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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9496fb66-15f0-4d2e-bc7e-ca3bb9b70577%2Fe045e686-b488-4475-b1b3-9825fc5ab101%2Fnhy5p_processed.png&w=3840&q=75)
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- Z 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."5. Consider the flat object bounded by the curves y = 4x and y = Vx +b where (b=2). The area density of the M object is o = yx where the relationship between the total mass M and y is = 0.0309. Find the y-coordinate of the center of mass of this object (do not find the x coordinate of the center of mass). 1 y em Ym = vdm MENGINEERING MECHANICS: STATICS (J.L.MERIAM) 2/4: The line of action of the 9.6-kN force F runs through the points A and B as shown in the figure. Determine the x and y scalar components of F. Ans. y, mm B (300, 100) X, mm F 9.6 kN A(-150,-200) 2/5: A cable stretched between the fixed sunnorts A and Bis under a tencien Tef 000 NL
- 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/53. Volume of Brillouin zone. Show that the volume of the first Brillouin zone is (27)³/V where Ve is the volume of a crystal primitive cell. Hint: The volume of a Brillouin zone is equal to the volume of the primitive parallelepiped in Fourier space. Recall the vector identity (×ā) × (axb) = c.(axb)ā.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)
- I desire to pull down a tree (object ABCDE). To do this, I tie a rope to the tree 1 meter off the ground. I then pass that rope around a nearby stump (G) and tie it to my car. The rope and all portions of the tree (limbs and trunk) are purely in the x, y, or z direction. For example, CBE is parallel to the Y axis, while DC is parallel to the X axis. Assume my car is applying 1000 N of tension to the rope. If the coefficient of static friction between the trunk (G) and the rope is .4, what is the magnitude of the force pulling on the tree at A. You may treat trunk G and the rope as a flexible flat belt over a fixed drum. 2 D X C 2 J Z B 3 E Fig 2: Using a car to pull down a tree.Find the center of mass of the structure about point A of the figure below. Assume a uniform thickness of 15 cm, and a uniform density of 4.0 g/cm³. sphere, radius = 10 cm 58 cm 3 cm XCM = ++ 28 cm ♦ A A -58 cm- 1 72 cm 10 cm 14 cm T YCM = width .5 cmHelp Required information Consider the following vectorial representations. Add the three vectors shown to form a resultant vector R, and report your result using polar vector representation. Take Y= 3 m. 2 m 3 m 30° m @ 2 (Enter a positive value for the phase angle.)
- Determine the following: 1. The position vector of point B with respect to point A: rBA = ( i + j + k)m 2. The unit vector in the direction of vector F: u = ( i + j + k) Express your results using three significant figures.2000Lbs 30° 60° y A' \ B The bar OA is fully constrained at O and attached to the cable AB. The bar length is 20', and it forms a 30° angle with the z-axis and its projection on the x– y plane forms a 60° angle with the x-axis. The point B is prescribed by the coordinates (8',16',0). If the force in the cable is 2000Lbs, what is the moment of this force about O? What is the moment of the 2000Lbs force about the axis OÁ.A triangular plate is supported by a ball and socketat point A, a roller at point B, and a rope at point C. Thedimensions are given along the line of AB. Determine thereactions at all supports and report your answers in cartesianvector form. Free Body Diagram.