Teaching Guidance for 14-16
Power in pathways fill stores
The power in a pathway can fill or empty a store, so the power can effect a accumulation of energy in the store (the accumulation can be either positive or negative). As both force and velocity are vectors, you really ought to write: VectorP = →F × →v .
⋅ represents a special kind of multiplication (a
dot product) for vectors, giving a scalar as a result – remember that power is a scalar.
Even in thinking about simple, one-dimensional situations, there are four possibilities:
- Velocity is positive, force is negative.
- Velocity is negative, force is positive.
- Velocity is negative, force is negative.
- Velocity is positive, force is positive.
With the first pair of possibilities the power is changing the energy in the store in the opposite sense to that in the second pair (reversing the flow, from filling to emptying, or from emptying to filling). In either case this depends on the physical situation: we'd recommend thinking about this rather than trying to memorise sign conventions and linking those to filling or emptying actions.