University:
Boston University
Course:
CAS PY 252 | Principles of Physics 2
Academic year:

2024
Views:

154

Pages:

23
Author:

Clint W.

11.7 Stability When an object is toppled, the center of gravity of that object is raised, lowered, or unchanged. 11.7 Stability It is nearly impossible to balance a pen upright on its point, while it is rather easy to stand it upright on its flat end. • The base of support is inadequate for the point and adequate for the flat end. • Also, even if you position the pen so that its CG is exactly above its tip, the slightest vibration or air current can cause it to topple. 11.7 Stability Change in the Location of the CG Upon Toppling What happens to the CG of a cone standing on its point when it topples? The CG is lowered by any movement. We say that an object balanced so that any displacement lowers its center of mass is in unstable equilibrium. 11.7 Stability A cone balances easily on its base. To make it topple, its CG must be raised. This means the cone’s potential energy must be increased, which requires work. We say an object that is balanced so that any displacement raises its center of mass is in stable equilibrium. 11.7 Stability A cone on lying on its side is balanced so that any small movement neither raises nor lowers its center of gravity. The cone is in neutral equilibrium. 11.7 Stability a. Equilibrium is unstable when the CG is lowered with displacement. 11.7 Stability a. Equilibrium is unstable when the CG is lowered with displacement. b. Equilibrium is stable when work must be done to raise the CG. 11.7 Stability a. Equilibrium is unstable when the CG is lowered with displacement. b. Equilibrium is stable when work must be done to raise the CG. c. Equilibrium is neutral when displacement neither raises nor lowers the CG. 11.7 Stability For the pen to topple when it is on its flat end, it must rotate over one edge. During the rotation, the CG rises slightly and then falls. 11.7 Stability Toppling the upright book requires only a slight raising of its CG. Toppling the flat book requires a relatively large raising of its CG. An object with a low CG is usually more stable than an object with a relatively high CG. 11.7 Stability Objects in Stable Equilibrium The horizontally balanced pencil is in unstable equilibrium. Its CG is lowered when it tilts. But suspend a potato from each end and the pencil becomes stable because the CG is below the point of support, and is raised when the pencil is tilted. 11.7 Stability A pencil balanced on the edge of a hand is in unstable equilibrium. a. The CG of the pencil is lowered when it tilts. 11.7 Stability A pencil balanced on the edge of a hand is in unstable equilibrium. a. The CG of the pencil is lowered when it tilts. b. When the ends of the pencil are stuck into long potatoes that hang below, it is stable because its CG rises when it is tipped. 11.7 Stability The toy is in stable equilibrium because the CG rises when the toy tilts. 11.7 Stability The CG of a building is lowered if much of the structure is below ground level. This is important for tall, narrow structures. 11.7 Stability The Seattle Space Needle is so “deeply rooted” that its center of mass is actually below ground level. It cannot fall over intact because falling would not lower its CG at all. If the structure were to tilt intact onto the ground, its CG would be raised! 11.7 Stability Lowering the CG of an Object The CG of an object tends to take the lowest position available. 11.7 Stability The CG of an object has a tendency to take the lowest position available. a. A table tennis ball is placed at the bottom of a container of dried beans. 11.7 Stability The CG of an object has a tendency to take the lowest position available. a. A table tennis ball is placed at the bottom of a container of dried beans. b. When the container is shaken from side to side, the ball is nudged to the top. 11.7 Stability The same thing happens when an object is placed in water: • If the object weighs less than an equal volume of water, the object is forced to the surface. The CG of the whole system will be lowered because the heavier water occupies the lower space. • If the object is heavier than an equal volume of water, it will be more dense than water and sink. The CG of the whole system is lowered. • If the object weighs the same as an equal volume of water, the CG of the system is unchanged whether the object rises or sinks. 11.7 Stability The CG of the glass of water is affected by the position of the table tennis ball. a. The CG is higher when the ball is anchored to the bottom. 11.7 Stability The CG of the glass of water is affected by the position of the table tennis ball. a. The CG is higher when the ball is anchored to the bottom. b. The CG is lower when the ball floats. 11.7 Stability What happens to the center of gravity when an object is toppled?