Tru Physics

Forces

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Tru Physics
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Forces are the “push” and “pull” interactions responsible for the motion and deformation of objects. They play a central role in classical mechanics, as well as in various engineering disciplines. Forces are vectors. This means they have both a magnitude and a direction. However, on this page, we will only treat the magnitude of each force. The direction of each one must generally be determined by the reader in the course of solving a problem.

Types of Forces

There are several types of forces that can act on objects, including:

  1. Gravitational Force: The force of attraction between two masses due to gravity (F_G = \frac{Gm_1m_2}{r^2}). For objects on Earth, this calculation can be simplified dramatically as F_g = mg where m is the mass of the object, and g is the acceleration due to gravity. On Earth, g \approx 9.81 \frac{\text{m}}{\text{s}^2}. When using F_g = mg, note that this force points strictly downward.
  2. Normal Force: The force exerted by a surface that supports the weight of an object. F_N always acts perpendicular to the surface. There is not a generic equation to calculate F_N. However, in problems involving flat surfaces, we generally deduce that the normal force balances out F_g. Thus it will commonly equal mg. When inclined surfaces are involved, F_N = mg \cos{(\theta)} is the common treatment (where \theta is the angle of inclination). Generally, F_N is determined by balancing forces via Newton’s Second Law.
  3. Frictional Force: The force that opposes the relative motion or tendency of such motion between two surfaces in contact. Static friction is calculated as f_s = \mu_s F_N and kinetic (sliding) friction is calculated as f_k = \mu_k F_N.
  4. Tension Force: The force transmitted through a rope, string, or cable when it is pulled tight by forces acting from opposite ends. We generally denote tension forces with T.
  5. Spring Force: The force exerted by a spring, proportional to its deformation (F_{sp} = -kx). The spring force can approximate the force for many things which we do not generally consider to be “springs.” For example, elastic materials like rubber bands fall under this category.
  6. Electromagnetic Force: The force between charged particles or magnets due to their electric or magnetic fields. The magnitude of this force is given by the equation: F_e = \frac{1}{4 \pi \varepsilon_0} \frac{|q_1q_2|}{r^2}

This is certainly not an exhaustive list. However, this does give an introductory treatment of the subject. Any forces which do not fall strictly under one of these categories can generally be called anything. However, one common practice is to use F_A, meaning some applied force which acts of the system.

Free Body Diagrams

Free body diagrams are graphical representations of the forces acting on an object. They are useful for visualizing and analyzing the different forces that influence the motion or equilibrium of an object. To create a free body diagram, follow these steps:

  1. Identify the object of interest.
  2. Isolate the object from its surroundings.
  3. Draw a vector (arrow) representing each force acting on the object. Begin (or terminate) each arrow at the object of interest to indicate the “push” or “pull” interaction caused by the force.
  4. Label the vectors with the appropriate force type and magnitude.
  5. Use the diagram to help solve problems involving forces and motion.

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