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36-406: The normal force is one type of ground reaction force . If the person stands on a slope and does not sink into the ground or slide downhill, the total ground reaction force can be divided into two components: a normal force perpendicular to the ground and a frictional force parallel to the ground. In another common situation, if an object hits a surface with some speed, and the surface can withstand

72-536: A normal force . However, in a more general case, the GRF will also have a component parallel to the ground, for example when the person is walking – a motion that requires the exchange of horizontal ( frictional ) forces with the ground. The use of the word reaction derives from Newton's third law , which essentially states that if a force, called action , acts upon a body, then an equal and opposite force, called reaction , must act upon another body. The force exerted by

108-453: A consequence of Pauli exclusion principle, but also of the fundamental forces of nature : cracks in the bodies do not widen due to electromagnetic forces that create the chemical bonds between the atoms; the atoms themselves do not disintegrate because of the electromagnetic forces between the electrons and the nuclei; and the nuclei do not disintegrate due to the nuclear forces. In an elevator either stationary or moving at constant velocity,

144-424: A net force of zero in the vertical direction: μ = m g N {\displaystyle \mu ={\frac {mg}{N}}} where μ {\displaystyle \mu } is the static coefficient of friction, and g {\displaystyle g} is the gravitational field strength. Ground reaction force In physics , and in particular in biomechanics ,

180-448: A particular element of the array by writing tablename[first index][second index] . The compiler computes the total number of memory cells occupied by each row, uses the first index to find the address of the desired row, and then uses the second index to find the address of the desired element in the row. When the third method is used, the programmer declares the table to be an array of pointers, like in elementtype *tablename[]; . When

216-434: A passenger were to stand on a weighing scale, such as a conventional bathroom scale, while riding the elevator, the scale will be reading the normal force it delivers to the passenger's feet, and will be different than the person's ground weight if the elevator cab is accelerating up or down. The weighing scale measures normal force (which varies as the elevator cab accelerates), not gravitational force (which does not vary as

252-481: Is a way of addressing elements of an array. This method is used since it is closest to how it is implemented in assembly language whereby the address of the first element is used as a base, and a multiple (the index) of the element size is used to address inside the array. For example, if an array of integers is stored in a region of the computer's memory starting at the memory cell with address 3000 (the base address ), and each integer occupies four cells (bytes), then

288-440: Is mass, and g is the gravitational field strength (about 9.81 m/s on Earth). The normal force here represents the force applied by the table against the object that prevents it from sinking through the table and requires that the table be sturdy enough to deliver this normal force without breaking. However, it is easy to assume that the normal force and weight are action-reaction force pairs (a common mistake). In this case,

324-473: Is often observed to evaluate force production in various groups within the community. One of these groups studied often are athletes to help evaluate a subject's ability to exert force and power. This can help create baseline parameters when creating strength and conditioning regimens from a rehabilitation and coaching standpoint. Plyometric jumps such as a drop-jump is an activity often used to build greater power and force which can lead to overall better ability on

360-411: Is the angle between the slope and the horizontal. Normal force is directly a result of Pauli exclusion principle and not a true force per se : it is a result of the interactions of the electrons at the surfaces of the objects. The atoms in the two surfaces cannot penetrate one another without a large investment of energy because there is no low energy state for which the electron wavefunctions from

396-401: Is the mass of the object, g is the gravitational field strength, and θ is the angle of the inclined surface measured from the horizontal. The normal force is one of the several forces which act on the object. In the simple situations so far considered, the most important other forces acting on it are friction and the force of gravity . In general, the magnitude of the normal force, N ,

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432-417: Is the normal force on the passenger, m {\displaystyle m} is the mass of the passenger, v {\displaystyle v} is the tangential velocity of the passenger and r {\displaystyle r} is the distance of the passenger from the center of the ride. With the normal force known, we can solve for the static coefficient of friction needed to maintain

