped around a cylinder - the Capstan Equation
I have the following problem:
A rope is wound round a fixed cylinder of radius $r$ so as to make n complete turns. The coefficient of friction between the rope and cylinder is $\mu$. Show that if ...
- 3,997
3
votes
3
answers
878
views
Newton's Second Law in vertical launch of a rocket
Consider a rocket being launched vertically.
Let $T(t)$ denote the thrust from the engine and $M(t)$ be the total mass of the rocket at time $t$.
At $t=0$, $T(0)=M(0)g$ (so that the normal force due ...
- 1,047
2
votes
4
answers
643
views
Work done by a vector field (Force field) on a particle travelling along a curve
Assume a particle travelling along a curve, the work done by any Force field on the particle while moving along a curve is given by the line integral of $\vec{\bf{F}} \cdot \vec{\bf{dr}}$, but shouldn'...
- 367
2
votes
1
answer
67
views
Forces along and perpendicular to a curve
A uniform rope of length $l$ is suspended from two hinges, making an angle of $\theta$ with the horizontal at the hinges. Find the depth $d$ of the lowest point of the rope.
Similar questions include ...
- 23
1
vote
2
answers
81
views
Is it possible to lift an object from rest with constant power?
This is inspired by the following question.
Consider some object which I want to lift from rest with a constant power throughout the whole process; the power I apply when lifting the object from rest ...
- 6,621
1
vote
1
answer
77
views
Equation for stationary string
I have some doubts on the following derivation of the EOM of a stationary string.
Let $F_x, F_y$ be horizontal and vertical tension of the string
$\mu$ be the mass per unit length of the string [kg/m]
...
- 180
1
vote
1
answer
169
views
Find $v(t)$ and $x(t)$, How do I treat $δt$? [closed]
We apply a force to a particle with a mass $m$ and inicial velocity $v_0$:
$$ F(t) = \left \{ \begin{matrix} 0 & \mbox{ $t<t_0$}
\\ \frac{p_0}{\delta t} & \mbox{ $t_0<t<t_0 +\...
- 39
0
votes
2
answers
83
views
Kinematics confusion regarding sign of integration
I was solving some problems regarding non-inertial frames, and Newtonian mechanics in general, when I faced a major doubt regarding one of the seemingly simple topics, and I'd appreciate it if someone ...
- 1,791
0
votes
2
answers
5k
views
Can you take the integral of $ d^2x\over dt^2$? [closed]
I am messing around with physics problems, and as silly as this maybe how do you take the integral of
$$\int_0^\infty xd^2x$$
For example taking Newton's Second law $F=ma$
$$
F=m{d^2x\over dt^2}
$$...
- 546
0
votes
2
answers
304
views
Is the Fundamental Theorem of Calculus really applicable to the definition of work?
When the force $F$ on an object is not constant, then the work it performs is defined as $$W = \int_{x_0}^{x} F(X)dX.$$
Now, the Fundamental Theorem of Calculus states that
$$\text{If}\,\,\, f(x) =...
user36790
0
votes
1
answer
1k
views
How to use Newton's second law to derive conservation of momentum and how to use derive conservation of momentum to derive the second law?
I know if taking the integral of $F=ma$, then I can get $p=mv$.
I'm weak in calculus, so I wondered how to do this exactly.
Is there anything wrong in my logic below?
\begin{align}\int F\left(t\...
- 1
0
votes
2
answers
294
views
Line integral confusion
Hi , so I was solving this example . I have no problem in calculation . But at the end of it , when they asked about the closed line integral , I wondered how did the line integral on both paths be ...
user65035
0
votes
0
answers
12
views
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 ...
0
votes
2
answers
180
views
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 = \...
- 1