Question

1. Show how the alternative definition of power, found in your book, can be derived by substituting the definitions of work and speed into the standard definition of power, P = W / delta t.
2. A real spring does not oscillate forever. Instead, it eventually comes to a stop. Does this violate the Law of Conservation of Energy? Explain why or why not.

Answer 1

1) Star from the definition of power:

P = work/ time = W / Δt

We know that work is given by force times displacement:
 W = F · Δd
Substituting in our formula: 
P = F · Δd / Δt

But we know by definition that Δd / Δt = velocity, therefore we can write:
P = F · v
which is the alternative formula saying that Power is equal to Force times Velocity

2) No, it is not a violation of the Law of conservation of energy because as the spring slows down, the kinetic energy is transformed into potential energy and their sum stays constant.