4. Mechanics + Materials

• Scalar quantity: A quantity that has only magnitude
• Vector quantity: A quantity that has magnitude as well as direction
• Acceleration is a vector quantity
• Mass is a scalar quantity
• Difference between mass and weight:

  • Mass is scalar and not dependent on gravity
  • Weight is a vector and depends on gravitational field strength (W = mg)
• If an object is in equilibrium:

  • Sum of anti-clockwise moments = sum of clockwise moments (principle of moments)
  • Object is not accelerating, so is either stationary or moving at a constant velocity
• How forces acting on an object can be shown to be in equilibrium:

  • Adding horizontal and vertical components of forces, showing they equal zero
  • For 3 forces, draw a scale diagram forming a closed triangle if the object is in equilibrium
• Moment: A turning force, force multiplied by perpendicular distance from point to line of action of the force
• Couple: A pair of equal and opposite coplanar forces
• Centre of mass: Point through which all mass of an object acts, for a uniform object, the centre of mass is at the centre of the object
• Velocity: Change in displacement per unit of time, instantaneous velocity found by measuring gradient of tangent to a displacement-time graph
• Area under a velocity-time and acceleration-time graph:

  • Displacement travelled and velocity respectively
• As speed increases, air resistance increases (proportional to the square of the speed)
• Horizontal velocity of a ball projected off a castle at 6m/s remains the same until it hits the ground
• SUVAT equations reflect that all objects fall at the same rate because mass is not included in the equations
• In projectile motion, vertical acceleration is equal to gravitational field strength (g)
• Terminal velocity: When forces acting on a falling object become balanced, acceleration becomes zero and object moves at maximum velocity
• Friction: Resistance to motion between an object and a surface or fluid, force that acts opposite to movement
• Newton's third law states 'every action force has an equal and opposite reaction force'
• Newton's second law: F = ma, where F is force applied and a is acceleration
• Newton's first law: An object stays moving at a constant velocity until a force acts upon it
• Difference between elastic and inelastic collisions:

  • Elastic: Kinetic energy before = kinetic energy afterwards
  • Inelastic: Kinetic energy at the end is not equal to the kinetic energy at the start
• Equation to calculate momentum: Momentum = mass × velocity
• Linear momentum is always conserved, not only in elastic collisions
• Rate of change of momentum is described as force
• Impulse: Change in momentum, F∆t = ∆mv
• Area under a force-time graph represents impulse, the change in momentum
• Fs cos( 𝜽 ) = The work done / the energy transferred
• Rate of work done is equal to power
• Efficiency = Useful output power / input power
• Principle of conservation of energy: Energy cannot be created or destroyed, only transferred into other forms, total energy in a closed system remains constant
• Lift: Upward force acting on objects in a fluid, caused by object changing direction of fluid flow, acts perpendicular to fluid flow
• Hooke’s law:

  • Extension (∆L) is directly proportional to force applied (F), given that the environmental conditions are kept constant
  • F= k∆L
  • k is the stiffness constant in Nm^-1
• Equation to calculate density:

  • Density = Mass / Volume
  • Density units: kgm^-3
  • Mass: kg
  • Volume: m^3
• Tensile stress:

  • The force applied per unit cross-sectional area
  • Stress = force / CSA
  • Stress units: Nm^-2
  • Force units: N
  • Cross-sectional area units: m^2
• Tensile strain:

  • A measure of how the material stretches: the extension (ΔL) divided by the original length (L), strain has no units
  • Strain = ΔL / L
• Difference between elastic and plastic deformation:

  • Elastic deformation: when the force is removed the object will return to its original shape
  • Plastic deformation: after the load is removed the object will not return to its original shape
• Breaking stress:

  • The minimum stress needed to break a material
• Brittle material:

  • Doesn’t deform plastically but breaks when the stress reaches a certain value
• Elastic limit:

  • The force above which the material will be plastically deformed (permanently stretched)