Static equilibrium problems

Static equilibrium problems

Lessons

In this lesson, we will learn:

  • Solving statics problems using both translational and rotational equilibrium

Notes:

  • An object or group of objects that are not moving are in static equilibrium.
  • In static equilibrium, the conditions for both translational and rotational equilibrium must be met.
Conditions for Translational Equilibrium

ΣF=0N\Sigma F = 0 N

or equivalently:

ΣFx=0N\Sigma F_{x} = 0 N and ΣFy=0N\Sigma F_{y} = 0 N

ΣF:\Sigma F: sum of all forces, in newtons (N)

ΣFx:\Sigma F_{x}: sum of all force components in x direction, in newtons (N)

ΣFy:\Sigma F_{y}: sum of all force components in y direction, in newtons (N)


Torque

τ=Fd\tau = F_{\perp}d

τ\tau: torque, in newton meters (N·m)

F:F_{\perp}: component of force perpendicular to dd, in newtons (N)

d:d: distance from point of rotation, in meters (m)


Conditions for Rotational Equilibrium

Στ=0\Sigma \tau = 0 N·m

or simpler equation:

total CWCW τ\tau = total CCWCCW τ\tau

Στ:\Sigma \tau : sum of all torques, in newton meters (N·m)

total CWCW τ\tau: magnitude of all torques in the clockwise direction, in newton meters (N·m)

total CCWCCW τ\tau: magnitude of all torques in the counterclockwise direction, in newton meters (N·m)

  • 1.
    Cable and beam in static equilibrium
    a)
    A 20.0 kg lamp is hung from a uniform 12.5 kg beam as shown. Find the tension in the wire, and the horizontal and vertical forces acting on the hinge. PHYS 8 3 1a

    b)
    A 25.0 kg lamp is hung from an 18.0 kg uniform beam as shown. The total length of the beam is 8.50 m. Find the tension in the wire, and the horizontal and vertical forces acting on the hinge. PHYS 8 3 1b


  • 2.
    Ladder beginning to slide

    An 80.0 kg painter climbs 85% of the way up a uniform 25.0 kg ladder before it starts to slip backwards along the ground. What is the coefficient of static friction between the ladder and ground? Assume the wall is frictionless.

    PHYS 8 3 2