2
votes
0answers
45 views

Calculating work [on hold]

How much work is required to lift a $1000\mathrm{kg}$ satellite from the surface of the earth to an altitude of $2\times10^6$ meters? The gravitational force is $F=\frac{GMm}{r^2}$, where $M$ is the ...
1
vote
2answers
26 views

Calculating appearance of size of object at given distance

Here's the problem I'd like to solve. If I'm 1 ft away from a computer screen and a word on the screen appears a certain size, is there an equation or calculation that will tell me how big that ...
2
votes
1answer
19 views

differential in integration cancelled but variable endpoint is changed

In kinetic energy equation in wiki. I have difficulty problem how endpoint in integral change from t to v. This doesn't look like it is using substitution method. ...
-1
votes
0answers
30 views

Find the center of mass of a region with uniform density [closed]

A region on the graph is bound by the lines $y=x/2$, $y=0$, $x=2$ How can I calculate the center of the mass assuming a uniform density of "p" throughout the region?
1
vote
1answer
37 views

Word Problem, Calculus estimation homework

Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to ...
5
votes
2answers
87 views

Solution of differential equation with Dirac Delta

Is it possible to solve a differential equation of the following form? $\partial_x^2y + \delta(x) \partial_x y = 0$ where $\delta(x)$ is the dirac delta function. I need the solution for periodic ...
1
vote
1answer
25 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
0
votes
1answer
30 views

How far will my car roll given a function representing the slope of the landscape I'm driving on?

So I was driving in my car thinking to myself "I wonder how far I would go (before starting to roll backwards) if I just took my foot off the brakes" I tried to figure it out myself but could not. SO ...
0
votes
1answer
51 views

Why do these acceleration computations contradict each other?

A rocket follows the path $(y-40)^2=160x$ after traveling vertically to the height of 40 feet (making for a very convenient continuity. The problem asks "If the component velocity in the vertical ...
0
votes
3answers
135 views

Is speed a function of position?

Let $x$ be a smooth function from $[0,\infty)$ to $\mathbb{R}^n$ satisfying the following differential equation $x''(t) = f(x(t))$, where $f$ is a smooth function from $\mathbb{R}^n$ to itself. Then ...
1
vote
2answers
39 views

is it necessary that curl of 2d vector is perpendicular to the plane.

I am just confused, help me guys. The question comes up, because we say that curl is either clockwise or anti-clockwise at a point.
1
vote
1answer
106 views

Please explain the logic behind $d(xy) = y(dx) + x(dy)$

I've seen $d(xy) = y(dx) + x(dy)$, but I don't understand the principle behind it and memorizing it is lame. Can anyone explain what is going on here? For example from physics, $$F = {{dP} \over ...
0
votes
1answer
77 views

I can't seem to find this derivative any help would be great.

A rocket of mass m = 1000 kg is traveling in a straight line for a short time. The distance in meters covered by the rocket during this time is described by the function $r(t)=t^3 −3t^2 +6t$ where ...
0
votes
4answers
69 views

Multiple choice question on rates of change (or so I thought)

If I were to find the resistance of the component (see image below), I would either find the equation of the curve and use differentiation or I'd draw a tangent at $V_2$ and then find the reciprocal ...
2
votes
2answers
37 views

simple question about $\nabla r$

In my physics notes, it says $\nabla r = \underline{e_r} = \frac{\underline{r}}{r}$ and $\nabla \frac{1}{r} = - \frac{\underline{r}}{r^3} = - \frac{1}{r^2} \underline{e_r}$ I don't quite ...
2
votes
1answer
54 views

Divergence Free Vector Fields that are undefined at the origin

I am aware of vector fields which are undefined at the origin but whose divergence everywhere else is 0. In particular, my students have already seen the inverse square vector field, i.e. ...
-1
votes
1answer
37 views

The phase plane and potential energy

I think I have spotted a mistake in my notes, however I need help verifying my assumption: I am given the equation: $d^2s/dt^2=-s$ m=1 for simplicity I have recast it at a first order system: ...
0
votes
3answers
41 views

Figuring out acceleration without knowing the time length

A car goes from 50mph to 20mph in an unknown amount of time. All that is known is that one of the car's wheels rotated 110 times during the process and that the wheel rotates at a rate that is uniform ...
1
vote
0answers
39 views

Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
1
vote
2answers
66 views

Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
1
vote
1answer
81 views

When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?

