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General Physics I:

Sunil Karna

Section 4.3 Translational Equilibrium

An object is in translational equilibrium if the vector sum of the forces acting on that object add to zero.
  1. An object in translational equilibrium continues moving in a straight line with a constant speed as described by Newton’s First law. That is
    \begin{equation*} \sum\vec{F} = 0 \end{equation*}
    (Graphical and vector algebra problems.) or equivalently
    \begin{equation*} \sum\vec{F}_{x} = 0 \end{equation*}
    (x-component of net force),
    \begin{equation*} \sum\vec{F}_{y} = 0 \end{equation*}
    (y-component of net force),
    \begin{equation*} w = m g \end{equation*}
    (weight equation), and
    \begin{equation*} f = \mu N \end{equation*}
    (friction equation). In translational motion \(v\neq 0, a = 0,\) and \(F= 0\text{.}\)
  2. Problem Solving Technique: To solve a translational equilibrium problem one needs to:
    1. Read problem, list given quantities, and label a drawing of the physical situation.
    2. Draw force diagrams for each body in translational equilibrium.
    3. Resolve the forces into components.
    4. Sum the x- and y-components of forces and set them to zero.
    5. Include a weight equation for each mass.
    6. Include a friction equation for each surface.
    7. Solve equations simultaneously for the quantities of interest.
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