Search results

  1. H

    How to determine force using a measured current

    Hi, I'm trying to calibrate a voltage divider circuit to measure force. I have measured the current output at two different weights, converted the weights to forces using "f=mg" and calulated a gradient from that using "y = mx + c" as well as the constant. However, I don't feel what I did...
  2. H

    Applying Bernoulli's equation to magnetohydrodynamic flow

    1. Homework Statement A static electrically conducting fluid, in the presence of electric and magnetic fields, experiences a Lorentz force. Determine the fluid pressure at point (1,2,1) when the pressure LaTeX Code: p_{0} at origin (0,0,0) is under the effect of gravity and the electric and...
  3. H

    Applying Bernoulli's equation to magnetohydrodynamic flow

    Homework Statement A static electrically conducting fluid, in the presence of electric and magnetic fields, experiences a Lorentz force. Determine the fluid pressure at point (1,2,1) when the pressure p_{0} at origin (0,0,0) is under the effect of gravity and the electric and magnetic field...
  4. H

    Proving tensor symmetry under transformation

    Homework Statement Using indical notation, prove that a 2nd order symmetric tensor D remains symmetric when transformed into any other coordinate system. Homework Equations Tensor law of transformation (2nd order): D'_{pq} = a_{pr}a_{qs}D_{rs} The Attempt at a Solution I think I'm...
  5. H

    Proof of transformational symmetry

    Homework Statement Using indical notation, prove that D retains it's symmetry when transformed into any other coordinate system, i.e. D'_{pq} = D'_{qp} (where D is a symmetric 2nd order tensor) Homework Equations D'_{pq} = a_{pr}a_{qs}D_{rs} (law of transformation for 2nd order tensors)...
  6. H

    Kronecker Delta

    Homework Statement Simplify/Evaluate these expressions involving the Kronecker delta, using Einstein's summation convention: a)\delta_{qr}\delta_{rp}\delta_{pq} b)\delta_{pp}\delta_{qr}\delta_{rq} Homework Equations \delta_{ij}=0 when i =/= j \delta_{ij}=1 when i = j The Attempt at...
  7. H

    Orthogonality of Sine and Cosine functions

    Hi, would anyone be able to explain how to evaluate a function using orthogonality (i.e. using orthogonality to solve a definite integration problem with sines/cosines)? Thank you
  8. H

    Partial Differential Equation using separation of variables

    Homework Statement Solve the heat flow problem using the method of separation of variables: Homework Equations PDE:\frac{\partial u}{\partial t}=k\frac{\partial^{2} u}{\partial t^{2}} for 0<x<L, 0<t<\infty BC's:\frac{\partial u}{\partial x}(0,t)=0,\frac{\partial u}{\partial x}(L,t)=0...
  9. H

    Partial Differential Equations Question

    Homework Statement Find the link between constants \omega and \beta so that http://www4e.wolframalpha.com/Calculate/MSP/MSP181963g2e5f4i43d3b00005ief8e24920ah323?MSPStoreType=image/gif&s=20 [Broken] is a solution of \frac{\partial^{2} u}{\partial x^{2}}=2\frac{\partial u}{\partial t} (A...
  10. H

    The path of crossing a stream

    Homework Statement A watercraft is crossing the stream to reach the pier. (See attached figure.) Basically, I have to derive an ordinary differential equation of the path the watercraft travels, which I can then solve using MatLab, etc. i.e. derive \frac{dy}{dx} in terms of V_{W}, V_{B}...
  11. H

    Integration of an inverse sqrt composite function

    Homework Statement “Geologist A” at the bottom of a cave signals to his colleague “Geologist B” at the surface by pushing a 11.0 kg box of samples from side to side. This causes a transverse wave to propagate up the 77.0 m rope. The total mass of the rope is 14.0 kg. Take g = 9.8 m/s². How...
  12. H

    Unit of the Determinant of a 2-space Matrix

    Do determinants of a 2-space matrix have a unit of [units]^2? Also, does A_parallelogram = || u x v|| have a unit of [units]^2 too? This has confused me as Area has a unit of [units]^ 2 but the examples from the Contemporary Linear Algebra (Anton and Busby) text book does not state any units...
  13. H

    Max. velocity with given coefficient of static friction (μ_s)

    Homework Statement A car goes around a curved stretch of flat roadway of radius R = 104.5 m. The magnitudes of the horizontal and vertical components of force the car exerts on a securely seated passenger are, respectively, X = 236.0 N and Y = 572.0 N. This stretch of highway is a...
  14. H

    Thrust force of an engine

    Homework Statement A plane of mass 1220 kg has an engine failure when flying with an airspeed of 138 km/h at an altitude of 2960 m on a calm day. It then glides at a constant glide angle (which is the direction of flight below the horizontal) 6.80 degrees towards a safe landing at this...
  15. H

    Rate of heat radiated from a person

    Homework Statement What is the percentage increase in the rate of heat radiated from a person with a surface skin temperature of 34.0 °C compared with the same person with a skin temperature of 33 °C? Homework Equations Stefan's Law of emission: P = σAeT^4 - P = rate of energy...
  16. H

    Density of water vapour in the air following compression if it were an Ideal Gas

    Density of water vapour in the air involving compression Homework Statement A volume Vi = 23.2 L of air at temperature T = 22 °C is compressed at constant temperature to a volume Vf = 11.0 L. The relative humidity of the air before compression is H = 59.4 %. The saturated vapour pressure of...
Top