Look at this picture of a poorly designed lever system. a) Redraw the lever showing an improved design.

1. Identify the essential elements of a lever: - A rigid bar (the lever) - A fixed pivot point (the fulcrum) - The point of load (where the resistance or weight is applied) - The point of applied force 2. In many poorly designed lever systems, the positions of the load, force, and fulcrum are not optimized to take full advantage of the lever’s mechanical advantage. An improved design should ensure that the applied force produces a sufficient moment (torque) about the fulcrum to overcome the load. Recall that the moment is given by \[ \text{Moment} = \text{Force} \times \text{Distance from the fulcrum} \] 3. One common way to improve performance is to place the load closer to the fulcrum and the applied force at a farther distance from it. This increases the distance ratio while using the same applied force, hence increasing the generated moment. 4. Below is one way to redraw the lever system with an improved design. In this diagram: - The fulcrum is placed at point \( F \). - The load, labeled \( L \), is applied closer to \( F \). - The force, labeled \( F_{\text{applied}} \), is applied at a farther point from \( F \). --- ```latex \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}[scale=1] % Draw the lever bar \draw[thick] (0,0) -- (8,0); % Mark the fulcrum at point F (improved location) \draw[fill] (2,0) circle (0.1); \node[below] at (2,0) {\(F\) (Fulcrum)}; % Mark the load L close to the fulcrum \draw[fill] (1,0) circle (0.07); \node[above] at (1,0) {\(L\) (Load)}; \draw[blue,->,thick] (1,0.2) -- (1,1.2); % Mark the point of applied force at a farther distance from the fulcrum \draw[fill] (7,0) circle (0.07); \node[above] at (7,0) {\(F_{\text{applied}}\)}; \draw[red,->,thick] (7,0.2) -- (7,1.2); % Optionally, indicate distances with double arrows \draw[<->, dashed] (1, -0.5) -- node[midway, fill=white]{\(\Delta x_1\)} (2, -0.5); \draw[<->, dashed] (2, -0.7) -- node[midway, fill=white]{\(\Delta x_2\)} (7, -0.7); \end{tikzpicture} \end{document} ``` --- 5. Explanation of the improved design: - The lever is drawn as a straight bar from \( 0 \) to \( 8 \) units. - The fulcrum \( F \) (at \( x=2 \)) is clearly indicated so that it is easy to see how distances on either side contribute to the moments. - The load \( L \) is moved closer to the fulcrum (at \( x=1 \)) reducing the necessary force to balance or move the load. - The force \( F_{\text{applied}} \) is applied at \( x=7 \), increasing the torque arm and so the overall moment available to overcome the load. This lever system is now optimized to maximize the mechanical advantage according to the relation \[ F_{\text{applied}} \times \Delta x_2 = L \times \Delta x_1, \] where \(\Delta x_1\) is the distance from the load to the fulcrum and \(\Delta x_2\) is the distance from the fulcrum to where the force is applied.