What Is the Maximum Acceleration a Plane Can Have Without a Coffee Cup Sliding?

[Cheddar]

Homework Statement

A cup of coffee is sitting on a table in an airplane that is flying at a constant altitude and a constant velocity. The coefficient of static friction between the cup and the table is 0.30. Suddenly, the plane accelerates, its altitude remaining constant. What is the maximum acceleration that the plane can have without the cup sliding backward on the table?

Homework Equations

fs(max) = coefficient of friction * normal force
Normal force = Work = mass * acceleration

The Attempt at a Solution

It doesn't give a force, work, or mass. All I can do is look at equations with 2 or 3 unknown variables. In addition to help with this problem, does anyone have any suggestions on solving problems that seem to be missing information? I'm coming across a lot of them and there's nothing worse than being stumped before even attempting to solve.

 

[Pupil]

You can't solve this problem because you don't know the whole story. The acceleration the cup of coffee could withstand without budging is different if it weighs 10 pounds or 1,000,000 pounds.

 

[Chrisas]

I think you can solve the problem. Usually in these types of problems with apparent missing values, you just go ahead and start writing out equations anyway and use a variable to represent the missing information. In this case, the mass is missing. However, if you do the force diagram and set the sum of horizontal forces = m*a, you will find that the mass cancels on each side. Usually when mass is not given, the problem is designed so that mass will cancel out. Try again and see if you get it.

 

[Cheddar]

I'm confused as to why the net horizontal force would be = mass * acceleration.
Mass * acceleration = Weight, which acts in the vertical direction.

 

[nickmai123]

I just wanted to mention that the normal force does not equal work. Work is Force * Distance. FYI only.

 

[Chrisas]

"Suddenly, the plane accelerates, its altitude remaining constant"

There is a normal force on the cup from the table that balances the weight (mass * g) of the cup. However, the plane is remaining at constant height and the cup is not flying through the air, but remaining on the table, so the net acceleration of the cup in the vertical direction is zero.

However, the plane is accelerating in the horizontal direction, so...