Question

A 50 kg box is dragged across a floor by pulling on a rope attached to the box and inclined at 30°
above the horizontal.
what minimum force magnitude is required from the rope to get the box moving?

Answer 1

Answer on Question #66272, Physics / Mechanics | Relativity

A $50\mathrm{kg}$ box is dragged across a floor by pulling on a rope attached to the box and inclined at $30{}^{\circ}$ above the horizontal.

what minimum force magnitude is required from the rope to get the box moving?

Solution

To make the box move, one needs to overcome the static friction $f$ .

$$f = \mu (m g - F \sin 3 0 {}^ {\circ}) = F \cos 3 0 {}^ {\circ};$$

where $\mu$ is the coefficient of static friction between he box and the floor.

$$\mu m g - \mu F \sin 3 0 {}^ {\circ} = F \cos 3 0 {}^ {\circ};$$ $$F = \frac {\mu m g}{\cos 3 0 {}^ {\circ} + \mu \sin 3 0 {}^ {\circ}};$$ $$F = \frac {\mu \times 5 0 \times 9 . 8 1}{0 . 8 6 6 + 0 . 5 \mu} = \frac {4 9 0 . 5 \mu}{0 . 8 6 6 - 0 . 5 \mu}$$

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