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A block with mass M is placed on an inclined plane with slope angle q and is connected to a second hanging block with mass m by a cord passing over a small, frictionless pully. The coefficient of static friction μs and the coefficient of kinetic friction is μk. For what range values of of m will the blocks remain at rest if they are released from rest.

A block with mass M is placed on an inclined plane with slope angle q and is connected to a second hanging block with mass m by a cord passing over a small fric class=

Respuesta :

whitneytr12

Answer:

The mass of the block m is:

[tex]m=M(sin(\theta)+\mu_{s}cos(\theta))[/tex]

Explanation:

Let's analyze the block by parts

For the block M

[tex]T-W_{x}-f_{f}=0[/tex] (1)

Where:

  • T is the tension
  • W(x) is the component of the weight in the x-direction
  • F(f) is the friction force

[tex]T-Mgsin(\theta)-\mu_{s}N=0[/tex]  

[tex]T-Mgsin(\theta)-\mu_{s}Mgcos(\theta)=0[/tex]  

For the block m

[tex]T-W=0[/tex]

[tex]T=mg[/tex] (2)

Now, let's combines equation (1) and (2):

[tex]mg-Mgsin(\theta)-\mu_{s}Mgcos(\theta)=0[/tex]  

Finally, let's solve it for block m.

[tex]mg-Mg(sin(\theta)+\mu_{s}cos(\theta))=0[/tex]

[tex]m=M(sin(\theta)+\mu_{s}cos(\theta))[/tex]

I hope it helps you!

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