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Two forces Upper FSubscript Upper A Baseline Overscript right-arrow EndScripts and Upper FSubscript Upper B Baseline Overscript right-arrow EndScripts are applied to an object whose mass is 10.6 kg. The larger force is Upper FSubscript Upper A Baseline Overscript right-arrow EndScripts. When both forces point due east, the object's acceleration has a magnitude of 0.554 m/s2. However, when Upper FSubscript Upper A Baseline Overscript right-arrow EndScripts points due east and Upper FSubscript Upper B Baseline Overscript right-arrow EndScripts points due west, the acceleration is 0.313 m/s2, due east. Find (a) the magnitude of Upper FSubscript Upper A Baseline Overscript right-arrow EndScripts and (b) the magnitude of Upper FSubscript Upper B Baseline Overscript right-arrow EndScripts.

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Answer:

Part a)

[tex]F_A = 4.59 N[/tex]

Part B)

[tex]F_B = 1.28 N[/tex]

Explanation:

As we know that when both the forces are acting on the object in same direction then we will have

[tex]F_A + F_B = ma[/tex]

as we know that

[tex]a = 0.554 m/s^2[/tex]

m = 10.6 kg

now we will have

[tex]F_A + F_B = 10.6(0.554)[/tex]

[tex]F_A + F_B = 5.87 N[/tex]

Now two forces are in opposite direction then we have

[tex]F_A - F_B = 10.6(0.313)[/tex]

[tex]F_A - F_B = 3.32 N[/tex]

Part A)

Now we will have from above two equation

[tex]F_A = 4.59 N[/tex]

Part B)

Similarly for other force we have

[tex]F_B = 1.28 N[/tex]

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