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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

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