As a follow-up to this related question, I'd like to know under what circumstances, if any, $\Delta x$, $\delta x$ and $dx$ all mean the same thing, and under what circumstances they can all be said ...
1
vote
4answers
102 views

Second order differential equation for acceleration

Can you help me understand and solve this question: A bullet is fired vertically upwards with an initial velocity of $u$. Form a second order differential equation for acceleration and by ...
2
votes
1answer
63 views

What's the proper interpretation of canceling infinitesimals?

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
0
votes
1answer
18 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
0
votes
2answers
50 views

Physics Related Watt Question

A 550 kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts ...
0
votes
1answer
48 views

Deriving Barometric formula

Recall idea gas law: $pV= NkT$ where $p$ equals pressure, V volume, N moles of atoms, k boltzmann's constant, T temperature. Also, density: $\rho = m/V = \mu N/N_A V$ where $\mu$ is average mole mass ...
1
vote
1answer
52 views

Integrating this physics expression

Recall: $dp= \rho g \ dh$ where $dp$ is the change in pressure, $ \rho$ is the constant of density and $dh$ is the change in height. This is a part of fluid dynamics (buoyancy). I am to integrate ...
1
vote
2answers
39 views

Help verifying a the correct partial differentiation of $v_0=R\sqrt{\frac{g}{2h}}$

I have to use partial differentiation to solve the below equation: $v_0=R\sqrt{\frac{g}{2h}}$ Where $g$, $R$, and $h$, are defined as follows: $g=9.80 \frac{m}{s^2}$ $R=155 cm$ $h=116.2 cm$ ...
3
votes
1answer
78 views

Solving Wave Equation with Initial Values

I am trying to solve the wave equation: $u_{tt}$ = $u_{xx}$ With initial values: $u(x,0) =\begin{cases} x^3 - x, &\text{for }|x|\le 1,\ \\0, &\text{for }|x|\ge1\end{cases}$ $u_t(x,0) ...
0
votes
1answer
80 views

Finding the ideal angle for the maximum range of a projectile when elevated?

I was thinking about physics, and I thought of something. How do we find the ideal angle for the maximum range of a projectile when elevated? Assumptions: Parabolic flight path No air friction ...
0
votes
1answer
57 views

Using definite integrals with velocity and acceleration

Rocket A is traveling 49 ft/sec at 80 seconds. Rocket B is launched upward with an acceleration of $$a(t)=\frac3{\sqrt{t +1}}$$. At time t=0 seconds, the initial height of the rocket is 0 feet, and ...
1
vote
1answer
76 views

Does distance increase equally in equal time intervals under the influence of gravity?

Quick question. If an object falls under the influence of gravity near the Earths surface, is the distance traveled increased by equal amounts in equal time intervals? I thought that this would be ...
0
votes
3answers
39 views

Finding the total distanced covered (physics)

A subway train starts from rest at a station and accelerates at a rate of $1.60\frac{m}{s^2}$ for $14.0 s$ . It runs at constant speed for $70.0 s$ and slows down at a rate of $3.50\frac{m}{s^2}$ ...
1
vote
0answers
36 views

Define a plane with double integral

For my transport physics I have to describe how much volume through a rectangular pipe goes. The speed is given by $\displaystyle V_x=V_0 \frac{y}{h}$. But I have to define the plane with a double ...
0
votes
0answers
78 views

Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
0
votes
1answer
63 views

Problem with friction [closed]

