Materials

• The up thrust a fluid acts upwards in an object is equal to the weight of fluid displaced
• upthrust = density of flyid x volume of object x gravity
• if an object is moving, drags acts in opposite direction to velocity (upthrust)
• If an object is a mix of materials, mass = m1 + m2 = pV1 + pV2
• Any object that deforms elastically obeys hookes law
• Hooked law states that force and extension are directly proportional
• elastic deformation means that the object returns to its original space
• Force = spring constant (k) x extension
• Force extension graphs area is Equal to the elastic potential energy
• The gradient of the force extension graph is the spring constant
• Elastic potential energy = 1/2 Fe = ½ K e^2
• If there are two springs in series (conjoined), k is halved as it extends more
• If 2 springs are parallel, k is doubled as object extends less
• Young’s modulus tells you how much an object will extend
• Stress = force / area
• Stress unit?

  Pa pascals
• Strain = extension / initial length
• Strain unit?

  there isn’t one
• Young’s modulus (E) = stress / strain
• The graph of stress against strain gives a gradient of Young’s modulus
• The limit of proportionality is where the curve of the stress - strain graph begins to curve and stress is no longer directly proportional to strain
• Youngs modulus = Fx L / A x change in L
• Area is proportional to diameter^2 as area = pi d^2/4
• Length is inversely proportional to A and diameter^2
• Can’t use youngs modulus past limit of proportionality, but will still behave elastically
• Area under Unloading curve is the energy (work done) to stretch the springs
• Enclosed area between loading and unloading curve is the energy lost as heat during change
• Once past elastic limit, it will experience plastic deformation and won’t return to original length
• When plastic deformation occurs, bonds break due to input with energy and become moved along in lattice structure then create new bonds.
• Ultimate tensile stress is the maximum stress that a material can withstand before breaking.
• ductile materials have large plastic regions
• Brittle materials have steep Young’s modulus then suddenly snaps
• Springs in parallel have a total spring constant of KT= k1 + k2 + k3
• Springs in series have total spring constant of 1/kT = 1/k1 + 1/k2
• To change g/cm^3 to kg/m^3 what do you multiply by?

  1000
• Units for ultimate tensile strength?

  kg/ (ms^2). Or Pa or N/m^2
• For a lift scenario, tension has to increase when moving upwards and when lift comes to a halt
• When tension hung On end of string is increased greatly, why would predicted frequencies change?

  due to diameter reducing when string stretched. this means the mass per unit length will decrease so frequency will change (higher usually than predicted)
• What is damping?


  when energy in oscillations is lost to environment, leading to reduced amplitude
• What is resonance?


  when amplitude drastically increases due to gaining energy from driving force (when natural frequency is equal to the driving frequency)