How Do You Calculate the Minimum Force to Prevent Slipping Between Two Masses?

[mmolteratx]

Homework Statement

I've got a few physics homework questions I need a bit of help with. All relate to friction.

Here's the first one:

The µs = .2 between the boxes. Mass 2 (80kg) is on an air table. What minimum force will keep mass 1 (40kg) from slipping? What is the maximum acceleration that will keep the mass from slipping?

Here's a pic I drew up with FBDs.

Homework Equations

0.2Fn+Fsin30=mg or 0.2Fcos30+Fsin30=mg

The Attempt at a Solution

If I solve for F I get 582. 289N but the answer I was given is 637N. Where did I go wrong? or is that the right answer? I think it's because I didn't account for mass 2 moving when the force is applied but I'm not sure how to do that.

 

[Delphi51]

There is no mention of a 30 degree angle in the question!
It appears that the 40 kg mass is about to fall straight down . . . but is prevented from doing so by friction with the 80 kg mass that presses against it when the 80 kg is being pushed to the left.

You need to work with the friction force and the gravitational force pulling the 40 kg mass downward. No angles!

 

[mmolteratx]

My bad. I forgot to put theta=30 in the diagram. The force is being applied at a 30 degree angle.

 

[Delphi51]

Oh, that makes it more complicated. It is a 2 dimensional problem so you should make two headings for the horizontal and vertical parts.
In the horizontal part, you just have F=ma for the horizontal component of the force causing the combined masses to accelerate. In the vertical part, you have Fg - F*sin(30) downward trying to make it slip and Ff holding it. System of 2 equations with unknowns F and a.

 

[mmolteratx]

Thanks! Got it and managed to figure out the rest of my problems.

 

[Delphi51]

Most welcome.