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The problem of calculating the force required to push a weight up an inclined plane (its mechanical advantage) was attempted by Greek philosophers Heron of Alexandria (c. 10 - 60 CE) and Pappus of Alexandria (c. 290 - 350 CE), but their solutions were incorrect.
This particular solution has three unstable directions and three marginal directions. Solutions of the Kuramoto–Sivashinsky equation possess rich dynamical characteristics. [ 11 ] [ 12 ] [ 13 ] Considered on a periodic domain 0 ≤ x ≤ L {\displaystyle 0\leq x\leq L} , the dynamics undergoes a series of bifurcations as the domain size L ...
A common problem presented in introductory physics classes is a block subject to friction as it slides up or down an inclined plane. This is shown in the free body diagram to the right. The component of the force of gravity in the direction of the incline is given by: [ 4 ]
In classical mechanics, the Udwadia–Kalaba formulation is a method for deriving the equations of motion of a constrained mechanical system. [1] [2] The method was first described by Anatolii Fedorovich Vereshchagin [3] [4] for the particular case of robotic arms, and later generalized to all mechanical systems by Firdaus E. Udwadia and Robert E. Kalaba in 1992. [5]
Examples of rope and pulley systems illustrating mechanical advantage. Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single pulley.
Any straight line drawn from the pole will intersect the Mohr circle at a point that represents the state of stress on a plane inclined at the same orientation (parallel) in space as that line. The second approach involves the determination of a point on the Mohr circle called the pole or the origin of planes. Any straight line drawn from the ...
Once the solutions to the planar problem have been constructed, the corresponding solutions to the spherical problem can be determined by inverting the stereographic projection. Even more generally, one can consider the problem of four tangent curves that result from the intersections of an arbitrary quadratic surface and four planes, a problem ...
Free body diagrams of a block on a flat surface and an inclined plane. Forces are resolved and added together to determine their magnitudes and the net force. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system.