A 30.3 cm-by-30.3 - cm checkerboard has a mass of 86.3 g. There are four 28.5-g checkers located on the Checkerboard, as shown in the figure. Relative to the origin located at the bottom left corner of the checkerboar s the center of mass of the checkerboard - checkers system? xcm = ;ycm = 11x
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- 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 cmA square plate with sides 1.5 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia of the plate is 16 kg - m². Use the values given in the figure to answer the following questions. (Assume 0 = 40°. Express your answers in vector form.) 30.0 N 60.0 N CM 20.0 N 40.0 N (a) What is the net torque acting on the plate?In the figure below, the masses of each object are: m₁ = 2.00 kg, m₂ = 2.00 kg, m³ = 3.00 kg. The labeled distances are: d₁ = 30.0 cm, d₂ = 106 cm, d3 = 60.0 cm (where d is the x distance for the center of the block). The height of each block is h₁ = 21.0, h₂ = 28.0 cm, and the h3 = 11.0 cm. Assume the center of mass for each individual object is at the center of the object. Hint: Consider the final center of mass (x,y) relative to the axes shown in the figure. Note the positions of the boxes relative to the axes and to one another. Determine the positions, x and y, of the center of mass for the system below. y Enter to 3 significant figures Center of mass (x, y): ( d1 m1 d3 d2 h1 cm m3 m2 h2 11h³ X ✔cm) Think and Prepare 1. For each of the boxes, m₁, m₂ and m3, where is the center of mass located? Carfefully, identify the
- For the area below, evaluate 1. The (x,y) coordinates of the centroid (please mark your origin or reference point on the diagram) 2. The 2nd moments and product of area in centroidal-based xy (horizontal-vertical) coordinates 3. The principal 2nd moments of area, and the direction of the first principal axis relative to the horizontal (x) axis (anticlockwise positive) 50 75 30 150 60 50 15 Figure 1: Cross section (all dimensions in mm) Quantity Xc (please mark your origin on the diagram) Yc (please mark your origin on the diagram) Ix ly Ixv I₁ I₂ a1 (please show the direction) Value 30 UnitsThe following diagram corresponds to questions 1 to 3. A beam rests on two sharp edges as shown on the image. The beam has a length of 7,50 m and a mass of 4,25 kg. Object 1 has a mass of 1,50 kg; object 2 has a mass of 2,35 kg. Point P is 0,50 m form the center of the beam. d 2 Pl CG 1. How much is the torque done by object 1 around point P? A. 55,2 N*m B. 7,36 N*m С. 62,5 N*m D. Object 1 doesn't exert a torque.3) A right circular cone of 30 mm diameter and 60 mm height is cut from a cylinder of 50 mm diameter and 120 mm height as shown in the figure. Find the position of the CG of the body from its base. 50 Ans CG of the given section is at (0mm, 62.87mm,0mm)
- It is common to hang objects on doorknobs and over-the-door hooks. There is a limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h = 2.5 m and width h/2 has a mass of M = 36 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door’s weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. 1.) calculate the force, with its sign in Newtons that the upper hinge exerts on the door in the x axis.…The following diagram corresponds to questions 1 to 3. A beam rests on two sharp edges as shown on the image. The beam has a length of 7,50 m and a mass of 4,25 kg. Object 1 has a mass of 1,50 kg; object 2 has a mass of 2,35 kg. Point P is 0,50 m form the center of the beam. CG 1. How much is the torque done by object 1 around point P? A. 55,2 N*m B. 7,36 N*m C. 62,5 N*m D. Object 1 doesn't exert a torque. 2. How much is the torque done by the force of gravity of the beam around point P? A. 20,8 N*m N-m ך177 .B C. 156 N*m D. 313 N*m 3. If you needed to cancel the nomal forces of the two objects, where you should place object 2? The axis of rotation is point P. A. 3,30 m from point B. 9,18 m from point P C. 5,69 m from point P D. 3,62 m from point PTwo forces act on the pipe assembly as shown in the figure. Determine the following: 3.1 The magnitude of the resultant FR is Blank 1 lb. 3.2 The coordinate direction angle Alpha of FR is Blank 2°. 3.3 The coordinate direction angle Beta of FR is Blank 3°. 3.4 The coordinate direction angle Gamma of FR is Blank 4°.
- Find the volume of a right circular cylinder of radius a and height h if the density varies as the distance from the base. Note :- By Triple Integrals |C0nsider the figure bel0w where each square is 1 ft on a side and A =58lb, B =58lb, and C =182lb. Calculate the resultant m0ment of the f0rces (in lb-ft) about point O. (Answer: -690.19lb-ft)Consider the U-beam section shown in the figure below. The beam section splits into 3 segments (assuming it to be made of uniform, material and the mass of the vertical segment is double the mass of the horizontal segments). Find the y-coordinate of the center of mass from the bottom of the beam section (in cm). 120 cm 30 cm 180 cm + 40 cm 30 cm Origin 120 cm O a. 120.0 Ob. 177.5 Oc 214.3 O d. 52.5 O e None of the choices