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In this question, we define the system to be astronaut and the instrument, and the center of mass of the system is initially at rest a distance of 10 meters from your spaceship. Since there are no external forces acting on the system and the center of mass is initially at rest, the location of the center of mass of the system can never change.
The solutions provided show students step-by-step methods for solving center of mass problems by using calculus, geometry, and algebra to find the x and y coordinates of the center of mass. Finding the center of mass of objects is important in physics.
Common center of mass problems involve composite objects made of simple uniform objects attached together, such as rods, disks, shells, and other basic shapes. The solutions to these problems use the formulas for the center of mass of basic uniform objects and the principle of superposition.
Locate the position of center of mass of the two point masses (i) from the origin and (ii) from 3 kg mass. Solution. Let us take, m1 = 3 kg and m2= 5 kg. (i) To find center of mass from the origin: The point masses are at positions, x1 = 4 m, x2 = 8 m from the origin along X axis. The center of mass xCM can be obtained using equation 5.4.
(a) Show that the centre of mass of the lamina is 26 cm from the edge AB . (b) Explain why the centre of mass of the lamina is 5 cm from the edge GF . (c) The point X is on the edge AB and is 7 cm from A , as shown in the diagram below. Answer all questions. A hot air balloon moves vertically upwards with a constant velocity. When the balloon is at
Give an explanation in terms of external forces and center-of-mass concepts. The net external Force on the system is zero, so there is charr in the position the center O-R mass.
4729 Mark Scheme June 2005 A1 1 (i) use of h/4 B1 com vert above lowest pt of contact B1 can be implied r = 5 x tan24° M1 r = 2.2 A1 4 2.226 (ii) No & valid reason (eg 24 ° 26.6 ) B1 1 Yes if their r ! 2.5 5 2 v2 = 2x9.8x10 M1 energy:½mv2=½mu2 + mgh v = 14 A1 ½v2 = ½.36 + 9.8x10 speed = √(142 + 62) M1 (must be 62) v2 = 36+196=232
