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A block of mass M resting on a 19.1° slope is shown. The block has coefficients of friction μs=0.788 and μk=0.482 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 1.86 kg. What is the minimum mass M1 that will stick and not slip?

http://capa.physics.mcmaster.ca/figures/kn/Graph08/kn-pic0836.png [Broken]

In terms of mass 1, following eqn can be written:

m1g sin 19.1 - T - Ff = 0

which can be rewritten as:

m1g sin 19.1 - T - m1g cos 19.1 (friction coefficient) = 0

right? since the object is at rest.

then i found T by equating it to m2g (T = m2g...see the diagram as to why i have donet this)

Hence m1g sin 19.1 - m2g - m1g cos 19.1 (0.788) = 0

and then solved for m1....but im not getting the right answer

I dont understand why my approach is wrong...where did i go wrong here?

http://capa.physics.mcmaster.ca/figures/kn/Graph08/kn-pic0836.png [Broken]

In terms of mass 1, following eqn can be written:

m1g sin 19.1 - T - Ff = 0

which can be rewritten as:

m1g sin 19.1 - T - m1g cos 19.1 (friction coefficient) = 0

right? since the object is at rest.

then i found T by equating it to m2g (T = m2g...see the diagram as to why i have donet this)

Hence m1g sin 19.1 - m2g - m1g cos 19.1 (0.788) = 0

and then solved for m1....but im not getting the right answer

I dont understand why my approach is wrong...where did i go wrong here?

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