\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Slipping Problems

• Theory: [Missing Link].

How do we recognize slipping problems

• A "slipping problem" is one where there is static friction that is in danger of breaking
• If the problem mentions something like "when will it slide?" or "what's the maximum value before it slides?", this is a slipping problem

Solving Slipping Problems

• Analyze the problem as usual, with a force table and force diagram. You should not write $\mu_S$ in the force table at all; just refer to the static friction as $S$ as usual.
• Get the equations from the force table.
• Add the inequality $S_{\Box} \le \mu_S N_{\Box}$, where $\Box$ refers to the surface where the static friction is in danger of breaking.
• Solve the first two equations for $S_{\Box}$ and $N_{\Box}$
• Substitute into the inequality.
• Solve the inequality for whatever you need to solve for.

Solving Inequalities

• Linear inequalities are mostly solved the same way equalities are.
• Pay close attention to the direction of the inequality.
• If you multiply or divide by a negative number, the inequality should be flipped. Multiplying or dividing by a number whose sign is unknown means that the direction of the inequality is uncertain.