Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x = -π/4, x = π/4.
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Find the center of gravity of the region
bounded by the x-axis, the curve y = sec x, and the lines x =
-π/4, x = π/4.
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- Pat builds a track for his model car out of wood. The track is 3 cm wide (along the z coordinate), 1 m high (along the y coordinate), and 2.7 m long (along the x coordinate starting from x = 0). The runway is cut such that it forms part of the left-hand side of a parabola, see figure below. Locate the horizontal position of the center of gravity of this track in m.A 84 gm meter stick has two objects attached to it, one of 92 gm at the 24 cm mark and the other of 183 gm at the 88 cm mark. At what mark on the meter stick is the center of gravity of the system?You are standing on flat ground. Your head and upper torso weighs 524.65 N, with a centre of gravity 1.248 m above the ground. The middle part of your body weighs 131.5 N, at 0.803 m above the ground. And the lower part of your body weighs 66.24 N, at 0.437 m above ground. Relative to the ground, find the location of the centre of gravity of your entire body.
- On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m^3, length 89.2 cm and diameter 2.45 cm from a storage room to a machinist. Calculate the weight of the rod, w. Assume the free-fall acceleration is g = 9.80 m/s^2. Express you answer in N.The uniform disk of mass m is rotating with an angular velocity of v0 when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass center. The coefficient of kinetic friction between the disk and the floor is μk.Consider the following distribution of objects: a 3.00-kg object with its center of gravity at (0, 0) m, a 5.20-kg object at (0, 3.00) m, and a 4.40-kg object at (4.00, 0) m. Where should a fourth object of mass 7.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)?
- A glass bead of diameter 1.70 mm and density 2.89 g/cm³ spins uniformly at a rate of 3T rad/s along a vertical nylon thread that cuts through an axis running through its center. Assuming the bead to be a regular solid sphere (lcom = (2/5)MR²) and neglecting the hole in the middle where the thread goes, report the kinetic energy of the bead in joules. 7.63 x 10-10 J 3.05 x 10-9 J 9.54 x 10-11 J 9.54 x 10-15 JA circular plate with radius r = 0.785 m lies next to a rectangular plate with base br = 0.948 m and height hr = 0.770 m which lies next to a triangular, plate with base bt = 1.41 m and height ht = 0.712 m. Determine the center of gravity of the rectangular plate in the y-direction if its surface density varies in the x and y-direction according to σr = 4.84 · x · y kg / m2.A 111 gm meter stick has two objects attached to it, one of 80 gm at the 10 cm mark and the other of 184 gm at the 76 cm mark. At what mark on the meter stick is the center of gravity of the system?