The (x, y) coordinates of the center of mass of the three-particle (m,=m2=1 kg, m3-4 kg) system shown below are: v (m) 4m m 3m 2m 1m 1m 2m 3 m 4m r (m)
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A: See below
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A: position of center of mass rcm = (m1 r1 +m2 r2 )/(m1 + m2 )
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- A metal soda can of uniform composition has a mass of 0.134 kg and is 12.6 cm tall (see the figure). The can is filled with 1.42 kg of soda. Then small holes are drilled in the top and bottom (with negligible loss of metal) to drain the soda. What is the height h of the center of mass of the can and contents (a) initially and (b) after the can loses all the soda? (c) If x is the height of the remaining soda at any given instant, find x when the center of mass reaches its lowest point. (a) Number i Units (b) Number i Units (c) Number i Units Splash!The figure shows a two-ended "rocket" that is initially stationary on a frictionless floor, with its center at the origin of an x axis. The rocket consists of a central block C (of mass M-6.50 kg) and blocks L and R (each of mass m-1.20 kg) on the left and right sides. Sm explosions can shoot either of the side blocks away from block C and along the x axis. Here is the sequence: (1) At time t-0, block Lis shot to the left with a speed of 3.30 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at timet -0.6 s, block R is shot to the right with a speed of 3.30 m/s relative to the velocity that block C then has (after the second explosion). At t -3.30 s, what are (a) the velocity of block C (including sign) and (b) the position of its center? (a) Number (b) Number Units UnitsPlease answer question 7
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- An outlaw cuts loose a wagon with two boxes of gold, of total mass 300 kg, when the wagon is at rest 50 m up a 6.0° slope. The outlaw plans to have the wagon roll down the slope and across the level ground, and then fall into a canyon where his accomplices wait. But in a tree 40 m from the canyon’s cliff wait the Lone Ranger (mass 75.0 kg) and Tonto (mass 60.0 kg). They drop vertically into the wagon as it passes beneath them (Fig.). (a) If they require 5.0 s to grab the gold and jump out, will they make it before the wagon goes over the cliff? The wagon rolls with negligible friction. (b) When the two heroes drop into the wagon, is the kinetic energy of the system of heroes plus wagon conserved? If not, does it increase or decrease, and by how much?Three particles have masses and position vectors as follows: a l br M 71 = i + 2j-3k-nx=Ley=2 T2 = 4i – j 73 = 3j+ 4k M1 3.0 kg m2 = 1.0 kg m3 = 5.0 kg y= 3 Z=4 Where is the center of mass of the system? The lo e to