The following masses m; are located at the given points P₁: m₁ = 6, P₁(1, -2) m₂ = 5, P₂(3, 4) m3 = 1, P3(-3,-7) m₁ = 4, P4(6,-1) Find the moments M₂, My, and the x and y-coordinates of the center of mass of the system. M₂ = My = z-coordinate of the center of mass: a = y-coordinate of the center of mass: y = 9.
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- The figure below shows the positions of the Centers of mass of the three disks on a rotating shaft. m. =6 kg, M2=4 kg, m3=5 kg, r-=100 mm, r2=200 ver3 = 300. B to dynamically balance the shaft it is desirable to place balancing masses of 3 kg each in their planes. Balancing find the positions of the center of mass (004) of mass A in the unit of cm and degrees. The D value in the figure is 200 mm. mlg my m1 37 53 200 mm 150mm 200 mm ma Please choose one nThe figure below shows the positions of the Centers of mass of the three disks on a rotating shaft. m1 =8 kg, m2=2 kg, m3=5 kg, r1=70 mm, r2=50 r3 = 110.B to dynamically balance the shaft balancing masses of 6 kg each are placed in their planes. A find the positions of the center of mass (ra, ra) of its mass in mm and degrees. The D value in the figure will be taken as 330 mm. Note: moment equations can be written according to the point 0 shown in the figure. B ma m2 60 40 320 mm 230 mm 350 mm t 50 mi Please select one: A.(17,068; OA=257, 270)Cartesian coordinat system; A(0,0,0) B(3,4,0) C(3,4,4) F=-20i +10 j+15k N is applied to point C Moment of force F about point A; M, Moment of force F about point B; M, Moment of force F about line AB; M AB Which following one is TRUE? ON MAB(-3i+4j)OM, O A) M = (3i – 4 j)®(-20i +10 j+15k) M, =(j)®(-20i +10 j +15k) O D Mg = 80i – 40j o M, = (3i+4 j+ 4k)® (-20i+10j+15k)
- Cartesian coordinat system; A(0,0,0) B(3,4,0) C(3,4,4) F = -20i+10j +15k N is applied to point C Moment of force F about point A; M, Moment of force F about point B; M, Moment of force F about line AB; MAE АВ Which following one is TRUE? Magnitude of moment about AB line {M(AB)} of force F is equal to the vector product of unit vector (3i+4j) and Moment vector of the force F about O A) point A. Moment magnitude of force Fabout AB line {M(AB)} is equal to the scaler product of unit vector (0.6 i + 0.8 j) and Moment vector of force F about point B) А. Moment vector of force F about AB line {M(AB)} is equal to the vector product the force Fand unit vector (0.6 i+ 0.8 i) Magnitude of moment about AB line {M(AB)} of force F is equal to the vector product of unit vector (0.6 i + 0.8 j) and Moment vector of the force F about D) point A. E) NONEFind the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. x² + y² = 36 x 20 y zo p=k(x² + y²) m = (x, y) =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.m
- A rod of mass M and length L is nonuniform such that its mass per unit length varies with x according to the expression x= a x*, where a is a constant. Find the x coordinate of the center of mass as a fraction of L. on -L▬ O a. 5L/6 O b. 3L/4 O c. 6L/7 O d. 4L/54) 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' bThe line of action of force F passes through points A and B. Find the moment of force F about axis CD in Cartesian vector notation, given : F = 45 N AX = 7 m, AY = 8 m, AZ = 10 m BX = 3 m, BY = 5 m, BZ = 5 m CX = 7 m, CY = 7 m, CZ = 8 m DX = 6 m, DY = 5 m, DZ = 4 m Answer Selection: MCD = <288, -74.5, -371> N·m <485, -61.9, -185> N·m <334, -51.3, -308> N·m <201, -44.3, -447> N·m <402, -30.9, -266> N·m
- Question 3 Three unbalance masses are as shown below, where m₁ = 150 g, m3 = 200 g, r₁ = 10 cm, 72 = 10 cm, 73 = 12 cm, l₁ = -20 cm, l₂ = 35 cm, l3 = 105 cm, l = 90 cm, 8₁ = -40°, 03 = 115°, and w = 20 rad/s. 1. Find mass m₂ and its angle 9₂ so that the magintude of the reaction in B is FB = 1.38 N and its angle is 0g = -78.4°. 2. Find magnitude and angle of the reaction in A. m₂ A 111₂ 1 110₂ 1₂ My 0₂ 11₂ m₂Find the only Reaction Force Bx (X-Component of the B Vector) 200 lb/ft 800 lb 37 B7 1 5 2' 4 25. Find the new location of point G; initially at G = [3 0 -1] If, (i) it is rotated by 60deg. about z-axis and then translated by 3 units along y-axis, and (ii) it is first translated by 3 units along y-axis and then rotated by 60deg bout z-axis. Are the two locations same? Check and justify, whether the final position in two cases is same or different.