Max and Min Applied Force for Stationary Block on Inclined Plane

[thenewbosco]

The problem is:

We have a 2kg block on a 30 degree incline, with the coefficient of static friction= 0.5. I am supposed to determine the maximum and minimum values of an applied force at 30 degrees to the plane that will keep the block stationary.

My positive x direction is down the ramp.

I have tried to sum the forces in the x direction as follows,

x component of gravity - x component of applied force - friction = 0

I am not sure if friction should be here in this form, considering that
Force of static friction < μs (Normal force)

Any help?

Bosco

 

[ponjavic]

I do not understand why it shouldn't be, use the gravity to calculate the normal force and then you can calculate the friction.

 

[thenewbosco]

I do not know how to get the two different forces- maximum and minimum though.

 

[robphy]

The strength of the static friction force is whatever it needs to be to prevent sliding... up to a maximum strength, given by mu*N.

As you apply your external force, the required static friction force varies.
Additionally, if your external force has a component perpendicular to the incline, the normal force will vary (and hence the maximum friction force will vary).

 

[thenewbosco]

great but how do i go about solving this problem now

 

[maverick280857]

Well looking at the very statement of the problem, you should reason that since there are two different kinds of forces (maximum and minimum) the effects they produce are different, perhaps with regard to the different slipping tendencies of the block :-).

 

[thenewbosco]

my answers were: force min = 1.18N and force max = 29.6 N

can anyone tell me if this is right/reasonable?

 

[maverick280857]

What have you done?