Slipping Problems

• Theory: The Breaking of Static Friction.

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.

Example

A 10N block is being pulled on by a rope with tension T. What is the maximum tension before the block slides? The coefficient of static friction is $\mu_S=0.6$.

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.