Recent content by lifeonfire

Homework Statement For a material given by U=C1PV2 and PV2=C2T Find the entropy Homework Equations dS/dU = 1/T; dU/dV = -P I don't know if I require anything else The Attempt at a Solution So from 2 equations I got U = C1 C2T But dU/dT is not equal to S. Which...

Homework Statement A gas fills a closed chamber connected to an evacuated piston chamber via a valve. The apparatus is diathermal (heat can flow through the walls of the chamber). The valve is opened to vent the gas into the piston. The piston then slowly compresses the gas back into the...

Homework Statement If a complex voltage and current are related by the expression v(t) = ( - 1 + j (3)^(1/2) ) i(t) What is the phase angle? Note j = sqrt(-1) Homework Equations The Attempt at a Solution So is the phase angle simply tan inverse (sqrt (3) / -1 )?? Or do I...

Homework Statement A force acting on a particle is given by: F = ( -(Am)/(y)^3 ) =( -(Am)/(y_0 - x)^3 ) The particle starts at rest at y = y_0. Solve for the motion of the particle x(t) BY INVOKING ENERGY CONSERVATION Homework Equations The Attempt at a Solution I have no idea...

Homework Statement Suppose a ray of light travels from (x,y) = (-1,1) to (x,y) = (1,1) in a region where the index of refraction is n(y) = e^y. (a) Find the path. Homework Equations The Attempt at a Solution Is this okay? The positions of the light ray are given by initial...

Thanks :)

Homework Statement Let a mass move in an orbit given by r = a*(theta) (a) If theta is a linear function of time t, what is the Force in terms of theta? (b) How should theta depend on t so that the force is central? Homework Equations The Attempt at a Solution Given that theta is...

Homework Statement Let a particle slides in a straight smooth tube passing obliquely through the Earth. Assuming no friction and no rotational effects. Describe the motion. Find Frequency and Period. Homework Equations F = -GMm/r^2 The Attempt at a Solution Don't know how to...

Do I do induction on m?? So that would mean , that by assumption ...+(nCm)(mCm) = (n+m C m)...then to prove ...+(nCm+1)(m+1Cm+1) = (n+m+1 C m+1) ...correct?

Homework Statement To Prove: (nC0)(mC0) + (nC1)(mC1) + ... + (nCm)(mCm) = (n+m C m) where nC0 = n choose 0 and so on. Homework Equations The Attempt at a Solution Tried expanding the whole thing using factorials - but didn't work. Any hints would be really welcome!

Homework Statement Prove that for two integers m,n: all the common divisors divides the g.c.d.(m,n). Homework Equations The Attempt at a Solution g.c.d = aA +bB ; where a, b are the integers and let d be a common divisor, then: d|a and d|b. After this I have no clue where...