Work, Energy, Conservative and Nonconservative Forces

• It is a way on how to multiply two vectors returning a scalar quantity.
• Just map the first component of the first vector to the first component of the second vector and so on.

Example:

\begin{align*} & a = \langle2, 2\rangle \\ & b = \langle5, -3\rangle \\ & a\cdot b = [(2)(5)] + [(2)(-3)] = 10 + -6 = 4 \end{align*}

Alternative Formula:

\begin{align*} & a\cdot b = \lvert a\rvert\lvert b\rvert cos\theta \\ & cos\theta = \frac{a\cdot b}{|a||b|} \end{align*}

Remember:

\begin{align*} & a = \langle A_x, A_y \rangle \\ & \lvert a\rvert = \sqrt{A_x^2 + A_y^2} \\ & \lVert a\rVert = abs(\lvert a \rvert) \end{align*}

\begin{align*} Average\ Power = \frac{Work}{time} \end{align*}

• The SI Unit of Power is Watts (W) which is just Joule/second.
• The power outputted by a powered object, such as an engine or muscles, is sometimes called the motive power.