The free-body diagram below illustrates three forces ( F 1 , F 2 , and the gravi

Question

The free-body diagram below illustrates three forces (F1, F2, and the gravitational force) acting on a 7.22 kg object, with

The free-body diagram below illustrates three forces (F1, F2, and the gravitational force) acting on a 7.22 kg object, with 23o. The magnitude ofF2 is 68.9 N. If the object's acceleration is solely in the y-direction (there is zero acceleration in the x-direction), what is the y-component of the object's acceleration? Your answer should be positive if in the +y-direction and negative if in the -y-direction. Write your answer to three significant figures.

Explanation / Answer

Let the magnitude of force F1 be F
F1 = -Fcos 23i^ + Fsin 23 j^ = - 0.9205F i^ + 0.39073 F j^

so.. net force along x-direction = - 0.9205F + F2 = - 0.9205F + 68.9
as accleration along x in zero.. so net force along x = 0

so.. - 0.9205F + 68.9 = 0
so.. F = 74.85023 N


so.. F1 = - 68.9 i^ + 29.2463 j^

so.. net force in y direction = 29.2463 j^ - (7.22*9.8) j^ = -41.509685 j^

so.. y-component of objects accelertiaon = -41.509685/7.22 = -5.74926 m/sec2

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