|Statement||by Richard Tregaskis ; in a letter to the editor.|
|Series||Landmarks of science II|
|LC Classifications||Q111 .H35, QC304 .H35|
|The Physical Object|
|Number of Pages||72|
-To calculate the work done on an object by a force during a displacement, we use only the force component along the object’s displacement. The force component perpendicular to the displacement does zero work. W F x d Fcos d F d () - Assumptions: 1) F=cte, 2) Object particle-like. 90 0 90 90File Size: KB. Elastic Deflection Castigliano’s Method If deflection is not covered by simple cases in Table (p) Stored Elastic Energy U Complementary Energy U’ U=U' =∆⋅Q 2 Incremental: dU=dU' =∆⋅dQ Deflection: ∆=dU dQ Castiglino’s Theorem: When a body is elastically deflected by any combination of loads, theFile Size: 1MB. Work done going from A to B by one-dimensional spring force. W spring,AB = −(1 2k)(x2 B −x2 A) W spring, A B = − (1 2 k) (x B 2 − x A 2) Kinetic energy of a non-relativistic particle. K = 1 2mv2 = p2 2m K = 1 2 m v 2 = p 2 2 m. Work-energy theorem. W net =KB −KA W net = K B − K A. Power as rate of doing work. For linearly elastic structures, the partial derivative of the strain energy with respect to an applied force (or couple) is equal to the displacement (or rotation) of the force (or couple) along its line of action. δ = ∂ U ∂ P or θ = ∂ U ∂ M ¯.
To calculate the magnitude of force vectors, you use the components along with Pythagoras’ theorem. Think of the x coordinate of the force as the base of a triangle, the y component as the height of the triangle, and the hypotenuse as the resultant force from both components. Extending the link, the angle the hypotenuse makes with the base is the direction of the force. The work W done by the net force on a particle equals the change in the particle’s kinetic energy K E: W = ΔKE = 1 2mv2 f − 1 2mv2 i W = Δ KE = 1 2 mv f 2 − 1 2 mv i 2. where vi and vf are the speeds of the particle before and after the application of force, and m is the particle’s mass. The purpose of this book is to provide relevant material for each subject in O-level education here Vapour and humidity Vapour Humidity Current electricity Electromotive force (emf) and potential tortional force (torque), stretching (elastic) force, compressional, repulsive, frictional force ;. WorkEnergy Theorem Reviewed Description: Simple questions about the workenergy theorem to test understanding, then one easy analytic question Hint 1. First step in computing the work One of the pioneers of modern science, Robert Hooke (), studied the elastic properties of springs and formulated the law that bears his name.
torsion) where Castigliano’s Theorem may be applied to solve for the deflection in a beam or cylinder. •Generate equations for the changes in height, base, or even force across the length of a beam/cylinder. Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation F (x) = a [ x + 9 m 9 m − (9 m x + 9 m) 2], where x is the stretch of the cord along its length and a is a constant. If it takes kJ of work to stretch the cord by m, determine the value of the constant a. The work-energy principle for elastic materials, that is, the fact that the work done by external forces is stored as elastic energy, can be used directly to solve some simple problems. To be precise, it can be used to solve problems involving a single force and for solving for the displacement in the direction of that force. Calculation Example - Calculate the Axial Forces of the Truss Members. Calculation Example – Calculate the moments of inertia Ix and Iy. Calculation Example – Calculate shear stress for temperature load. Calculation Example – Calculate tension force using virtual work. Calculation Example – .