Recent content by A330NEO

Homework Statement Length of action Z(Length of line of action) is Z=\sqrt{(r_{p}+a_{p})^{2}-(r_{p}cos\phi )^{2}}+\sqrt{(r_{g}+a_{g})^{2}-(r_{g}cos\phi )^{2}}-Ccos\phi How can I drive it? Homework EquationsThe Attempt at a Solution

you mean this equation? this is from Wikipedia, and it's based on momentum equation p=mv, thus F=dp/dt. F=m(t)\frac{dv}{dt} - u\frac{dm}{dt} When I put this I that question, I found something like this. 5-x= x\frac{d^{2}x}{dt^{2}} - \left ( \frac{dx}{dt} \right )^2 Looks similar to the...

may I ask you how to apply it?

Homework Statement A uniform 10-foot-long heavy rope is coiled loosely on the ground. One end of the rope is pulled vertically upward by means of a constant force of 5lb. The rope weighs 1lb/ft. Use Newton's second law to determine a differential equation for the height x(t) of the end above...

Homework Statement >A gas flows through a small orifice in a pipe as shown above. On the higher pressure side, the gas is at 1Mpa and temperature of 300K. The pressure reduces to 1kPa after it flows through the orifice. The equation of state for the gas is v=\frac{RT}{P}+10^{-6}T^2 If the...

Then, what kind of property is it?

Homework Statement -\left ( \frac{\partial U}{\partial V} \right )_{S, N} is a definition of an imporant thermodynamic property,where S denote the entropy and the subscript 0 denotes reference state, so they must be constant. show what is this property. In your analysis, use the equation...

Homework Statement Estimate partial pressure of nitrogen in atm in a room where you are at this moment. Use an ideal gas approximation and assume that air is composed of only nitrogen and oxygen. Show how you arrive the final answer in detail. Homework Equations pv=RT, while p stands for...

I tried, but it was way too complexed. Anyway, if my algebra and switghing to polar coords is not bad, is it presumable that the 'answer sheet' is wrong?

Homework Statement ##\iint_S (x^2+y^2)dS##, ##S##is the surface with vector equation ##r(u, v)## = ##(2uv, u^2-v^2, u^2+v^2)##, ##u^2+v^2 \leq 1## Homework Equations Surface Integral. ##\iint_S f(x, y, z)dS = \iint f(r(u, v))\left | r_u \times r_v \right |dA##, The Attempt at a Solution...

I think the amount would be same, but will have negative value. But is that an enough explanation?

Homework Statement I have to explain why this vector field is not conservative. Homework Equations Maybe it is: if ##\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}## then F(x, y) = p(x, y)i + Q(x, y)j is a conservative field. I tried to figure out what P and Q is, but that...

First, I already know that when we have to do linear approximation of ##f(x, y)## if ##\Delta z = f_{x}(a, b)\Delta x + f_{y}(a, b)\Delta y + \epsilon_{1}\Delta x + \epsilon_{2}\Delta y ##. and ##\epsilon_{1}## and ##\epsilon_{2}## approaches to nought wneh ##(\Delta x, \Delta y)## approaches...

Understood. But, if we approach (0, 0) along the y-axis, regardless of if y >0 or y<0, isn't it continuous? Is it considered discontinuous because there is no 'width' of the contacting point?

The question looks like this. Let $f(x, y)$ = 0 if $y\leq 0$ or $y\geq x^4$, and $f(x, y)$ = 1 if $0 < y < x^4 $. (a) Show that $f$ is discontinuous at (0, 0) (b) Show that $f$ is discontinuous on two entire curves. In regarding (a), I know $f(x, y)$ is discontinuous on certain...