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Following points are the summary of these Lecture Slides : Static Equilibrium, Object, Translating, Static Equilibrium, Particular Inertial, External Forces, Sum, External Torques, any Point, Gravity
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An object that is neither translating (in a particular inertial reference frame) nor rotating is in static equilibrium. For such an object:
∑ (^) i
i
∑ (^) i
i
The center-of-gravity of an extended body, r cog , is the location at which the weight effectively acts when calculating a torque due to gravity. In near-Earth gravity, the center of gravity is identical to the center of mass. € τ grav = r cog × W
Two workers are hauling a tall case of select goat cheeses at constant speed up an inclined ramp. They lift vertically on either end of with forces needed to keep the board in equilibrium. At what incline angle θ will the force exerted by the first (front) worker become zero?
Lego Robots - CC: BY-NC-SA Don Solo (flickr) http://creativecommons.org/licenses/by-nc-sa/2.0/deed.en
A solid will behave somewhat like a spring in response to competing forces, or stress, acting on it. It can stretch or shrink (or bend), depending on how forces are applied. Consider these simple ways of applying stress to a bar. F F F
applied forces type of stress what the bar does tension stretch compression shrink shear bend or twist
The strain is linearly proportional to stress up to a limit (the Yield strength). Too much stress leads to permanent deformation and breaking. The highest stress a material can take is known as its Ultimate strength.
where B is the bulk modulus. The sign of the above equation reflects the fact that an increase in surrounding pressure leads to a decrease in volume, and vice- verse. If a solid of initial volume V 0 is moved to an environment in which the surrounding pressure (applied perpendicular force per area) changes by an amount Δ P , then the solid will change in volume by a fractional amount, Δ V/V 0 , that is linearly proportional to the change in pressure Δ P = – B (Δ V / V 0 ) (volume deformation)
The radius of a solid sphere of some material is found to shrink by 0.001% when placed in a pressure chamber under 8 atmospheres of pressure. If a sphere made out of the same material, but with twice the radius of the first, were placed in the same chamber under 8 atmospheres of pressure, what would be the fractional decrease in its radius?
