Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Consider a block of mass m at rest on an inclined plane of angle theta. An acrobat of mass m_A is standing on the top corner of the block so that their weight presses vertically (perpendicular to the flat ground under the incline) downward. If the coefficient of static friction between the block and the incline is mu_s find an expression relating m_A, m, theta, and mu_s just before the block begins slipping. If the condition for slipping does not involve some of these parameters, leave them out.
Enter your expression as best you can and I will check it. Do not forget to upload your work as well.

Sagot :

Answer:

μ = tan θ

Explanation:

For this exercise let's use the translational equilibrium condition.

Let's set a datum with the x axis parallel to the plane and the y axis perpendicular to the plane.

Let's break down the weight of the block

         sin θ = Wₓ / W

         cos θ = W_y / W

         Wₓ = W sin θ

         W_y = W cos θ

The acrobat is vertically so his weight decomposition is

         sin θ = = wₐₓ / wₐ

         cos θ = wₐ_y / wₐ

         wₐₓ = wₐ  sin θ

         wₐ_y = wₐ cos θ

let's write the equilibrium equations

Y axis  

     N- W_y - wₐ_y = 0

     N = W cos θ + wₐ cos θ

X axis

        Wₓ + wₐ_x - fr = 0

         fr = W sin θ + wₐ sin θ

the friction force has the formula

         fr = μ N

         fr = μ (W cos θ + wₐ cos θ)

we substitute

         μ (Mg cos θ + mg cos θ) = Mgsin θ + mg sin θ

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

 

         μ = tan θ

this is the minimum value of the coefficient of static friction for which the system is in equilibrium.

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.