What Is the Correct Magnitude of F2?

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To find the correct magnitude of force F2 acting on a mass of 6.0 kg, the equation F = m*a is used, leading to F1 + F2 = m*a. The components of F1 are given as 7.0i + 4.0j + 3.0k, with a magnitude of 8.6 N, while the acceleration vector is 2.0i + 7.0j + 4.0k, resulting in a magnitude of 8.31 m/s². The error in the calculation arises from attempting to replace the vectors with their magnitudes instead of solving for the vector components of F2. The correct approach requires calculating the components of F2 and then determining its magnitude. Proper vector analysis is essential for accurate results in this scenario.
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Homework Statement



Two forces F1 and F2 are acting on a mass m=6.0 kg. The force F1 = 7.0i + 4.0j + 3.0k, in N. The acceleration of the mass is given by a = 2.0i + 7.0j + 4.0k, in m/s2. Calculate the magnitude of F2.

Homework Equations



F=m*a

The Attempt at a Solution



F1+F2=m*a
F2=(m*a)-F1

Magnitude of F12=72+42+32
Magnitude of F1=8.6 N

Magnitude of a2=22+72+42
Magnitude of a=8.31 m/s2

so...

shouldnt F2=(6.0 kg * 8.31 m/s2) - 8.6 N ?? (which is 41.24 N)The website where I submit my answer tells me that I am wrong please help me out.

Thankss!
--Graham
 
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g.uricchio said:
F1+F2=m*a
F2=(m*a)-F1
This is good. Note that this is a vector equation. Use it to find the three components of F2, then find the magnitude.

Magnitude of F12=72+42+32
Magnitude of F1=8.6 N

Magnitude of a2=22+72+42
Magnitude of a=8.31 m/s2

so...

shouldnt F2=(6.0 kg * 8.31 m/s2) - 8.6 N ?? (which is 41.24 N)
You can't just replace the vectors F and a with their magnitudes.
 
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