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While moving in, a new homeowner is pushing a box across the floor at a constant velocity. The coefficient of kinetic friction between the box and the floor is 0.43. The pushing force is directed downward at an angle θ below the horizontal. When θ is greater than a certain value, it is not possible to move the box, no matter how large the pushing force is. Find that value of θ.

Respuesta :

Answer:

[tex]\theta = 66.7 degree[/tex]

Explanation:

since force is applied downwards at some angle with the horizontal

so here we will have

[tex]F_n = mg + Fsin\theta[/tex]

now we know that the box will not move if applied force is balanced by frictional force on it

so we will have

[tex]Fcos\theta = \mu F_n[/tex]

[tex]F cos\theta = \mu (mg + F sin\theta)[/tex]

[tex]F(cos\theta - \mu sin\theta) = \mu mg[/tex]

[tex]F = \frac{\mu mg}{cos\theta - \mu sin\theta}[/tex]

so here we can say

[tex]cos\theta - \mu sin\theta > 0[/tex]

[tex]tan\theta = \frac{1}{\mu}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\mu}[/tex]

[tex]\theta = tan^{-1}(\frac{1}{0.43})[/tex]

[tex]\theta = 66.7 degree[/tex]

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