All Questions
27
questions
0
votes
0
answers
24
views
Force due to pressure on a curved surface/wall [closed]
Most solutions that I found on the internet concerning the net force due to pressure on a curved wall were using free-body diagrams and I could not find any using a calculus approach
Assuming the ...
- 19
0
votes
1
answer
66
views
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 $...
- 1
0
votes
2
answers
291
views
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 ...
1
vote
1
answer
130
views
Finding velocity $v$ and position $r$, given a time $t$ under the acceleration of a gravitational force [closed]
I was messing with the maths, when I tried to find the velocity as a function of time, $v(t)$, and the position, also, as a function of time, $r(t)$ under the gravity force.
$$ m \ddot{r} = -G \frac{...
- 1,525
2
votes
1
answer
67
views
Forces along and perpendicular to a curve
A uniform rope of length $l$ is suspended from two hinges, making an angle of $\theta$ with the horizontal at the hinges. Find the depth $d$ of the lowest point of the rope.
Similar questions include ...
- 23
0
votes
1
answer
167
views
Maximum height of a projectile when $g$ is not constant [closed]
How can I calculate the maximum height of a projectile that is launched from the surface of the earth with a given initial velocity? (ignoring air resistance in the atmosphere)
I understand how to ...
0
votes
1
answer
25
views
Issue with a derivation in Marion's Dynamics [closed]
I was solving problem 2-14 in Marion's "Classical dynamics of particles and systems" edition 5. In this problem we calculate the range of a trajectory to be $d=\frac{2{v_0}^2\cos{\alpha}\sin{...
- 93
1
vote
2
answers
81
views
Is it possible to lift an object from rest with constant power?
This is inspired by the following question.
Consider some object which I want to lift from rest with a constant power throughout the whole process; the power I apply when lifting the object from rest ...
- 6,621
0
votes
3
answers
165
views
Power and work contradiction
A body is starting from rest. A force is acting on it for a short period of time. In that given time, power delivered to it at any instance $t$ is given
$$P = F \cdot v_1 = ma \cdot v_1 = mv_1^2/t,$$
...
0
votes
1
answer
33
views
Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial ($P$) and final ($Q$) positions is [closed]
Question is as follows:
Average torque on a Projectile of mass $m$ with initial speed $u$ and angle of projection $θ$ between initial $(P)$ and final $(Q)$ positions is
I researched a lot but wherever ...
1
vote
1
answer
80
views
Problem finding Centre of Mass [closed]
My Question: For finding the Center of Mass ($COM$) of a hollow cone, why do we use its area to define its elemental mass ($dm$) and not its volume, which we use to find the $COM$ of a solid cone.
The ...
- 111
1
vote
2
answers
83
views
For regular moving objects around us, how many times can I differentiate their position with respect to time until I reach a constant? [duplicate]
When I practise problems, I come across ideal situations like constant velocities, constant accelerations, etc. But in real situations, objects usually don't magically gain momentum or acquire ...
- 385
-2
votes
1
answer
154
views
What is wrong with my approach? What error did I make mathematically? [closed]
A $4$ kg object is moving in one dimension along the x-axis. The linear momentum of the object increases with the position of the object according to the following equation:
$p(x)=6+3x$
At $t = 0$ s ...
- 1
11
votes
6
answers
2k
views
Does the logarithm of a non-dimensionless quantity make any sense?
A train consists of an engine and $n$ trucks. It is travelling along a straight horizontal section of track. The mass of the engine and of each truck is $M$. The resistance to motion of the engine and ...
- 1,047
1
vote
1
answer
169
views
Find $v(t)$ and $x(t)$, How do I treat $δt$? [closed]
We apply a force to a particle with a mass $m$ and inicial velocity $v_0$:
$$ F(t) = \left \{ \begin{matrix} 0 & \mbox{ $t<t_0$}
\\ \frac{p_0}{\delta t} & \mbox{ $t_0<t<t_0 +\...
- 39
5
votes
1
answer
228
views
What are the scalar equations for velocity and displacement if acceleration obeys the inverse-square law?
In basic high school physics/calculus you learn that you can formulate equations for velocity and displacement under constant acceleration as:
$a(t) = a_0$
$v(t) = a_0t + v_0$
$x(t) = \frac{1}{2}...
- 151
0
votes
1
answer
949
views
Proving the centre of mass formula with integral [closed]
I came across a question:
Find $f(r)$ and prove the centre of mass formula:
$$\vec{r_{cm}} = \frac{1}{V} \int f(r) \vec{dS} $$
Where $V$ is the total volume and our surface integral is ...
- 113
0
votes
1
answer
2k
views
calculating the length of a hanging spring
If we assume the slinky to have a uniform mass (mass per unit length around the circumference of slinky to be constant, or simply slinky is made of same material and has uniform thickness) and that ...
- 315
0
votes
2
answers
560
views
Writing Riemann sums for physics problems
If I want to find the mass of a rod of length l and density $\rho = kx$ where $x$ is the distance from one end.
If I want to find the gravitational potential due to a hollow sphere at a distance x ...
- 1,096
1
vote
2
answers
144
views
Why can I assume the force to be constant in this particular interval?
If I have force, or any function $f(z)$, I was told that I can assume it to be constant only in the interval $dz$.
However, in this case, I had to calculate the work done by the spring force as a ...
- 1,096
4
votes
2
answers
967
views
Maximizing Time of Flight in Projectile Motion [closed]
Is (or How is) it possible to maximize the time of flight of projectile subject to the following conditions?
Given :
Fixed horizontal range
Interval in which velocity lies
For example, let the ...
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
1
vote
2
answers
1k
views
Proof that SHM is sinusodial?
If we have an object attached to a spring, and the net force on that object is $-kx,$ how do we prove that its motion (if you move the object to $x\ne 0$) is sinusoidal? I know that you must ...
- 215
0
votes
1
answer
75
views
Question from Kline's Calculus: A physical and intuitive approach [closed]
A train runs at a velocity of 66 ft/ sec along a straight track. When the brakes are applied, the deceleration is $4/3$ ft/$sec^2$. For how long and how far should the brakes be applied so that the ...
- 379
-2
votes
2
answers
103
views
Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$ [closed]
Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$
My approach:
First I find the line segment formed by $A,B$ which is $\vec l(t)=\vec{OA}+t\vec{AB}=(1,0,-1)+t(1,...
- 107
2
votes
1
answer
1k
views
Taylor series expansion of $\ln$ and $\cosh$ in distance fallen in time $t$ equation
I want to find the Taylor expansion of $y=\frac {V_t^2}{g} \ln(\cosh(\frac{gt}{V_t}))$
I have tried using the fact $\cosh x= \frac {e^x}{2}$ for large t, which works, I just need help on small values ...
- 345
0
votes
1
answer
667
views
Investigation of a pendulum's period, problem creating equation to sum the dynamic velocity
I am investigating the period of a pendulum swing. This is a simple harmonic pendulum and I am already aware of the common, but slightly inaccurate,
$2\pi \sqrt{\frac{L}{G}}$ formula.
My problem is ...
- 1,229