Question

Determine the magnitude and direction of the smallest force F. shown in
Fig. Q.12(a) which will maintain the package shown in equilibrium. Note
that the force exerted by the rollers on the package is perpendicular to
the incline.
30 kg
1501
Fig. Q.12(a)
Or
c​

Answer 1

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Answer 2

Complete question:

Determine the magnitude and direction of the smallest force F which will maintain the package shown in equilibrium. Note that the force exerted by the rollers on the package is perpendicular to the incline.

Answer:

The magnitude of force F is 76.1 N and the direction of force is 15° with the horizontal

Explanation:

Free-Body Diagram. We select the bundle as a free body, assuming that it is able to be treated as a particle. We draw the corresponding free-body diagram. Equilibrium Condition. Since the simplest 3 forces act on the free body, we draw a force triangle to specify that it is in equilibrium. Line 1 - 1'  represents the recognized path of P. In order to attain the minimum value of the force F, we select the path of F perpendicular to that of P. From the geometry of the triangle obtained, we find

F = (294 N) sin 15° = 76.1 N    α = 15°

F = 76.1 N ⦩15°

Therefore, the magnitude of force F is 76.1 N and the direction of force is 15° with the horizontal.

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