The idea of momentum Modelling collisions Understanding collisions Explosions and crash-landings Speed Distance and displacement, scalar and vector Speed and velocity Displacement–time graphs Combining displacements Combining velocities Subtracting vectors Other examples of scalar and vector quantitiesĭoing work, transferring energy Gravitational potential energy Kinetic energy Gravitational potential to kinetic energy transformations Down, up, down: energy changes Energy transfers Power The meaning of acceleration Calculating acceleration Units of acceleration Deducing acceleration Deducing displacement Measuring velocity and acceleration Determining velocity and acceleration in the laboratory The equations of motion Deriving the equations of motion Uniform and non-uniform acceleration Acceleration caused by gravity Determining g Motion in two dimensions: projectiles Understanding projectiles Work, energy and power 5.1 5.2 5.3 5.4 5.5 5.6 5.7įorce, mass and acceleration Identifying forces Weight, friction and gravity Mass and inertia Moving through fluids Newton’s third law of motion Understanding SI units Well done to all of our nominees for your dedication to learning and for inspiring the next generation of thinkers, leaders and innovators.Ĭongratulations to our incredible winner and finalistsįor more information about our dedicated teachers and their stories, go toĬontents Introduction How to use this series How to use this book Resource index 1 Thank you to everyone who nominated this year, we have been inspired and moved by all of your stories. Our Dedicated Teacher Awards recognise the hard work that teachers put in every day. Teachers play an important part in shaping futures. The results are applied to a few hitherto unexplained natural phenomena.Physics for Cambridge International AS & A Level Coursebookĭavid Sang, Graham Jones, Gurinder Chadha & Richard Woodside The ratio T/P was constant at 0♳ approx, in the inertia region, and at 0.75 approx, in the viscous region. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U/d y was found for the viscous case, when T is the whole shear stress. according to whether grain inertia or fluid viscosity dominate. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U/d y is large or small, i.e. Both the stresses T and P, as dimensionless groups Tσ D 2/λη 2, and Pσ D 2/λη 2, were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½σ D 2(d U/d y)lη for all the values of λ< 12( C= 57% approx.) where d U/d y is the rate of shearing of the grains over one another, and η the fluid viscosity. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The torque on the inner drum was also measured. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. A substantial radial dispersive pressure was found to be exerted between the grains. The volume concentration C of the grains was varied between 62 and 13 %. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums.
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