# A cup of coffee is on a table in an airplane flying at a constant altitude and a constant...

## Question:

A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity. The coefficient of static friction between the cup and the table is 0.100. Suddenly, the plane accelerates forward, its altitude remaining constant. What is the maximum acceleration that the plane can have without the cup sliding backward on the table? Use {eq}g = 9.81 {/eq} m per {eq}s^2 {/eq}.

## Pseudo-Force:

The pseudo force is defined as the force that is assumed to act opposite to the direction of the motion on the objects which move in an accelerated frame of reference to make the Newtonian laws of motion work.

Given:

• Constant velocity
• Constant altitude
• Coefficient of friction, {eq}\mu=0.1 {/eq}

As the airplane accelerated forward, pseudo-force acts on the cup of coffee backward and a friction force acts forward to keep the cup,

Therefore,

{eq}ma=\mu mg\\ a=\mu g\\ a=0.1\times9.8\\ a=0.98 \ \rm m/s^{2} {/eq}

Thus, the maximum acceleration is {eq}0.98 \ \rm m/s^{2} {/eq}. 