Imagine two boxes stacked on top of each other. The bottom box is larger than the top box and it rests on a surface. So: Between the boxes is a friction force constant $\mu_s$ and between the ...
2
votes
1answer
41 views

Angle that car is at after angular acceleration

A car starts from rest on a curve with a radius of $150m$ and tangential acceleration of $\displaystyle 1.5\frac{m}{s^2}$. Through what angle will the car have traveled when the magnitude of its ...
1
vote
1answer
52 views

Vector functions applied to a football game

A wide receiver is standing $40$ ft to the left ($x=-40ft$) of the quarterback who is standing at the origin. The receiver immediately accelerates at $\displaystyle 9.79 \frac{ft}{s^2}$ at an unknown ...
0
votes
3answers
93 views

Finding velocity in optimization problem

Given $s=-16t^2+192t+144$, what is the velocity when $s=0$? This is part of a larger optimization problem which I solved, except for this last part. The critical point occurs at $t=6$, so after ...
2
votes
3answers
75 views

How do you solve this differential equation?

Though I've read questions on this site and really appreciate the quality of the answers, this is my first question, so I hope it follows the site's guidelines. When working with potential energy ...
0
votes
1answer
29 views

When to use trig substitution?

I'm trying to solve this physics equation: $$E=\frac {\lambda y} {4\pi \epsilon_{0}} \int_{-\frac l 2}^\frac l 2 \frac {dx} {({x^2+y^2})^\frac 3 2} $$ However, my calculus is a little rusty and am ...
2
votes
1answer
76 views

Physics and calculus?

A box slides down a slope described by: $$y = 0.05x^2$$ where $x$ is the x coordinate of the slope and y is the y co-ordinate (both in meters). Find the $y$ component of acceleration at $0.4 m$ if ...
3
votes
2answers
130 views

calculation of Stefan's constant

In the calculation of Stefan's constant one has the integral $$J=\int_0^\infty \frac{x^{3}}{\exp\left(x\right)-1} \, dx$$ which according to Wikipedia is equal to $\frac{\pi^4}{15}$. In this page of ...
0
votes
2answers
102 views

trouble understanding integration

I am reading through this physics book and have trouble understanding how they integrated one of the problems the conditions are Conditions: // ignoring the constant for simplicity $$r = \sqrt{x^2 + ...
-1
votes
2answers
57 views

Prove the average quantum mechanical energy using l'Hôpital's rule

I am trying to prove that taking the limit as $h\to0$ for the average quantum mechanical energy $$\dfrac{hν}{e^{hν/kBT}−1}$$ yields the average classical energy, $kBT$. How would you use l'Hôpital's ...
3
votes
1answer
114 views

Non-Linear ODE Strategy

I encountered the following $2^{nd}$-order, non-linear ODE while working on a classical mechanics problem: $$ \frac{d^2r}{dt^2}-\frac{\alpha^2}{r^3}+\beta=0 $$ where $\alpha \ \text{and}\ \beta$ are ...
0
votes
1answer
47 views

Vector functions and motion along a curve

A particle moves along the curve $x=\ln y$ with a constant speed of $4$ units per second. Find the normal scalar component of acceleration as a function of $x$. Honestly, what I don't understand ...
1
vote
1answer
317 views

Pumping Water out of Parabolic tank?

First of all, I understand how to do the integration part of this problem, but I am confused about the setup. Here is the question: Use integration to find the work done pumping all the water ...
0
votes
1answer
1k views

Calculus help. Find the work required to empty a cone shaped tank.

A tank in the shape of an inverted right circular cone (the ice cream goes on top) has height 7 meters and radius 3 meters. It is filled with 3 meters of hot chocolate. Find the work required to empty ...
2
votes
1answer
485 views

Solving differential equation regarding temperature change (Newton's law)

I'm solving a differential equation problem set and I bumped into the following DE problem where I got few question marks: The temperature of a body at time $t$ is $T(t)$ and the temperature of ...