•• A meter stick is moving with speed relative to a frame S. (a) What is the stick’s length, as measured by observers in S, if the stick is parallel to its velocity v? (b) What if the stick is perpendicular to v? (c)What if the stick is at to v, as seen in the stick’s rest frame? [HINT: You can imagine that the meterstick is the hypotenuse of a 30–60–90 triangle of plywood.] (d) What if the stick is at 60° to v, as measured in S?

Not hand-writing please (only if it is very clear).

I only need part c and d.

2. A 15-MΩ resistor and a 48-nF capacitor get connected in series to a 15-V battery. a. How long will it be until the capacitor is “fully” charged? b. If the battery is then disconnected from the circuit, how long will it be until the capacitor’s voltage is 9.0 V? What is the charge of the capacitor at that moment? c. If we’d like the capacitor’s voltage in this circuit to decrease from 15-V to 9.0-V in 1.5 seconds after the battery gets disconnected, how should the capacitance of the capacitor change (increase or decrease, and by how much)?

A capacitor of unknown capacitance C is charged to 130 V and connected across an initially uncharged 75 uF capacitor. if the final potential difference across the 75 uF capacitor is 47 V what is C? After you find the value of C, you charge this capacitor C to a potential difference V=140 V between its plates. The charging battery is now disconnected and a slab material ( k=7.20 is slipped between the plates. what is the potential energy of the device, both before and after the slab is introduced?

ive an example of a simple, undirected graph that has a single source shortestpath tree which breadth-first search will not return for any ordering of its vertices.Your answer must

(a) Specify the graphG= (V, E)by specifying V and E.

(b) Specify the single source shortest path treeT= (V, ET) by specifying E T and also specifying the roots∈V.

(c) and include a clear explanation of why the breadth-first search algorithm we discussed in class will never produce T for any orderings of the vertices.

Determine the quality (if saturated) or temperature (if superheated) of the following: (show details of your answer, not just write the final answer)

a) Water at p=50 kPa, v=1 m3/kg

b) Water at p=1.6 MPa, v=0.15 m3/kg

c) Water at p=7 MPa, h=3160 kJ/kg

d) Refrigerant R-134a at p=200 kPa, v=0.009 m3/kg

e) Refrigerant R-134a at p=0.2 MPa, v=0.12 m3/kg

Annotate these equations

v=d/t a=∆v/t average speed =total distance/total time v=v0+at d=v0t+1/2at² Fnet=ma w=mg ac=v²/r Fc=mv²/r W=Fd   P=W/t   

EK=1/2mv² W= ∆EK   Es=1/2kx² Eg=mgh TC=5/9(TF−32) TF=9/5TC+ 32 TK=TC+ 273 Q=mc∆t Q=±mL

Which of the following are true?

(1) The sum of two invertible matrices is invertible

(2) The determinant of the sum is the sum of the determinants

(3) The determinant of the inverse is the reciprocal of the determinant

(4) An nxn matrix is invertible if and only if its determinant is zero

(5) The product of two invertible matrices is invertible (so long as the product is defined)

(6) If A is a diagonal 3x3 matrix [a,0,0;0,b,0;0,0,c] then its determinant is the product of its diagonal entries

(7) The union of two subspaces is a subspace

(8) The intersection of two subspaces is a subspace

(9) The set of solutions [x,y,z,u,v] to the equations 3x + 4y + 5z + u + 3v = 12 and 4x + y + z + u - v = 13 form a vector space

(10) If V is a vector space of polynomials and p and q are in V then the product pq is also in V

(11) If V is a subspace of R^3 and w is a vector in v then whenever the dot product w dot u = 0, u must also be in the subspace V

(matrices are written as e.g. [a,b,c; d,e,f; g,h,i; j,k,l] to mean the matrix whose first row is [a,b,c], whose second row is [d,e,f] whose third row is [g,h,i] and whose fourth row is [j,k,l].)

MATLAB question!

4. (a) Modify the code, to compute and plot the quantity E = 1/2mv^2 + 1/2ky^2 as a function of time. What do you observe? Is the energy conserved in this case?

(b) Show analytically that dE/dt < 0 for c > 0 while dE/dt > 0 for c < 0.

(c) Modify the code to plot v vs y (phase plot). Comment on the behavior of the curve in the context of the motion of the spring. Does the graph ever get close to the origin? Why or why not?

given code
---------------------------------------------------------------

clear all;   
m = 4; % mass [kg]
k = 9; % spring constant [N/m]
c = 4; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 =-0.8; v0 = 0.3; % initial conditions
[t,Y] = ode45(@f,[0,15],[y0,v0],[],omega0, p); % solve for 0<t<15
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'ro-',t,v,'b+-');% time series for y and v
grid on; axis tight;
%---------------------------------------------------
function dYdt = f(t,Y,omega0,p); % function defining the DE
y = Y(1); v = Y(2);
dYdt=[ v ; -omega0^2*y-2*p*v]; % fill-in dv/dt
end

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Vapor pressure of a pure liquid lab experiment

Why is the value of the heat of vaporization for sucrose greater than water? comment on the effect of a non-electrolyte such as sucrose on the vapor pressure and delta vap H.

What can be the possible systematic source of error in this experiment?