Biomechanical Systems and Static Equilibrium

Static Equilibrium

• A body is in static equilibrium if both its linear and angular acceleration are zero.
• The sum of the force acting on the body, as well as the sum of torques produced by these forces, must be zero.

The Work

• In Physics, work is done only if an object is moved through some displacement while a force is applied to it.
• Force and displacement are two essential elements of work.
• Only the force parallel to the direction of motion does work on the object.
• Work (W) is defined as the magnitude F of the force times the magnitude s of the displacement: W = Fs.
• The unit of work is Newton.Meter (N.m) in SI unit, which is also referred to as a joule (J).
• Work is a scalar quantity and does not convey directional information.
• If the distance s is zero, the work is zero, even if a force is applied.
• The idea of work is intimately tied up with the idea of motion.

Force and Displacement at an Angle

• If the force and displacement do not point in the same direction, only the component of the force along the displacement is used to define the achieved work: W = (Fcosθ)s.
• When the force points in the same direction as the displacement, θ = 0 and W = Fs.
• The force component perpendicular to the displacement does not work.
• If the entire force is perpendicular to the displacement, the angle θ is 90°, and the force doesn't work at all.

Positive and Negative Work

• Work can be either positive or negative, depending on whether the component of the force points in the same direction as the displacement or in the opposite direction.
• Example: bench press, where the weight lifter raises the barbell a distance of 0.65 m above his chest, resulting in positive work during the lifting phase and negative work during the lowering phase.

Examples of Work

• Example 1: Lifting a barbell with a weight of 710 N, the work done by the weight lifter is 460 J during the lifting phase and -460 J during the lowering phase.
• Example 2: A box is pushed with a force of 40 N and moves steadily through a distance of 3 m in the direction of the force, resulting in a work done of 120 J.
• Example 3: A 600 N force is applied to a dresser that moves 2 m, resulting in different work done depending on the direction of the force and displacement.

Energy

• In Physics, energy is defined as the ability to do work.
• Energy is an important concept, it is a scalar quantity with SI units of joules (J).
• Energy is a derived unit equivalent to newton meters (N m).
• Energy is associated with widely different phenomena, such as Atomic Energy, Heat energy, Potential Energy, Solar Energy, Kinetic Energy, etc.
• The concept of work is similar to that of energy, but we usually associate energy with a body and work with a force.
• In all physical processes, energy is conserved.
• There is one-to-one correspondence between work and energy, it takes 2J of energy to do 2J of work.