Physics: Forces and Equilibrium

Physics: Forces and Equilibrium

1. 1. Moments

   • Defined as the product of the force and the perpendicular distance from the pivot to the line of action of the force.
     • Moment of a force about the pivot = F x d , where F= force and d=perpendicular distance from the pivot
       • Moments have a unit of Nm
       • The equation of moments can also be t = r x F , where t = torque (another term for moments), r = radius (picture the distance from the pivot as a radius) and F = force.
     • is a vector quantity, since force is also a vector quantity.

2. 2. Centre of Mass and Centre of Gravity

   • Centre of Mass
     • The Centre of Mass of a body is a single point at which the entire mass of the body is considered to act.
   • Centre of Gravity
     • The Centre of Gravity of a body is a single point at which the entire weight of the body is considered to act.
   • At places with uniform gravitational fields, (where gravitational force is constant), the Centre of Mass coincides with the Centre of Gravity.
     • Objects close to the ground are under uniform gravitational fields, so their Centre of Mass and Gravity coincides.
     • Gravitational force decreases with increasing distance from the ground.
       • A tall building has a Centre of Gravity that is lower than its Centre of Mass.

3. 3. Stability

   • An object is said to be in stable equilibrium if it returns to its original position after being displaced slightly.
     • Toppling occurs when the centre of gravity of an object falls outside of its base.
       • Increasing Stability
         • Increasing the base area of an object.
           • Because a larger base area means that an object would have to be displaced greatly in order for the centre of gravity to fall outside of its base.
         • Lowering the Centre of Gravity of an object.
           • A lower Centre of Gravity does not fall outside of the object's base easily

4. 4. Equilibrium

   • For an object acted upon by two or more coplanar forces (forces acting in the same plane) to be in static equilibrium (at rest or uniform motion)...
     • The resultant force on the system is zero.
       • This is translational equilibrium = no linear acceleration, i.e. no acceleration in a straight line in one direction.
         • When doing vector additions, the vector sum of the forces would be 0.
         • Graphical methods (drawing the vectors in a triangular/polygonal shape) will yield a closed triangle/polygon.
     • The resultant moment of the system about every axis is zero.
       • This is rotational equilibrium
         • Principle of moments: sum of anticlockwise moments = sum of clockwise moments

5. 5. Hooke's Law

   • When the top of a spring is attached to a fixed point and a force (weight) is applied at the bottom of the spring, the spring will extend.
     • Hooke's Law states that within the limit of proportionality, the extension produced in a material is directly proportional to the load attached to the spring.
       • F = kx , where F=force/load (i.e. weight), x = the extension of the spring, k= spring constant
       • The weight attached to the bottom of the spring is the load.

6. 6. Pressure

   • Pressure is defined as the force per unit area acting in the direction perpendicular to the surface of the object.
     • P = F/A
       • With the SI unit Nm^-2 or Pa (Pascal)
       • where P=pressure, F=force, A=area
   • Atmospheric Pressure
     • Is the force per unit area exerted against a surface by the weight of air above the surface at any given point in Earth's Atmosphere.
       • Earth's atmospheric pressure is 101kPa (101kN/m^2)
         • but this value varies at different altitudes
           • it decreases at higher altitudes
           • it increases at lower altitudes
   • Hydrostatic Pressure
     • Is the pressure at any given point in a non-moving, static liquid. (Such as water)
       • It is calculated by the formula: P = hpg, where P=pressure, h=height of the liquid above the point. p (rho)=density, g=gravitational acceleration
         • However, the actual pressure at a given point in the liquid is: hpg+atmospheric pressure on the surface of the liquid.
     • The hydrostatic pressure of a static liquid is equal at the same level/height.
       • If a liquid had different hydrostatic pressures at the same height, it would mean that the liquid is moving.