2) A uniform slender rod has a length, L, cross sectional area, A and a planar mass density distribution of p (kg/m^2). Determine the second moment of mass about an axis passing through the mass center perpendicular to the longitudinal axis. ANS. mL^3/12 N Z N dm X
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- 6. A cubical mass m2 is immersed in seawater (sg = 1.025), as shown, and balanced by another mass m1 = 850 grams. If the dimensions of mass m2 are (75 mm x 75 mm x 75 mm), determine the mass of m2, in grams. * - beam balance mass mass m2 seawater (sg = 1.025)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/5Two uniform, solid spheres (one has a mass M1= 0.3 kg and a radius R1= 1.4 m and the other has a mass M2 = 2M, kg and a radius R2= 2R;) are connected by a thin, massless rod of length L= 4R1. Find the moment of inertia (in kg.m2) about the axis through the center of sphere 1. (Igphere = MR?). Axis of rotation R, R2 a. 59.74 b. None of the choices O c. 117.13 d. 97.37 O e. 45.04
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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 nChoose the following systems that are equivalent to the one shown. Choose all that apply. (Remember conditions for equivalency require the sum of forces to be equal and the sum of moments about on arbitrary point to be equal) 50 N DA OB. OC OD. 1m 1 m 1 m 50 N 1 m 50 N 1 m 100 N 1 m 50 N 1m 50 N 1 m 50 N-m 1 m 100 N-m 1 m3) A slender rod of mass, m and length, L forms an angle 0 with the vertical axis A'-A'. Determine the mass moment of inertia and the radius of gyration of the rod with respect to the axis A'-A'. ANS. | = ML² sin²0 k= 3 L sin e √3 X L dm Ꮎ A' A'
- The mass moment of inertia I of a homogeneous sphere about its diameteris I = (2/5)m R², where m and R are its mass and radius, respectively. Find thedimension of I in terms of the base dimensions of (a) a gravitational [FLT] systemand (b) an absolute [MLT] system.Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2) * k1 Jo- k2 m2Z 50 N 3 m y 300 Nm 70 N 2 m 3 m 40 N 2 m 30 N Questions: (a) Reduce the system of forces and moments acting on the structure to a single resultant force (Fro) and a couple (Mro) acting at the origin of coordinates. (b) Determine the "parallel component” (M₁₁) of the couple (Mro), i.e., the compo- nent lying parallel to (F). State (M₁₁) in vector form. (c) Determine the corresponding "perpendicular component” (M₁). State (M₁) in vector form. (d) Reduce the force and couple at the origin to a "wrench resultant" and determine a precise and complete description of the line of action of the "wrench resultant."