Two masses on an inclined plane with a massless pulley

  • Thread starter JefeNorte
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  • #1
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Homework Statement


A block of mass m resting on a 20 degree slope. The block has coefficients of friction mu_s =0.80 and mu_k =0.50 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.

What is the minimum mass m that will stick and not slip?

If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?


Homework Equations


T-f_k-(mg*sin(theta))=m*a
f_k=u_k*(mg*cos(theta))


The Attempt at a Solution


I completed the first part of the problem and determined that the minimum mass is 1.829 kg. I calculated the tension on the rope by multiplying the mass of the hanging block by 9.8. But when I plug these values into the equation I keep getting 2.76 m/s^2 which is not the correct answer. Is there something wrong with my equations or the tension value?
 

Answers and Replies

  • #2
Dick
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The tension in the rope is only equal to the weight of the hanging block if the objects aren't accelerating. You need to write the sum of the forces = ma for each object, where the sum of the forces includes the unknown tension T. Then you have two equations and two unknowns and you solve for T and a.
 
  • #3
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Do you mean like T-(u_k*(mg*cos(theta)))-(mg*sin(theta))=m*a?
 
  • #4
Dick
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I mean something exactly like that.
 

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