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Answer. We know that center of mass will move under the action of force of gravity So $\mathbf{r_c}=\mathbf{v_c}t+\frac{1}{2}\mathbf{g}t^2$ Or $\mathbf{r_c}=\frac{m_1\mathbf{v_1}+m_2\mathbf{v_2}}{m_1+m_2}t+\frac{1}{2}\mathbf{g}t^2$ Multiple Choice Questions Question 23 Two masses m 1 and m 2 separated by thin rod of length L.
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.
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.
(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
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
----- Problem 2 ----- Find the COM of a solid uniform right triangle. Answers 1. x_COM = 0.5786 m 2. x_COM = (2/3)*b for the "base" side on the x-axis, and the hypotenuse slanted in 1st quadrant and passing through the origin.
1. A 60 kg woman and a 90 kg man are standing 10 meters apart on frictionless ice. a. How far from the woman is the center of mass of the system? b. If they hold on to the two ends of a rope, and the man pulls the rope so he moves 2 meters, how close is he to the woman now? c. How far will the man have moved when he collides with the woman? 6 m ...
