4) Use the parallel axis theorem to determine the second moment of mass about the z-axis through the origin for a thin rectangular plate with base b, and height h. Ул ANS. Z 3 [b² + h²] (kg-m^2) h z' b
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- Let A and B be two nonparallel vectors that lie in a common plane S. If C=A(AB), which of the following statements are true: (i) C = 0; (ii) Clies in plane S; and (iii) C is perpendicular to plane S?It can be show that a plane area may he represented by a vector A=A, where A is the area and represents a unit vector normal to the piano: of the area. Show that the area vector of the parallelogram formed by the vectors a and b shown in the figure is A=ab.A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what distance d will kx for the new region be the same as kx (for the region before the cutout was removed?
- Determine and locate the resultant of the system shown in fig (3). If you know that the values of Ax=240 N. Ay=2000 N. F=160 N, N=2400N, W=400 N and M=2N.mDetermine the resultant of the following concurrent forces: 8 N, 60o N of E and 40N, 45o N of W using: a. law of sine and cosine, andb. parallelogram method For b use the scale: 2N =1 cm.The uniform lamina of density 2.2 kg/m2. for a=2.2 m,b=4.8 m,c=8 m,d=8.9 m, 1- x-co-ordinate of shape (1) is: (a. 1.78 - b. 2.23 - c. 4.45 - d.8.90 - e. 2.97 ) 2- y-co-ordinate of centroid of shape (2) is: (a. 3.80 - b. 4.52 - c.2.33 - d. 5.28 - e. 4.60 ) 3- The total area is: (a.81.50 - b. 150.78 - c. 52.98 - d. 69.27 - e. 110.03) 4- The total mass is: ( a. 163.00 - b. 326.00 - c. 244.50 - d. 81.50 - e. 40.75 )
- Object A, whose center is at (2.0m, 2.0m) has a mass of 40 kg. Object B has its center at (10m, 4.0m) and has a mass of 30 kg. What are the components of their center of mass in m?Objects 1 and 2 have masses M1 and M2, respectively, where M1<M2. The objects are in outer space far away from any other objects, as shown above. Point PP is located halfway between their centers. At what location, if any, is the gravitational field due to the two objects equal to zero?The collar C is fixed to AB and supports a weight W=15 N, acting in the negative z direction. What is the vector component of the weight that is perpendicular to AB?
- For the vectors A = 8.0m South and B = 15.0 m, 300 E of N, use the method of components to find the magnitude and direction of the vector difference A – B.2 - Constant thickness homogeneous planar plate in the figure coordinates of the center of gravity M (Xm, Ym) of the surface area, Find it on the (x, y) set. t = 3 cm and a = 9 cm. Find the coordinates (Xm; Ym) of the rectangle extracted from this planar plate in the x and y axes.A) (9; 25.5)B) (9; 13)C) (9; 18)D) (9; 15)E) (9; 22.5)Consider the image below: A horizontal beam of length 8 m is pinned at its left end so that it is free to rotate about that end. It has a nonuniform linear mass density given by λ(x) = 78 x (kg/m). Its right end is secured by a rope, the angle shown being 45 degrees. Calculate the magnitude of the tension in the rope, in N. (Please answer to the fourth decimal place - i.e 14.3225)