Block on a slope, friction related

[Revolt]

A 300kg block is sitting on a slope of 20 degrees, the coeff of friction is 0.75, if the block is connected to a mass hanging vertically via a pulley, what is the mass of the hanging block such that it will overcome friction but not move the block

F = mgsin20 for the force acting down the slope
F = mgcos20 for the force acting perpendicular to the slope



Have attached a PDF of my attempt, but basically I found the force acting down the slope and then used this as the force in my next equation to calculate the mass,

Getting a result of 384kg, I now realize I haven't properly taken friction into account and I am unsure of how to do this.

 

[apelling]

In your attempt you've added the two vector components together as if they are scalar quantities ie 1006 + 2765 = 3771. I suggest you draw a free body force diagram for the 300kg block. Are we to assume it is on the point moving upwards?

 

[Revolt]

Indeed, got another solution ill upload in a minute

 

[Revolt]

For some reason the scanner isn't working, but basically i found the force required to in effect keep the block on the slope still, using

F = mgsin20 + umgcos20

and from this force i used m=F/g to get the mass of the block, 314kg... this seem right ?

 

[Revolt]

Could someone maybe run through this and tell me if they get a matching 314kg for the other block? thanks

 

[Revolt]

Have uploaded a new file with my method, anyone comment please?

 

[lep11]

Have uploaded a new file with my method, anyone comment please?

Well...you should draw all the forces and components acting on the block and also show clearly your reasoning. Otherwise your calculations are correct.