Three balls are located on x axis as
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. Break it down: The system consist of three objects. Three balls All of objects lie on the “x” axis and system is in equilibrium state. When a system is in equilibrium state it either does not move or move with constant speed. are located on “x” axis as shown in the picture, find the center of gravity for the system. For a rigid system center of gravity is a point that we can assume all forces (here weight) applied to the system are applied to this point A rigid system is a system that masses do not move relative to each other. In other words the distances between all masses in the system is constant. Physicsfix. com
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. Solution: Ø Draw a diagram m 2 = 1 kg m 1 = 4 kg 2. 0 m 1. 0 m m 1 g m 3 = 3 kg m 2 g m 3 g The total force applied to this system is [(m 1 + m 2 + m 3) * g] Physicsfix. com
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. +Y Solution: We have to find a point that we can assume this force is applied to that. This point is center of gravity. -X +X Ø Choose a coordinate system (x-y) When the system is in equilibrium it does not matter where we locate the axes. To simplify, it’s better to locate the origin (0, 0) on one of the masses. Let’s put the origin on m 2. Physicsfix. com -Y
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. Solution: Ø Determine known parameters m 1 = 4 kg X 1 = -1 m m 2 = 1 kg X 2 = 0 m 3 = 3 kg X 3 = +2 m negative sign shows that m 1 is located on the left hand of the origin m 2 is located on the origin m 3 is located on +x axis, 2 m far from the origin Ø Calculate location of center of gravity We use notation Xcg to show the location of center of gravity on X axis (x coordinate of center of gravity) We calculate it by equation: Xcg = Σ (mi * Xi)/ Σ mi Where (Σ (mi * Xi) is the sum of the produt of each mass and its distance from the origin. Σ (mi * Xi) = m 1 X 1 + m 2 X 2 + m 3 X 3 and Σ mi = m 1 + m 2 + m 3 Physicsfix. com
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. Solution: Ø Calculate the enumerator and denominator Σ (mi * Xi) = m 1 X 1 + m 2 X 2 + m 3 X 3 Σ (mi * Xi) = [4*(-1) + 1*(0) + 3*(+2)] Σ (mi * Xi) = - 4 + 0 +6 Σ (mi * Xi) = +2 kg. m Σ mi = m 1 + m 2 + m 3 Σ mi = 4 + 1 + 3 Σ mi = 8 kg Calculate Xcg by dividing Σ (mi * Xi) to Σ mi Xcg = Σ (mi * Xi)/ Σ mi Xcg= +2 kg. m/8 kg = + 1/4 m or Xcg = + 0. 25 m The positive sign shows that Xcg lies on +x axis, 0. 25 m far from the origin. Physicsfix. com
Three balls are located on “x” axis as shown in the picture, find the center of gravity for the system. Solution: we can have: These two systems are equal and it is much easier to use the second system. Physicsfix. com
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