dissipative force

(noun)

A force resulting in dissipation, a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some irreversible final form.

Examples of dissipative force in the following topics:

  • Problem Solving with Dissipative Forces

    • In the presence of dissipative forces, total mechanical energy changes by exactly the amount of work done by nonconservative forces (Wc).
    • Here we will adopt the strategy for problems with dissipative forces.
    • Since the work done by nonconservative (or dissipative) forces will irreversibly alter the energy of the system, the total mechanical energy (KE + PE) changes by exactly the amount of work done by nonconservative forces (Wc).
    • Therefore, using the new energy conservation relationship, we can apply the same problem-solving strategy as with the case of conservative forces.
    • Express the energy conservation relationship that can be applied to solve problems with dissipative forces

  • Energy in a Simple Harmonic Oscillator

    • Because a simple harmonic oscillator has no dissipative forces, the other important form of energy is kinetic energy (KE).
    • This statement of conservation of energy is valid for all simple harmonic oscillators, including ones where the gravitational force plays a role.
    • It is also greater for stiffer systems because they exert greater force for the same displacement.
    • This observation is seen in the expression for vmax; it is proportional to the square root of the force constant k.
    • For a given force, objects that have large masses accelerate more slowly.

  • Period of a Mass on a Spring

    • The mass and the force constant are both given.
    • In one dimension, we can represent the direction of the force using a positive or negative sign, and since the force changes from positive to negative there must be a point in the middle where the force is zero.
    • The deformation of the ruler creates a force in the opposite direction, known as a restoring force.
    • It is then forced to the left, back through equilibrium, and the process is repeated until dissipative forces (e.g., friction) dampen the motion.
    • The force constant k is related to the rigidity (or stiffness) of a system—the larger the force constant, the greater the restoring force, and the stiffer the system.

  • Forced motion

    • Later we will see that it is no loss to treat sinusoidal forces; the linearity of the equations will let us build up the result for arbitrary forces by adding a bunch of sinusoids together.
    • The forcing function doesn't know anything about the natural frequency of the system and there is no reason why the forced oscillation of the mass will occur at $\omega_0$ .
    • In the first place the spring would stretch to the point of breaking; but also, dissipation, which we have neglected, would come into play.
    • The motion of the mass with no applied force is an example of a free oscillation.
    • Otherwise the oscillations are forced.

  • The energy method

    • Unfortunately, we're forced into this by the Newtonian strategy of specifying forces explicitly.
    • For systems in which energy conserved (no dissipation, also known as conservative systems), the force is the gradient of a potential energy function.
    • (The work done by a force in displacing a system from $a$ to $b$ is $\int _ a ^ b F ~dx$ .
    • Since energy is a scalar quantity it is almost always a lot easier to deal with than the force itself.
    • After all, force is a vector, while energy is always a scalar.

  • Mechanical Work and Electrical Energy

    • Mechanical work done by an external force to produce motional EMF is converted to heat energy; energy is conserved in the process.
    • As the rod moves and carries current i, it will feel the Lorentz force
    • Since the rod is moving at v, the power P delivered by the external force would be:
    • Note that this is exactly the power dissipated in the loop (= current $\times$ voltage).
    • More generally, mechanical work done by an external force to produce motional EMF is converted to heat energy.

  • Power

    • Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.
    • Power delivered to an RLC series AC circuit is dissipated by the resistance alone.
    • The inductor and capacitor have energy input and output, but do not dissipate energy out of the circuit.
    • The forced but damped motion of the wheel on the car spring is analogous to an RLC series AC circuit.
    • The shock absorber damps the motion and dissipates energy, analogous to the resistance in an RLC circuit.

  • Latent Heat

    • Work is done by cohesive forces when molecules are brought together.
    • The corresponding energy must be given off (dissipated) to allow them to stay together.
    • The energy involved in a phase change depends on two major factors: the number and strength of bonds or force pairs.
    • The strength of forces depends on the type of molecules.
    • Both Lf and Lv depend on the substance, particularly on the strength of its molecular forces as noted earlier.

  • Phase-Space Density

    • If there is no dissipation, the phase-space density along the trajectory of a particular particle is given by
    • where ${\bf F}$ is a force that accelerates the particles.
    • The requirement of no dissipation tells us that $\nabla_{\bf p} \cdot {\bf F} = 0$.

  • What is Power?

    • The power expended to move a vehicle is the product of the traction force of the wheels and the velocity of the vehicle.
    • For example, a 60-W incandescent bulb converts only 5 W of electrical power to light, with 55 W dissipating into thermal energy.