HELP Find the mass in this inclined pulley system, required to move the 2 masses

[dani123]

In this problem they show a diagram of a pulley system with an inclined plane (25 degree incline). There is a box called m1=47kg resting on the incline plane and m1=35kg hanging on the vertical line. The question reads: The coefficient of friction between m1 and the surfvace of the inclined plane are Ustatic=0.42 and Ukinetic=0.19.
a)if the masses are held in place and then released , will they start to move? ------> I know the answer is NO.
b)how much mass would you have to add to m2 to cause the masses to begin to move? ----> The answer should be 2.8kg but I don't know how the book got this answer.
c)If you said no to a) and added the mass that you calculated in b), what would be the acceleration of the masses? ---> answer given in the back of textbook is 5.7 m/s^2

ANY help with this problem would be greatly appreciated! THANK YOU SO MUCH in advance :)

For m1=47kg
Fparallel=mgsin(25)=194.7N
Fg=47*9.8=461N
Fperpendicular=Fn=417N
Ffk=uk*Fn=0.19*417=79N

Applying Newton's 2nd law to m1
Fparallel-Ff-Ft=194.7-79-Ft=47*a

For m2=35kg
Fg=35*9.8=343N

Apply Newton's 2nd law to m2
Ft-343N=35*a

combine the two equations involving acceleration and cancelling out the force of tensions... this only leads us to an equation that ends up giving us a=-2.77m/s^2... but this is where I am stuck... how do I find the mass required to get both masses to move?!

can we assume the acceleration is equal to 1 when we are trying to determine the mass of m2, since they did not specify in the question?

 

[dani123]

Would it be safe to say that the acceleration is equal to 1 if they do not specify in the question?

 

[ehild]

You know that the force of static friction is Fs≤μmgcos(25). Calculate the static friction when a=0 and check if it is less than μmgcos(25). Then suppose that Fs =μmgcos(25) and find the mass to add to m2 so you get a=0.

ehild

 

[dani123]

Do I use the m2 for both of those equations?

 

[ehild]

The force of friction is calculated for m1=47 kg.
Do what you did in the first post: Collet the forces acting both m1 and m2, and cancel the tension.

ehild