468-1152: Is the projection of the net surface interaction force, T , in the normal direction, n , and so the normal force vector can be found by scaling the normal direction by the net surface interaction force. The surface interaction force, in turn, is equal to the dot product of the unit normal with the Cauchy stress tensor describing the stress state of the surface. That is: N = n N = n ( T ⋅ n ) = n ( n ⋅ τ ⋅ n ) . {\displaystyle \mathbf {N} =\mathbf {n} \,N=\mathbf {n} \,(\mathbf {T} \cdot \mathbf {n} )=\mathbf {n} \,(\mathbf {n} \cdot \mathbf {\tau } \cdot \mathbf {n} ).} or, in indicial notation , N i = n i N = n i T j n j = n i n k τ j k n j . {\displaystyle N_{i}=n_{i}N=n_{i}T_{j}n_{j}=n_{i}n_{k}\tau _{jk}n_{j}.} The parallel shear component of

504-407: Is the row number and the second is the column number. Juxtaposition is also used as notation for multiplication; this may be a source of confusion. For example, if then some entries are For indices larger than 9, the comma-based notation may be preferable (e.g., a 3,12 instead of a 312 ). Matrix equations are written similarly to vector equations, such as in terms of the elements of

540-418: Is used to specify the elements of an array of numbers. The formalism of how indices are used varies according to the subject. In particular, there are different methods for referring to the elements of a list, a vector , or a matrix , depending on whether one is writing a formal mathematical paper for publication, or when one is writing a computer program . It is frequently helpful in mathematics to refer to

576-411: The ground reaction force ( GRF ) is the force exerted by the ground on a body in contact with it. For example, a person standing motionless on the ground exerts a contact force on it (equal to the person's weight ) and at the same time an equal and opposite ground reaction force is exerted by the ground on the person. In the above example, the ground reaction force coincides with the notion of

612-425: The C standard defines the array indexing form as a transformation to pointer form. Coincidentally, since pointer addition is commutative, this allows for obscure expressions such as 3[base] which is equivalent to base[3] . Things become more interesting when we consider arrays with more than one index, for example, a two-dimensional table. We have three possibilities: In C, all three methods can be used. When

648-414: The cab accelerates). When we define upward to be the positive direction, constructing Newton's second law and solving for the normal force on a passenger yields the following equation: N = m ( g + a ) {\displaystyle N=m(g+a)} In a gravitron amusement ride, the static friction caused by and perpendicular to the normal force acting on the passengers against

684-459: The contact force is known as the frictional force ( F f r {\displaystyle F_{fr}} ). The static coefficient of friction for an object on an inclined plane can be calculated as follows: μ s = tan ⁡ ( θ ) {\displaystyle \mu _{s}=\tan(\theta )} for an object on the point of sliding where θ {\displaystyle \theta }

720-411: The elements of an array using subscripts. The subscripts can be integers or variables . The array takes the form of tensors in general, since these can be treated as multi-dimensional arrays. Special (and more familiar) cases are vectors (1d arrays) and matrices (2d arrays). The following is only an introduction to the concept: index notation is used in more detail in mathematics (particularly in

756-417: The elements of this array are at memory locations 0x3000, 0x3004, 0x3008, …, 0x3000 + 4( n − 1) (note the zero-based numbering ). In general, the address of the i th element of an array with base address b and element size s is b + is . In the C programming language , we can write the above as *(base + i) (pointer form) or base[i] (array indexing form), which is exactly equivalent because

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792-412: The equations are explicitly Hence, index notation serves as an efficient shorthand for More than one index is used to describe arrays of numbers, in two or more dimensions, such as the elements of a matrix, (see also image to right); The entry of a matrix A is written using two indices, say i and j , with or without commas to separate the indices: a ij or a i,j , where the first subscript

828-438: The first method is used, the programmer decides how the elements of the array are laid out in the computer's memory, and provides the formulas to compute the location of each element. The second method is used when the number of elements in each row is the same and known at the time the program is written. The programmer declares the array to have, say, three columns by writing e.g. elementtype tablename[][3]; . One then refers to

864-435: The ground is conventionally referred to as the reaction, although, since the distinction between action and reaction is completely arbitrary, the expression ground action would be, in principle, equally acceptable. The component of the GRF parallel to the surface is the frictional force. When slippage occurs the ratio of the magnitude of the frictional force to the normal force yields the coefficient of static friction. GRF

