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Block-stacking Problem
In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire , also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table. Statement The block-stacking problem is the following puzzle: Place N identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang. provide a long list of references on this problem going back to mechanics texts from the middle of the 19th century. Variants Single-wide The single-wide problem involves having only one block at any given level. In the ideal case of perfectly rectangular blocks, the solution to the single-wide problem is that the maximum overhang is given by \sum_^\frac times the width of a block. This sum is one half of the corresponding partial sum of the harmonic series. Because the harmonic series diverges, the maximal overhang tends to infinity as N increases, meaning that it is poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Stacking Problem
Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 the Block '' * WFNZ-FM, a radio station licensed to Harrisburg, North Carolina, United States, branded as ''92.7 The Block'' * "Blocked", an episode of the television series ''The Flash'' Music * Block Entertainment, a record label * Blocks Recording Club, a record label * Woodblock (instrument), a small piece of slit drum made from one piece of wood and used as a percussion instrument * "Blocks", by C418 from ''Minecraft – Volume Beta'', 2013 Toys * Toy block, one of a set of wooden or plastic pieces, of various shapes * Unit block, a type of standardized wooden toy block for children Video games * Blocked (video game), a puzzle game for the iPhone and iPod Touch Building and construction * Concrete block, cinder block or cement b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PBS Digital Studios
PBS Digital Studios is a non-profit organization through which PBS distributes original educational web video content. Based in Arlington, Virginia, it comprises both original series and partnerships with existing YouTube YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in ... channels. Most of the series are about science, popular culture, art, food, news, and music. History PBS Digital Studios was founded by Jason Seiken in June 2012.Looking Back On A Year Of PBS Digital Studios July 18, 2013. They had their first viral hit with a "remix" of [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years. Friction can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from asperity deformation to the generation of charges and changes in local structure. When two bodies in contact move relative to each other, due to these variou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust
Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system's functional body. In the same line ''robustness'' can be defined as "the ability of a system to resist change without adapting its initial stable configuration". "Robustness in the small" refers to situations wherein perturbations are small in magnitude, which considers that the "small" magnitude hypothesis can be difficult to verify because "small" or "large" depends on the specific problem. Conversely, "Robustness in the large problem" refers to situations wherein no assumptions can be made about the magnitude of perturbations, which can either be small or large.C.Alippi: "Robustness Analysis" chapter in ''Intelligence for Embedded Systems.'' Springer, 2014, 283pp, . It has been discussed that robustness has two dimensions: resistance and avoidance.Durach, C.F. et al. (2015)Antecedents and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Stacking Problem Skintled 4 Diamond
Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 the Block '' * WFNZ-FM, a radio station licensed to Harrisburg, North Carolina, United States, branded as ''92.7 The Block'' * "Blocked", an episode of the television series ''The Flash'' Music * Block Entertainment, a record label * Blocks Recording Club, a record label * Woodblock (instrument), a small piece of slit drum made from one piece of wood and used as a percussion instrument * "Blocks", by C418 from ''Minecraft – Volume Beta'', 2013 Toys * Toy block, one of a set of wooden or plastic pieces, of various shapes * Unit block, a type of standardized wooden toy block for children Video games * Blocked (video game), a puzzle game for the iPhone and iPod Touch Building and construction * Concrete block, cinder block or cement b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Field
In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as the '' gravitational force field'' exerted on another massive body. It has dimension of acceleration (L/T2) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s2). In its original concept, gravity was a force between point masses. Following Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century, explanations for gravity in classical mechanics have usually been taught in terms of a field model, rather than a point attraction. It results from the spatial gradient of the gravitational potential field. In general relativity, rather than two particles attracting each other, the particles distort spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. 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. The center of mass may be located outside the Phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torque
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. When being referred to as moment of force, it is commonly denoted by . Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque to force it into an object, which is applied by the screwdriver rotating around its axis to the drives on the head. Historical terminology The term ''torque'' (from Latin , 'to twist') is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in the first edition of ''Dynamo-Electric Machinery''. Thompson describes his usage of the term as follows: Today, torque is referred to using d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterweight
A counterweight is a weight (object), weight that, by applying an opposite force, provides balance and stability of a machine, mechanical system. The purpose of a counterweight is to make lifting the load faster and more efficient, which saves energy and causes less wear and tear on the lifting machine. Counterweights are often used in traction force, traction elevator, lifts (elevators), Crane (machine), cranes and fair, funfair rides. In these applications, the expected load multiplied by the distance that load will be spaced from the central support (called the "tipping point") must be equal to the counterweight's mass times its distance from the tipping point in order to prevent over-balancing either side. This distance times mass is called the Moment (physics), load moment. By extension, a counterbalance force balances or offsets another force, as when two objects of equal weight, power, or influence are acting in opposition to each other. Examples ;Trebuchet: There are fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statics
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in mechanical equilibrium, equilibrium with its environment. If \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system, Newton's second law states that \textbf F = m \textbf a \, (the bold font indicates a Euclidean vector, vector quantity, i.e. one with both Magnitude (mathematics), magnitude and Direction (geometry), direction). If \textbf a =0, then \textbf F = 0. As for a system in static equilibrium, the acceleration equals zero, the system is either at rest, or its center of mass moves at constant velocity. The application of the assumption of zero acceleration to the summation of Moment (physics), moments acting on the system leads to \textbf M = I \alpha = 0, where \textbf M is the summation of all momen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Stacking Problem Compare 3
Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 the Block '' * WFNZ-FM, a radio station licensed to Harrisburg, North Carolina, United States, branded as ''92.7 The Block'' * "Blocked", an episode of the television series ''The Flash'' Music * Block Entertainment, a record label * Blocks Recording Club, a record label * Woodblock (instrument), a small piece of slit drum made from one piece of wood and used as a percussion instrument * "Blocks", by C418 from ''Minecraft – Volume Beta'', 2013 Toys * Toy block, one of a set of wooden or plastic pieces, of various shapes * Unit block, a type of standardized wooden toy block for children Video games * Blocked (video game), a puzzle game for the iPhone and iPod Touch Building and construction * Concrete block, cinder block or cement b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
