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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
(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
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.
The center of mass is located 2.5 m from 3 kg point mass, (and 1.5 m from the 5 kg point mass) on X-axis. This result shows that the center of mass is located closer to larger mass. If the origin is shifted to the center of mass, then the principle of moments holds good.
----- 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.
MA 114 Worksheet #19: Centers of Mass 1. Find the center of mass for the system of particles of masses 4, 2, 5, and 1 located at the coordinates (1;2), ( 3;2), (2; 1), and (4;0). 2. Point masses of equal size are placed at the vertices of the triangle with coordinates (3;0), (b;0), and (0;6), where b > 3. Find the center of mass. 3.
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 ...
