# Find the Applied force

## Homework Statement

Two objects are on an incline plane. One object with larger mass is lower down on the plane. The other with smaller mass is leaning on the larger object but not one the surface of the plane. If both masses, the angle β, coefficient of static friction and the coefficient of kinetic friction are given what is the required Fa to keep the second block from falling.

## The Attempt at a Solution

I've been working on this for several hours but have been unable to figure out the solution. What I tried doing was starting with the second block which I will call m.

Fnety = ma = 0
Fstatic friction - mgcosβ = 0
Fstatic = mg cosβ
$$\mu$$Fn=mgcosβ
Fn=mgcosβ/$$\mu$$

Fnet x = ma = mgcosβ/$$\mu$$ - mgsingβ
a = gcosβ/$$\mu$$k - gsinβ

Then for both blocks combined I did

Fnety = ma = 0
Fn - (M+m)gcosβ = 0
Fn = (M+m)gcosβ

Fnetx = Fa - Fkinetic friction = (M+m)a
Fa = $$\mu$$s(M+m)gcosβ + (M+m)(gcosβ$$\mu$$k - gsinβ)

This is the answer I got but my teacher told me its wrong, can anyone give me some help as to where I am messing it up

I don't understand the set-up, and I doubt that I'm the only one, could you explain it more or give a diagram? I don't understand where the smaller mass is. Is it on top of the the other mass? If not, how is it resting on the plane without being in contact with the plane, by rollers or something? How the smaller block is resting is very critical.

Another thing that I don't understand from the problem description is why you would need the coefficient of kinetic friction. The whole point is for the blocks not to move.

The photo I attached is of the given diagram. The smaller mass is leaning on the larger mass but above the ground. The coefficient of static and kinetic were given, I assumed the static was for between the two masses and the kinetic was for between the larger mass and the plane.

#### Attachments

• photo.jpg
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Treat the two blocks as a system, don't split it up. So I guess what you want to do is figure out what force in addition to static friction will prevent the blocks from sliding. I agree with most of what you've done in that case; however, the normal force should not have both masses, but the force of gravity should. Then make an inequality showing that the applied force must be greater than or equal to your result.