Numerade

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Q2. Blocks A and B are positioned as shown in the figure. Block A has a mass of 3 kg, and block B has a mass of 5 kg. The blocks are connected by a cable, and there is friction at the surfaces between block A and block B, as well as between block B and the ground, with coefficients of static friction $\mu_s$=0.4 and kinetic friction $\mu_k$=0.3 for both. (i) Draw the free body diagrams of block A and B for the static case. (ii) Determine the maximum external force P in Newtons that can be applied to block A to initiate motion (impending motion). (iii) Calculate the corresponding tension on the cable. Now you can analyze the system under dynamical conditions where the acceleration is different than zero. (iv) Draw the free body diagrams of block A and block B for the dynamical case. (v) If P=55 N calculate the acceleration of block A and the acceleration of block B. Please state the directions of accelerations for each of them together with magnitudes. (vi) Calculate the tension on the cable for this case. (vii) Compare the tension you calculated in step (iv) (dynamic case) with the one from step (iii) (static case). Comment on why the tensions are different, even though the applied force P=55 N is close to the maximum static force found earlier. (viii) Calculate the tension if there is no friction in either surfaces. Compare the values of tensions and corresponding accelerations with the previous ones as well.

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Q3. (a) In Fig. Q3-1, a memory chip has 17 address pins (i.e., from A0 to A16) and 8 data pins. What is the memory range assigned to the memory chip? (4 marks) (b) Consider a 2-way set associative cache with eight sets, two blocks per set, 4 bytes per block, and a memory address size of 13 bits. Fig. Q3-2 shows the content of the cache memory. Note that invalid cache lines are left blank. (1) Show the memory address format for tag, set, and byte fields. (3 marks) (2) What is the memory address to access the memory content "99" in the cache? (4 marks) (3) How to update the content of Set 5 Tag 6E in the cache? (6 marks) Set Tag Data (byte field) 00 01 02 03 0 09 FF 01 23 80 1 45 80 3F 90 99 2 EB 3 06 4 C7 FF FF FF FF 5 71 01 AA 21 58 6 91 00 00 00 FF 7 46 Tag Data (byte field) 00 01 02 03 00 30 00 00 00 38 OB 32 45 32 00 F2 05 F2 00 23 23 6E FO DE 10 00 00 00 Fig. Q3-2

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Metronidazole is NOT effective in the treatment of which of the following? A) Pseudomembranous colitis B) Amebiasis C) Trichomoniasis D) Infections due to Bacteroides fragilis Giardiasis F) Infections due to Pneumocystis jiroveci

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A particle is moving along a straight line such that its acceleration is defined as , where v is in meters per second. If when and , determine the particle’s position, velocity, and acceleration as functions of time.

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The graph of a function $f$ on the interval $[0, 10]$ is shown in 8 6 4 2 2 4 6 8 10 Estimate the area under the graph of $f$ by dividing $[0, 10]$ into 10 equal subintervals and using right endpoints as sample points. 1. area $\approx$ 56 2. area $\approx$ 53 3. area $\approx$ 57 4. area $\approx$ 54 5. area $\approx$ 55

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The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, $\hat{y} = b_0 + b_1x$, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 24 26 44 46 49 Number of Bids 1 2 3 4 9 Table Copy Data Step 4 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable $\hat{y}$. Answer How to enter your answer (opens in new window) 2 Points Tables Keypad Keyboard Shortcuts

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[9](b) Commutator algebra As will be seen in week #5, the regular way of solving the Schrodinger equation and finding the wavefunction is very tedious in math, thus we will introduce a much easier and more elegant alternative to determine the eigenvalues and eigenfunctions of a harmonic oscillator. Define two operators: $\hat{a}_{+} = \frac{1}{\sqrt{2}}(\hat{x} - i\hat{p})$ and $\hat{a}_{-} = \frac{1}{\sqrt{2}}(\hat{x} + i\hat{p})$ Please use the commutator formula (in formula sheet) and the Dirac's Quantum Condition $[\hat{x}, \hat{p}] = i$ ($\hbar = 1$ in the reduced unit) to prove by algebra that $[\hat{a}_{+}, \hat{a}_{-}] = -1

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V1 RRef RRef VD1 VD2 (a) V1 (b) Figure 3: Left, one diode as a reference. Right, doubling our reference. Assuming we are using the same diodes as in the previous section, compute the ex- expected values of VD1, VD2. Now assume that the source voltage has a sinusoidal noise component (i.e V1 = VDC + Vn sin(2?100t)). Derive an expression for the incremental output voltage (?Vo) in terms of the diode incremental resistance $r_d$ for each circuit.

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4) y = 13 1.75w + 8.95 - 0.6w³ 5) Suppose a round-trip airline ticket from Buffalo to Syracuse sells for price \"p\" (measured in dollars). For this route, a regional airline found that daily demand for tickets \"x\" can be represented by: $x = 256 - 0.01p^2$ 5a) For this round-trip airline ticket, find the expression for Elasticity of Demand \"n\" and simplify. 5b) Evaluate the Elasticity of Demand for p = $100. Solve Elasticity of Demand to 3 decimal places. • Classify the type of Elasticity you found at this price. • Then predict impact on Revenue of a price increase in \"neighborhood\" of this price point.

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Q3. [16+16 = 32 points] Consider the pulley system as shown below. The 20-kg mass is hanging from the bearing of the pulley C. The stepped-pulley A is formed by fastening two light pulleys (as one integral unit). The stepped pulley A is prevented from turning about the bearing at O by the two cables wound securely around the two steps and fastened to points P and Q. The radii of the two steps are shown in the figure. Determine: (a) The tension T in the cable around the smaller step (b) Components of the bearing forces $O_x$ and $O_y$

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ronald d.