What Is the Minimum Static Friction Coefficient to Prevent m1 from Moving?

[chaotixmonjuish]

Two blocks with mass m1 = 4.6 kg and m2 = 5.6 kg are connected by a massless string over a frictionless and massless pulley. The angle of the incline is equal to 55.0°. The kinetic coefficient of friction between m1 and the incline is 0.17. What is the minimum value of the static friction coefficient that will prevent m1 from starting to move if it is at rest.

img:http://s242.photobucket.com/albums/ff106/jtdla/?action=view&current=prob02a.gif

I'm not exactly sure what this question is asking. I went ahead and set up a few equations.

M1
x: T-f-m1g*sin(theta)=m1a
y: N-m1g*cos(theta)=0

M2
y: T-m2g=ma

 

[TVP45]

Remember that a string is always ONLY in tension and any transmitted force must therefore be in the same direction as the string.

 

[chaotixmonjuish]

I'm having another problem calculating the acceleration if m1 were going down the incline (I was able to calculate if it were going up).

 

[Doc Al]

For the static friction case, realize that the acceleration of the blocks must be zero.

When the blocks move, realize that kinetic friction always opposes slipping.

 

[TVP45]

In this kind of problem, it is usually helpful to draw a free-body diagram. That is the block M1 with all the forces on it shown. Use arrows to show which way the forces act; if you don't know which direction, make a good guess. Don't worry about x-y components of the forces till you have them all accounted for. Before writing any equations, talk to yourself and say "Self, have I included every force mentioned in the problem? If not, why not." Ask yourself what will move (if anything) and in what direction. You should be able to reason this out before you start the math. If necessary, build a simple physical model and play with it. All this takes a lot of time but presumably you came here to learn Physics not to learn how to do this particular problem.

 

[chaotixmonjuish]

I actually got it. Though I need help justifying one part of me answer. later in the problem it asks about acceleration if M1 is moving up and down the incline. Why is it that the =m1a part stays negative while the friction stuff doesn't change.

 

[Doc Al]

Why is it that the =m1a part stays negative while the friction stuff doesn't change.

I don't understand this statement. The acceleration stays positive (up the ramp) while the friction changes direction depending upon which way m1 is moving.