What Is the Correct Magnitude of F2?

[g.uricchio]

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

 

[Doc Al]

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.

 

[thomate1]

Dear Graham,

Thank you for your explanation of your attempt at solving this problem. However, there are a few errors in your calculations.

Firstly, the magnitude of F1 is incorrect. The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the magnitude of F1 is √(7.0^2 + 4.0^2 + 3.0^2) = √74 = 8.6 N.

Secondly, the magnitude of a is also incorrect. The magnitude of a is √(2.0^2 + 7.0^2 + 4.0^2) = √69 = 8.31 m/s^2.

Finally, when calculating the magnitude of F2, you must use the correct values for F1 and a. So, the correct equation is F2 = m*a - F1 = (6.0 kg * 8.31 m/s^2) - 8.6 N = 41.86 N.

I hope this helps clarify the correct approach to solving this problem. Keep up the good work in your studies as a scientist!

Best,