Statics Problems

Static is the part of mechanics that studies the conditions for a body to be at rest (static equilibrium). It is applied in architecture and civil engineering to do structural calculations.

For a body to be in static equilibrium, two conditions must be met:

The first condition implies that the acceleration of the center of mass of the system is null, so it has no translational motion.

The second condition implies that the angular acceleration of the system is null, so it has no rotational motion. It must be fulfilled regardless of the point that is used to calculate the torques of the forces.

Therefore, Statics is a particular case of application of the rotational motion.

When you try to solve problems of Physics in general and Statics in particular, it is important to follow a certain order. Try to be systematic when you solve these problems, and you will see how it gives good results. It is worth spending a bit of time on the analysis of a problem before starting to solve it.

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When solving a Statics problem, follow these steps:

  • Read carefully the problem statement.
  • Draw a picture of the physical situation described in the problem.
  • Write in your notebook the givens in the problem statement.
  • Identify the elements that make up the system that should be in static equilibrium: if it is a single body or if on the contrary you must take into account several objects. This step is important because it will allow you to distinguish the internal and external forces that act on the system.
  • Draw the external forces that act on the system.
  • Remember that the forces are physical interactions. Therefore, if a system is supported on another system, a normal force will act on it; if it is close to the surface of the Earth, the weight will act on it, and so on with the rest of the interactions that the system experiences.
  • In this link you can see how the forces exerted by the different types of support are represented.
  • Add a Cartesian coordinate system on the drawing, indicating which is the positive direction of each of the axes. you should also indicate which point you are going to use as an origin to calculate the torque of the external forces acting on the system.
  • Write the first condition of a static equilibrium in a vectorial form, including in the vectorial sum the different external forces you have identified.
  • Project the resulting equation on the Cartesian axes. Take into account the sign of the different projections.
  • Calculate the torques of the different external forces with respect to the point you have chosen as origin.
  • Write the second condition of a static equilibrium in a vectorial form.
  • Project the resulting equation on the Cartesian axes. Take into account the sign of the different projections.
  • Solve the system of equations that you have obtained after projecting on the axes the two conditions of a static equilibrium. In this way you will be able to determine magniudes asked for in the problem.
  • Do not forget to include the units in your results.
  • Review the problem and check that the results you have obtained make sense.

On the following pages you will find solved problems of Statics. Try to do them before looking at the solution.

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