where γ is defined in the usual way. Starting from the expression for x′ and using the analogous expression for x (See book), derive the given expression for t′.
where γ is defined in the usual way. Starting from the expression for x′ and using...
Let clo, π] := {f : [0, π] → R I f is continuous). With addition and scalar multiplication defined in the usual way, this is a vector space. Let the inner product on CO,T] be defined analogous to (21), that is, (me) :-o u(z)r(z) dz. sinx and g(x) = 2.2. Which is "bigger": f or g? (a) Let f(x) (b) g? xplain. (c) Find a nontrivial function in CIO, π], which is orthogonal to f. d) Find a nontrivial...
For the tank system given below, the variables are defined in the usual way. a. For all the variables in the diagram below, using the same systems (e.g. English system), give units 6. for every variable. b. On the schematic diagram below, draw a feedback (FB) tank temperature control system with Qt) as the manipulated variable using P&ID notation. n the schematic diagram below, draw a feedforward (FF) tank temperature control system based on Ti(t) and combine it with your...
V. HEAT CAPACITY OF PLATINUM The usual expression for the Debye temperature involves the speed of sound, v. However, this result is too simplistic because there are two types of waves in the solid: transverse waves which travel at a speed of v, and longitudinal waves, which travel at a speed of vi. In general these speeds are not the same. a) [2 marks] Derive a new expression for the Debye temperature using the identity that the aver- age speed...
PHYS10121 2. The Lorenta transformations between two inertial frames S and S may be written z' = γ(x-Vt), -y a) A ruler of length L is at rest in S. Use the appropriate Lorentz transformation 3 marks) b) Using the appropriate Lorentg transformation formulae derive the following velocity formula to derive an expression for the length of the ruler as measured in S transformation formulae and T-T, 10 marks)
1. Assume n i.id. draws from Y ~ Weibull(9,%), with pdf: where γ-γ0 is a given value and the only unknown parameter is θ. (a) Show that the distribution of Y (for given γ-γ°) admits MyBU estimation of a particular function ψ(0) by showing that the joint pdf. f(y|θ, γ0), belongs to the exponential family with: TL K (e) TL (b) It can be shown that the median of Y is median(Yja, γο-θ(log 2) 1/γο, Take as a given (i.e....
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 31 Upper C 2
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 32C₃ 32 C₂ = 0
1. Starting with one of Newton's laws and your free body diagram, derive an expression for the normal force exerted on the block by floor. - Assess you answer in the following way: If you let \(\theta\) = 0, what does your solution predict for the normal force? Does this make physical sense? 2. Starting with one of Newton's laws and your free body diagram, derive an expression for the coefficient of kinetic friction \(\mu_{k}\) between the block and the...
7. a) Starting with the expression for heat added to a system: dq = Cydt + (P + (**).) av and letting S = S(VT), show that the second law of thermodynamics requires that all equations of state must have the form: (P+ **)n) = ctf(V) where c is a constant and f(V) is a function only of V. b) Show that this is true for an ideal gas and a van der Waal's gas. c) For a Virial gas...
The relative volatility, defined below, is often used as a simple way to relate the liquid and vapor compositions for a binary system. This worksheet examines the impact of relative volatility on the split between two components in a batch distillation process. An equimolar mixture of A and B is charged to a still. The mixture is distilled until 50% of A (the more volatile component) is vaporized a) Species A and B are present in a batch distillation still....