Derive the error expression for the following:
Derive the error expression for the following: b. where g is an exact constant but m,...
where g is an exact constant but m, v and h are measured values with uncertainties.
Posting together because I already posted one of them on accident without an explanation. Both of these want to find the error propagation, using the rules attached. b.Em+ mgh where g is an exact constant but m, v and h are measured values with uncertainties. C. U Vo cos θ where both vo and θ are measured values Review of Measurement Uncertainty Calculations Here are the rules for propagating uncertainties through a calculation: Addition: z-x + y δΖ 6x +...
please solve #3 2. Given the error in measuring H and L to be equal to propagated error in py , derive an expression for the block, mass M mass m Now the block is tied to string that passes over a frictionless pulley. The other end of the string is tied to a mass m. Mass m is increased until the block slides at constant speed. 3. Derive a new expression for pue in terms of m and M...
Review of Measurement Uncertainty Calculations Here are the rules for propagating uncertainties through a calculation Addition: z m x + y δ,: 8x + 6y This works for any nunter of terms Subtraction:zx-y o&x + 5y This also works for any number of terns Multiplication by an exact value: z kx 82-kEx General multiplication/division: z-xy or z-:-a-Irl ) (This works for any number of factors) Exact power: z r-δε-121k] sine function: Z t, sin χ-82 tt lcos xlsr Cosine function...
Derive the expression for the initial velocity v of a ballistic pendulum in terms of the swept-out angle theta. Use the following equations of momentum and energy conservation... When the projectile and the pendulum stick together, they have total mass m + M and we define their combined velocity to be V⃗ . The relationship from conservation of momentum is: mv = (m + M)V⃗ Conservation of energy requires the initial kinetic energy of the pendulum system to equal the...
Question 6: a) Derive and expression for the steady state error of the system described below when a unit ramp function is used as input. r(t) —+ Q G.(s) Gy(s) y(t) H(s) 10 b) Find the steady state error with a ramp input as a function of K, when the transfer functions of the system are given as: Gc= + 3 G p = Gips? +45 +10 and H= 0.1 c) For what values of K would the system have...
2. Derive an expression for (as) for a gas with the equation of state: P(V-nB) = nRT, where B is a constant. 2. Derive an expression for (as) for a gas with the equation of state: P(V-nB) = nRT, where B is a constant.
Derive the following relation: h/mec (1 − cos θ) = λ ′ − λ It is suggested you use the following strategy: First, use the momentum equations and the relation cos2 φ + sin2 φ = 1 to eliminate φ. Next use the energy equation and the relativistic relation E^2 = m^2 c^4 + p^2 c^2 to find an expression for the square of the momentum of the electron that does not depend on v (or γ). Finally, use this...
In the lecture we derived an expression for the heat capacity of a 3-dimensional solid. Derive a) 1 mark] Work out the density of modes in terms of wavenumber k, ie g(k)dk. b) [1 mark] Work out the density of modes in frequency space, g(w)dw. c) 12 marks] Work out the 2D Debye frequency W2 and temperature 62D in terms of the areal density PA-L2. d) [2 marks] Derive an exact expression for the total energy of vibrations U in...
3. The potential energy of an object is given by P=m.g.h, where m is the mass, g is the gravitational constant (9.81m/s), and h is the height of that object above some reference point. If we measure m and h, as well as their uncertainties om and Oh, and we know the value of g, which is a constant, we want an algebraic expression for the uncertainty on the potential energy, op. (a) First, lets break this up into P...