Unit 4: Forces, Density and Pressure

• When a resultant force F acts on a body with mass m, the body will accelerate in the direction of the resultant force
• The resultant force is related to mass and acceleration by the formula F = ma
• Common forces and their brief explanations:

  • Weight: gravitational force acting on an object through its centre of mass
  • Friction: force that arises when two surfaces rub against each other
  • Drag: resistive force on an object travelling through a fluid (e.g. water or air)
  • Tension: force within a stretched cable or rope
  • Upthrust: upward buoyancy force acting on an object in a fluid
  • Normal Contact Force: force arising when an object rests against another object, acting perpendicular to the plane of contact
• Drag is a frictional force that opposes motion, experienced by an object moving through a fluid
• Centre of gravity of an object is the point where all the mass of the object can be considered to act through
• Principle of moments: For an object in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments
• A moment is a turning force calculated as force multiplied by the perpendicular distance from the point to the line of action of the force
• A couple is a pair of equal and opposite coplanar forces with equal magnitude and opposite direction, causing rotation of the object
• In equilibrium, a lever must have clockwise moments equal to anti-clockwise moments
• Centre of mass of a uniform object is at the geometric centre of the object
• Density is the mass per unit volume of a substance, measured in kg m^-3
• Pressure is the normal force exerted on a surface per unit area, measured in Pascals (Pa) where 1 Pa = 1 Nm^-2
• An object submerged in a fluid experiences an upwards force called upthrust due to the pressure difference between the top and bottom surfaces
• Equation derivation: Δp = ρgΔh

  • Pressure equation: P=F/A = mg/A = ρVg/A = ρΔhAg/A = ρgΔh where ρ=m/V so m = ρV and V=AΔh
• Archimedes’ principle for upthrust in a fluid: F = ρgV where F is the upthrust, and ρ and V are the densities and volumes of the object respectively