What is the Acceleration of an Elevator with Friction?

[Oblivion77]

Homework Statement

A man standing in an elevator that is moving with a constant acceleration holds a 3-kg block B between two other blocks in such a way that the motion of B relative to A and C is impending. Knowing that the coefficients of friction between all surfaces are μs = 0.30 and μk = 0.25, determine (a) the acceleration of the elevator if it is moving upward and each of the forces exerted by the man on blocks A and C has a horizontal component equal to twice the weight of B, (b) the horizontal components of the forces exerted by the man on blocks A and C if the acceleration of the elevator is 2.0 m/s2 downward

Homework Equations

Newton's 2nd law
sum of the forces in x = 0
sum of the forces in y = ma

The Attempt at a Solution

I am stuck on part a. I tried drawing a FBD of block B to find the acceleration of the elevator but it didn't work out.

 

[rl.bhat]

When the lift is moving up with an acceleration a, the net acceleration is ( g + a)
When the lift is moving down with an acceleration a, the net acceleration is ( g - a).
In part (a), find the net frictional force on B and equate it to the apparent weight of B to find a.

 

[tiny-tim]

Hi Oblivion77!

I tried drawing a FBD of block B to find the acceleration of the elevator but it didn't work out.

It should have done … F = ma should give you a.

Show us your full calculations, and then we can see what went wrong.

When the lift is moving up with an acceleration a, the net acceleration is ( g + a)
When the lift is moving down with an acceleration a, the net acceleration is ( g - a).

Surely the acceleration of B is always a?

 

[mannie]

Hi there,
I did the work assuming that block B was not moving i.e. force < UsN where N was the force applied horizontal by blocks A and C and got answers for both parts A, and B.
How would I know that block B was not moving in which case i would use Uk instead of Us. My prof said I would have to assume it was not moving and test to see if F <= UsN if not then F= UkN, but don't know how I would do that in this case.

Thanks!

 

[tiny-tim]

Hi there,
I did the work assuming that block B was not moving i.e. force < UsN where N was the force applied horizontal by blocks A and C and got answers for both parts A, and B.
How would I know that block B was not moving in which case i would use Uk instead of Us. My prof said I would have to assume it was not moving and test to see if F <= UsN if not then F= UkN, but don't know how I would do that in this case.

Thanks!

Hi mannie!

(are you the same person as Oblivion77? have a mu anyway: µ and try using the X₂ tag just above the Reply box )

Just calculate F as the vertical force necessary to keep B stationary …

then if F ≤ µ_sN, the available force (of static friction) is sufficient … if not, then it isn't, and some other force would be needed (and of course that other force would have to make up the difference, not between F and µ_sN, but between F and µ_kN).