1. Find the center of mass of a thin plate (lamina) of constant density p located between the curves y = x and y = x2. 2. Miscellaneous exercise 9 (p. 510): 15. 3. A spring has a natural length of 20cm. A 25N force is required to stretch the spring to a length of 30cm. How much work is required to stretch the spring from its natural length to a length of 25cm?
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- The opposite figure is composed of a rectangle (b=12.2 , h=6.1 m , density 4 kg/m2) and a triangle (b=12.2 , a=3.05 m , density 8 kg/m² ). The mass of total shape is E a TD h x b/4 h/3 A В Select one: O A. 446.52 O B. 723.36 O C. 1035.93 O D. 1125.23 O E. 98.23 XG = Select one: O A. 9.39 О В. 6.04 O C. 8.65 O D. 3.73 O E. 0.82 YG = Select one: O A. 0.90 ОВ. 1.23 OC. 2.37 O D. 4.22 O E. 0.76For the section shown below, composed of a semicircle together with a ¼ circle, we are asked to determine the polar moment of inertia about O in cm^4. Tip: use the geometric property tables of the sections to solve the problem. Source: Porto (2014, p. 51). PORTO, M. A. Exercises for vector mechanics. Sao Paulo: University of Sao Paulo, 2014. 4 question options: a) The moment of inertia is 8654.21 cm^4. B) The moment of inertia is 3926.99 cm^4. c) The moment of inertia is 10865.98 cm^4. d) The moment of inertia is 7853.98 cm^4. e) The moment of inertia is 11708.97 cm^4.Given: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael Swanbom
- During a bicep curl on a bicep curl machine, I'm curling a weight stack of 100 pounds (single arm...I'm jacked like that). At this very moment, the weight stack has a moment arm of 0.12m, my elbow has an angle of 63deg, my muscle force vector has an angle of 23deg, and it attaches 3cm below my elbow joint on my radius. How much force must my bicep create right at this moment to hold the weight stack in place?A rectangular tube of outer width w = 7.5 m, outer height h = 5 m and thickness t = 0.17 m experiences bending through the x axis. What is the moment of inertia of the cross-sectional area In? y -- X MATLAB input variables: format shortEng W = 7.5; h = 5; t = 0.17; moment of inertia I, = m4m, zm 2. Two particles of equal masses move on a frictionless harizontal surface. Their center of kr? mass is fixed and their potential energies are krž and Also, they interact with each other with potential 2 akr2 Ris the distance between the masses, and k and a are positive constants. a. Find the Lagrangian in terms of the center of mass position CM, R and the relative position r. b. Solve the Lagrange equations for the relative coordinates X,Y and x,y. c. Explain the physical outcome of the results obtained in b.
- 2. In class, we derived an expression for hR/RT for a gas that obeyed the Pressure Explicit Virial Expansion truncated after the third term. In class, we assumed that B and C were not functions of temperature. a. Please rework the derivation with B = B(T) and C = 0. b. Please continue the derivation under the assumption that B(T) = mT + b. Where m and b are the slope and y-intercept of a straight, respectively. %3DA physics lab Consist of a large bowl attached to wire. Students hold onto one of the wire the whirl the ball around in circles and count the number of rotations per second. One group finds these numbers: ball mass=320g, wire length=1.3m, number of rotations/second=2.5. The wire is made of steel with a diameter of 1mm and a Young’s modulus of 20x10^10 N/m^2. How much does the wire stretch due to the tension on it? Should the students correct their data for the wire stretching?The following related values of the pressure p in kN/m2 and the volume V in cubic meter where measured from the compression curve of an internal combustion engine indicator diagram. Assuming that P and V are connected by the law PVn: C, find the value of n. p 3450 2350 1725 680 270 130 V .0085 .0113 .0142 .0283 .0566 .0991
- This problem is (16.23) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"The left and right water edges of a river are 2.75m and 62.45m, respectively, from an initial reference point. Verticals are located at distances 11.25, 19.25 26.75, 34.45, 40.95, 46.95, and 54.45 m, respectively from the reference point. The corresponding depths of verticals are 5.00, 9.60, 9.80, 10.00, 10.40, 10.00, and 4.80m. Mean velocities in the verticals are 0.16, 0.60, 0.75, 0.92, 0.97, 0.98, and 0.65 m/s respectively. A. Determine the Total Discharge of the river. B. Determine the average velocity of the river flow.3G 9:.. %79 Final 1st attem... F2 У - ахis Fs F4 F1 х - ахis X- axis y - axis F3 F2 F1 Figure (1) Figure (2) 250 N 36.87 D F2 60° 0.5 m 1 m o! 0.2 m 1 m 300 NE F1 1 m Figure (3) Figure (4) Q1] Answer the following questions: For figure (1): The object is subjected to two forces F1 = 25 N, and F2 = 50 N. Set x = 30°, 0 = 45° , and ß = 30°. 1- What is the magnitude of the resultant of these two forces? a) 39.4 N b) 80.1N c) 41.6 N d) 69.8 N e) 71.4 N f) 46.1 N g) None of them 2 - What is the direction of the resultant force measured counterclockwise from the positive x-axis? а) 14.30 b) 392.6° c) 9.2° d) 322.9° e) 6.8° f) 344.2° g) None of them For figure (2): The arm in is subjected to five forces as follows: F1 = 135 N, F2 = 98 N, F3 = 210 N, F4 = 56 N. If the y – direction resultant force is 144 N, and x = 40°, 0 = 50°, B = 70°: 3 – What is the magnitude of the force F5? a) 318.4 N b) 99.1N c) 151.6 N d) 36.5 N e) 111.2 N f) 18.8 N g) None of them 4 - What is the magnitude of the…