The physics of a tea cup on an accelerating airplane

[jess_08]

Homework Statement

Imagine being on an airplane in flight. You have a cup of tea on a table in front of you. The plane then starts to accelerate at the same altitude it had initially. The coefficient of static friction between the cup and the table is 0.250. What is the maximum acceleration of the plane before the cup beings to slide on the table?

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

Have you any ideas?

 

[Shooting Star]

If the accn of the plane in the horizontal dircn is 'a', then in the frame of the plane, there is an inertial force of ma acting on an object of mass m, opp to the direction of accn. This must be balanced by the frictional force if the cup is static. For the limiting case, equate frictional force to ma. You know the relationship between frictional force and weight of the object.

 

[Hootenanny]

While what Shooting star said is correct, you should be aware that the 'inertial force' is what is known as a d'Alembert force or pseudo force and is so called because such forces don't arise from any physical interactions, instead they arise when we consider an interaction in a non-inertial (accelerating) reference frame. There's nothing wrong with using non-inertial reference frames, but in general while studying elementary mechanics it is better to only use inertial reference frames.

 

[Shooting Star]

Have you any ideas?

When I gave hints to the solution, I didn't notice that this post belonged to Introductory Physics. I should have allowed more time for the OP to come up with his own ideas. Sorry. Won't happen next time.

 

[Hootenanny]

When I gave hints to the solution, I didn't notice that this post belonged to Introductory Physics. I should have allowed more time for the OP to come up with his own ideas. Sorry. Won't happen next time.

Don't worry bout it, there's nothing wrong with the advice you gave!