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Calculate the energy, corrected to first order, of a harmonic oscillator with potential:
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- The continuity equation satisfied by u = 4xy+y?, v= 6xy+ 3y 10 u= 3x^2-2y^2, v=-6xy .II O u=x-4y, v=y-4x .IIIOGrowth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The num- ber after t hours is shown in the accompanying figure. 250 200 150 100 50 0 1 2 3 4 5 6 7 a. Explain what is meant by the derivative P'(5). What are its units? b. Which is larger, P'(2) or P'(3)? Give a reason for your answer. c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by P(t) = 6.10r2 – 9.28t + 16.43. Find the instantaneous rate of growth when t = 5 hours.w = FjAc = F .Aë , W = m(v;)* - m(u,)* , v 1 zm(us)* - m(v,)* , W = Problem 1: (a) à = 3â – 2ŷ, B = 4â& – 5ŷ. à ·B =? Answer: 22 (b) à = -2â + 4ŷ, B = 3âu – lŷ. Ā·B =? Answer: –10 (c) à = 5â – 3ŷ, B = -3â – 5ŷ. ÷B =? Answer: 0 1 | F,dx , W = F. dř , F, dU W = -AU dx d = 4m F = 20 N 0 = 30° m = 4 kg Hk = 0.5) m = 2 kg F = 40 N Hk = 0.2 Ө — 30° Problem 2: In the figure above on the left we have a force F = 20 N pulling a box to the right at an angle 0 = 30° above the horizontal. The box has a mass m = 2 kg, the coefficient of kinetic firction between the box and the ground is uk = 0.2, and the block moves a distance d = 4 m to the right. (a) What is the work done by the force F? Answer: 69.3 J (b) What is the normal force from the ground? Use g = 10 m/sec² Answer: 10 N (c) What is the work done by the kinetic friction force? Answer: -8 J (d) What is Wnet, the net work done on the box? Answer: 61.3 J (e) The box has an initial speed of 4 m/sec. What is the speed of the box after it has…
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- If u⃗=<8,5>and v⃗=<−9,−2>, find projv⃗uO A) F(AD)*[(-0.5714) i+ (-0.0428) j+(0.4571) k] N O B) F(AD)*[(-0,3714) i+ (-0.5428) j]N O O F(AD)*[(-0.3714) i+ (-0.7428) j+ (0.5571) k] N O D) F(AD)*[(-0.7428) j+ (0.5571) k] N O E) F(AD)*[(-0.1714) i+ (0.3428) j- (0.3714) k] NS Can 6 PAR к Торс K Unit K In x K Moti = Cop K Unit S Spee S Topo S Math Micr eb.kamihq.com/web/viewer.html?source-filepicker&document_identifier=137VZR5BZOVSAIMOA55WU555_CvJ9NacO + 100 P e Interpreting Graphs Answer the questions following the graphs on each side Dietance va. Time 2 7 10 11 12 13 14 Time in soconds 1. From 1 second to 2 seconds, how fast is the object traveling. (Take the difference in distance and divide it by the time in between the 2 distances) 2. Is the object going as fast between 9 and 12 seconds as it is between 1 and 4 seconds? How can you tell? 3. What is the motion of the object between 4 and 6 seconds? acer
- and zr?> br Pr00 (rit)The continuity equation satisfied by u=x-4y,v=y-4x .1O U = 4xy+ y2, v= 6xy+ 3y .IIO u= 3x^2-2y^2, v=-6xy.III OThe state of an ideal gas is changed isothermally from position 1 to position 2 is shown below. What is the change in the internal energy of the gas during this process? ... P 1 2 >
