* What is work? * Work (W) is the
energy change of a system due to an external force.

When work is done on a system, W > 0.

When the system does work on the external environment, W < 0.

* How do we calculate work? * There are three situations to consider:

- Constant net force
with the displacement;**colinear** - Constant net force
with the displacement;**non-colinear** -
net force.**Variable**

1. Constant colinear force: W = F x
x = distance traveled.

2. Constant non-colinear force: W = ** F **•
**Δr** = F Δr cos θ = F_{x} Δx + F_{y} Δy + F_{z} Δz

* See
transparencies for definition of dot product.*

Note that: W > 0 when the force is in the same direction as the
displacement;

W < 0 when these are in opposite directions;

W = 0 when
**F** ⊥ **Δr**;

W is maximized when **F** || **Δr**.

3. Variable force: dW = **F**(**r**)
• d**r** → W =
$\int $_{a}^{b} **F**(**r**)
• d**r**

Justification: From Newtons' 2nd law:

F_{s} = m a_{s} = m
dv_{s}/dt = m (dv_{s}/ds) (ds/dt) = m v_{s}
(dv_{s}/ds).

Multiply by ds: F_{s} ds = m
v_{s} dv_{s}.

Integrating gives:
∫_{a}^{b} F_{s} ds =
∫_{vi}^{vf} m
v_{s} dv_{s}= ½ mv_{f}^{2} -
½ mv_{i}^{2}

→ W = Δ K