### Force

In a system dynamics model, the influence of one stock on another may be treated like a force. Activity in one stock, the source, causes another stock, the target, to accelerate. In mechanics, forces are said to “do work” on a system, either injecting or removing energy. Likewise, in the Newtonian Interpretative Framework, a source stock may inject energy into a target stock, causing it to increase in activity. The activity of a stock is measured by its kinetic energy.

Consider an example. Let stock *y* influence stock *x* (see Figure 1). This influence is like a force. If *y* is constant, that is, g(t) = 0, then x increases uniformly. If *g(t)* is constant, *y* changes, and *x* accelerates.

Let *g(t)* = -1, then y declines (Figure 2). While *y* is positive, *x* is increasing but decelerating. When *y* becomes negative, x accelerates and is not declining. *g(t)* = -1 is a negative force of *y* on *x*.

### Impact

This force has “impact,” which measures force as the ratio of the acceleration imparted on *x* with the rate of change of *x*. “Impact” is negative while x slows down and becomes positive as *x* accelerates. The polarity of this stock-to-stock impact determines whether *x* accelerates or decelerates. This negative force slows down a growing stock and turns it around so that it declines.

### Kinetic Energy

The stock *x* has a “kinetic energy,” which represents its rate of change. Kinetic energy measures how “change” occurs in the stock, a level of its “activity.” Figure 3 shows the change in *x*‘s kinetic energy over time. Initially, the kinetic energy falls until *x* becomes stationary. That is, it is momentarily at rest, the maximum of (Figure 1). After this point, the kinetic energy of *x* increases (Figure 3).

As *x* is losing kinetic energy, where does that energy go? Forces do work. The force of *y* on *x*, measured by impact, does work on *x*. In the first phase, negative impact, the force removes energy from *x*. In the second phase, positive impact, the force injects energy into *x*. Because this “dynamic” energy is conserved in a stock-flow system, the graph of the work done by *y* on *x* is identical to the kinetic energy (Figure 3).

### Energy Sink

Modify the model of Figure 1 to include a drain on *x* (Figure 4). The force is now made positive, *g(t) = 1*, so that *y *now accelerates *x*. The balancing loop, B, opposes this force. Thus, *x* grows, initially accelerating but tending towards uniform change (Figure 5). The curve of *x* is becoming straighter. The impact of *y* on *x* is declining, indicating a reduction in acceleration.

From the energy perspective, stock *y* is injecting energy into stock *x, *with loop *B* acting as an energy sink. Energy flows into *x*, initially increasing its kinetic energy – *x* accelerates. But *B* removes more and more energy, causing *x* to lose kinetic energy, slowing it down until kinetic energy becomes constant.

Figure 6 shows the energy balance on *x*. The energy injected from *y* (red dashes) is positive. The energy removed by *B* is negative (black dots). Their sum is equal to the change in kinetic energy (blue solid).

*change in kinetic energy of x = work done by y on x + work done by B on X*

The energy injected into x by y is partly absorbed into the kinetic energy of *x*, making it change faster. The remainder is removed from the system by *B*. For example, at time = 10, the work done by *y* on *x* is 0.370, and the change in kinetic energy is 0.2. The remainder is the work done by *B*, -0.170. Eventually, the kinetic energy stops changing, and *x *continues to change uniformly (Figure 5).

### Summary

One stock can inject or remove energy from another stock. First-order balancing loops remove energy from a stock-flow system. It can be shown that first-order balancing loops inject energy, second-order balancing loops exchange energy, and, under some conditions, may be conserved. In all other loops, energy is injected into a system regardless of their order, whether they are reinforcing or balancing. **A first-order balancing loop is the only structure that removes energy from stocks.** **They are essential for stability to be possible.**