Question

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.

Answer 1

Answer:

$\theta = 66.7 degree$

Explanation:

since force is applied downwards at some angle with the horizontal

so here we will have

$F_n = mg + Fsin\theta$

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

so we will have

$Fcos\theta = \mu F_n$

$F cos\theta = \mu (mg + F sin\theta)$

$F(cos\theta - \mu sin\theta) = \mu mg$

$F = \frac{\mu mg}{cos\theta - \mu sin\theta}$

so here we can say

$cos\theta - \mu sin\theta > 0$

$tan\theta = \frac{1}{\mu}$

$\theta = tan^{-1}\frac{1}{\mu}$

$\theta = tan^{-1}(\frac{1}{0.43})$

$\theta = 66.7 degree$