900-533: The impact, the normal force provides for a rapid deceleration, which will depend on the flexibility of the surface and the object. In the case of an object resting upon a flat table (unlike on an incline as in Figures 1 and 2), the normal force on the object is equal but in opposite direction to the gravitational force applied on the object (or the weight of the object), that is, F n = m g {\displaystyle F_{n}=mg} , where m

936-675: The matrices (aka components) for all values of i and j . Again this expression represents a set of equations, one for each index. If the matrices each have m rows and n columns, meaning i = 1, 2, …, m and j = 1, 2, …, n , then there are mn equations. The notation allows a clear generalization to multi-dimensional arrays of elements: tensors. For example, representing a set of many equations. In tensor analysis, superscripts are used instead of subscripts to distinguish covariant from contravariant entities, see covariance and contravariance of vectors and raising and lowering indices . In several programming languages, index notation

972-413: The normal force and weight need to be equal in magnitude to explain why there is no upward acceleration of the object. For example, a ball that bounces upwards accelerates upwards because the normal force acting on the ball is larger in magnitude than the weight of the ball. Where an object rests on an incline as in Figures 1 and 2, the normal force is perpendicular to the plane the object rests on. Still,

1008-407: The normal force on the person's feet balances the person's weight. In an elevator that is accelerating upward, the normal force is greater than the person's ground weight and so the person's perceived weight increases (making the person feel heavier). In an elevator that is accelerating downward, the normal force is less than the person's ground weight and so a passenger's perceived weight decreases. If

1044-403: The normal force will be as large as necessary to prevent sinking through the surface, presuming the surface is sturdy enough. The strength of the force can be calculated as: F n = m g cos ⁡ ( θ ) {\displaystyle F_{n}=mg\cos(\theta )} where F n {\displaystyle F_{n}} is the normal force, m

1080-474: The playing field. When landing from a safe height in a bilateral comparisons on GRF in relation to landing with the dominant foot first followed by the non-dominant limb, literature has shown there were no significances in bilateral components with landing with the dominant foot first faster than the non-dominant foot on the GRF of the drop-jump or landing on vertical GRF output. Indicial notation In mathematics and computer programming , index notation

1116-434: The programmer subsequently specifies a particular element tablename[first index][second index] , the compiler generates instructions to look up the address of the row specified by the first index, and use this address as the base when computing the address of the element specified by the second index. In other programming languages such as Pascal, indices may start at 1, so indexing in a block of memory can be changed to fit

Normal force - Misplaced Pages Continue

1152-435: The representation and manipulation of tensor operations ). See the main article for further details. A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): Index notation allows indication of the elements of the array by simply writing a i , where the index i is known to run from 1 to n , because of n-dimensions. For example, given

1188-405: The two surfaces overlap; thus no microscopic force is needed to prevent this penetration. However these interactions are often modeled as van der Waals force , a force that grows very large very quickly as distance becomes smaller. On the more macroscopic level, such surfaces can be treated as a single object, and two bodies do not penetrate each other due to the stability of matter, which is again

1224-410: The vector: then some entries are The notation can be applied to vectors in mathematics and physics . The following vector equation can also be written in terms of the elements of the vector (aka components), that is where the indices take a given range of values. This expression represents a set of equations, one for each index. If the vectors each have n elements, meaning i = 1,2,… n , then

1260-496: The walls of the ride counteracts the pull of gravity on the passengers, resulting in suspension above ground of the passengers throughout the duration of the ride. When we define the center of the ride to be the positive direction, solving for the normal force on a passenger that is suspended above ground yields the following equation: N = m v 2 r {\displaystyle N={\frac {mv^{2}}{r}}} where N {\displaystyle N}

1296-399: The walls results in suspension of the passengers above the floor as the ride rotates. In such a scenario, the walls of the ride apply normal force to the passengers in the direction of the center, which is a result of the centripetal force applied to the passengers as the ride rotates. As a result of the normal force experienced by the passengers, the static friction between the passengers and

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