Work ($W$) is a transfer of [[Energy|energy]]. It is a [[Scalars|scalar quantity]] describing the action of a [[Forces|force]] over **displacement**. The greater the force, then the greater the distance an object will travel. ## Formula $\vec{F} \cdot d \cdot cos \theta$ where $\vec{F}$ is the force acting over a displacement of $d$, and possibly at an angle of theta, $\theta$. ![[Screen_Shot_2020-11-22_at_11.27.21_AM.png]] Only the force acting in the direction of the motion is calculated in work. The formula for work is the multiplication of two vector quantities, and leads to a scalar quantity. This is because we are using the "dot product" rather than a "cross product." A dot product uses the magnitudes of the two vectors and multiplied by the cosine of the angle. ## SI Unit The SI unit for work is the joule (J), a derived unit of newton meter ($\frac{kg \cdot m^2}{s^2}$). This is the same unit as energy. > [!important] > Do not confuse newton@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css')⋅\cdot⋅meter for a joule with the newton@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css')⋅\cdot⋅meter of torque. The SI authority suggest not to use newton@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css')⋅\cdot⋅meter for energy or work; however, consider that work is an action done by a parallel component of a force "through" a displacement, whereas, torque is the perpendicular component of a force through a displacement. Example: Carrying a book Lifting a book is an example of doing work. No work is done if the an object is carried horizontally at a constant velocity. ## Calculations Horizontal Sample Calculation If a 50 N force is exerted on a box, and the box travels 5 meters then the work accomplished is ______. ## Angle Sample Calculation An issue arises when the force and displacement are not parallel to each other. The angle of the vectors must be taken into account. This leads to the final equation. W = $\vec{F} \cdot d \cdot cos \theta$ Keep in mind that the $cos (0\degree)$ is 1 and $cos (90 \degree)$ is 0. Use the cosine function to calculate maximum and minimum work. If the force on the box is 45°, and the box travels 5 meters then the work accomplished is __________. ![[Screen_Shot_2020-11-21_at_4.09.31_PM.png]] ## Force-Displacement Graph We can graph the force over displacement, in the same manner we graphed velocity versus time in kinematics. The area under the curve of a force v. displacement is equal to work. Integral $W = \int \vec{F} \cdot ds$ ### Related Topics --- [[Home|Home]] | [[Energy]] | [[Mechanical Energy]] | [[Kinetic Energy]] | [[Work-Energy Theorem]] | [[Potential Energy]] | [[Law of Conservation of Energy]] | [[Power]]