Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Each box weighs 10lb. The coefficient of static friction between box A and box B is 0.24, and the coefficient of static friction between box B and the inclined surface is 0.3. What is the largest angle for which box B will not slip​

Sagot :

onyebuchinnaji

The largest angle for which box B will not slip​ is 16.7⁰.

The given parameters:

  • weight of box, W = 10 lb
  • coefficient of static friction between box A and box B, [tex]\mu_s_1[/tex] = 0.24
  • coefficient of static friction between box B and the inclined surface, [tex]\mu_s_2[/tex] = 0.3

The frictional force between box A and box B is calculated as;

[tex]F_f_1= \mu_s_1 (mg)[/tex]

The frictional force between box B and inclined surface is calculated as;

[tex]F_f = \mu_s_2 (2mg) cos(\theta)[/tex]

The net force on the boxes that results in no movement is calculated as;

[tex](2mg) sin(\theta) - F_f= 0\\\\(2mg) sin(\theta) = F_f\\\\(2mg) sin(\theta) = \ \mu_s_2 (2mg) cos(\theta)\\\\ sin(\theta) = \mu_s_2 cos(\theta)\\\\\mu_s_2 = \frac{sin(\theta)}{cos(\theta)} \\\\\mu_s_2 = tan(\theta)\\\\\theta = tan^{-1} (\mu_s_2)\\\\\theta = tan^{-1} (0.3)\\\\\theta = 16.7 \ ^ 0[/tex]

Thus, the largest angle for which box B will not slip​ is 16.7⁰.

Learn more about coefficient of static friction here: https://brainly.com/question/25050131

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.