All Questions
27
questions
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