The concept of center of gravity or weight was studied extensively by the ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse. 2.4 Systems with periodic boundary conditions.The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. Calculations in mechanics are often simplified when formulated with respect to the center of mass. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. Theoretical (6 ) Case 2: Theoretical, Case 3: Theoretical For the Results and Conclusion sections, include a comparison of experimental and theoretical results.This toy uses the principles of center of mass to keep balance when sitting on a finger. m e) (cm) m(s) (cm) m(B) x (cm) Case I 15 NA NA Case 2 3 0 70 Case 3 10 90 NA NA (cm) x=, Laboratory 9: Torque, Equilibrium, and the Center of Gravity Find the location of the center of mass, ie, the point where the stick will balance Data and Data Analysis - center of mass of meter stick= m = mass of meter stick m = mss of hanger clamp Note: Form, my, and m, remember to include the mass of the hanger clamp, m. Place 100 g at the 10 cm position and 200 g at the 90-cm position. Repeat the activities of 2, except use the following masses, 100 g at the 30-cm position and 200 g at the 70-cm position Suspend m = 50 and find y, so this mass will balance out the meter stick. If you use the hanger clamps to suspend the masses, remember to include their masses in m 3. Suspend a second mass, 200 g on the opposite side of the stick as my, and place it at the distances needed to balance the meter stick. With the meter stick on the support stand at suspenda mas 100 g at the 15-em position on the stick. Tighten the clamp and record the distance of the balancing point from the zero end of the meter stick 2. Place a knife-edge clamp on the meter stick at the 50-cm lime and place the meter stick on the support and Ad the meter stick through the camp at the meet stick is balanced on the stand. Transcribed image text: Laboratory #9 Report Sheet: Torque, Equilibrium and Center of Gravity Objective The purpose of this laboratory is the Tid bodies mechanical equilibrium toque and how it apo Suggested Procedure 1.
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