One way of thinking about the center of mass of an object is that the center off
ID: 2877366 • Letter: O
Question
One way of thinking about the center of mass of an object is that the center off mass is the object's balencing point. With a lamina (ie: a 2D solid), the center of mass will be a point in that figure. For the center of mass of a collection of points, you can visualize this same thing happening by drawing a polygon which connects your points, and then imagine that you placing weights at each of the designated points. Consider a regular hexagon whose sides have length 2 and whose center has been placed at the origin. Suppose that you have six weights (really masses), one of which you will place at each vertex of the hexagon. The masses are 1/2, 1, 2, 2, 3, and 5. You would like for the hexagon to balence at the origin once that masses have been placed on its vertices. To do this, you have ordered the vertices: P_1(-1, - squareroot 3), P_2(1, -squareroot 3), P_3(2, 0), P_4(1, squareroot 3), P_5(-1, squareroot 3), and P_6(-2, 0). Then you place the masses as follows: m_1 = 5, m_2 = 1, m_3 = 2, m_4 = 2, m_5 = 1/2, and m_6 = 3. Sketch a diagram of this situation (i.e: draw a picture). Find the total mass: m = M_y = M_x = What is the center of mass? Is the hexagon balenced where you wanted? If not, is it close?Explanation / Answer
b) Total mass = 13.5
c) My = -3.5 sqrt(3)
d) Mx =-4.5
e) Center of mass : left ( - rac{7 sqrt{3}}{22} ight ,- rac{9}{27})
f) No
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.