Question

Two forces F₁ and F₂ are acting on a mass M = 5.0 kg. The force F₁ = 5.0i + 6.0j + 9.0k, in N. The acceleration of the mass is given by a = 1.0i + 7.0j + 2.0k, in m/s². Calculate the magnitude of F₂.

Answer 1

`|F_2|=24.83N`

Step-by-step explanation:

Newton's second law states that the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object:

`\Sigma F=F_n_e_t=m*a`

Let's find the magnitude of
`F_1` and
`a` using the next concept:

`|u|=√(u_1^2+u_2^2+u_3^3+...+u_n^2)`

`|F_1|=√(5^2+6^2+9^2) =11.91637529N`

`|a|=√(1^2+7^2+2^2)=7.348469228N`

Finally:

`|F_1|+ |F_2|=m*|a|\\|F_2|=m*|a|-|F_1|\\|F_2|=5*7.348469228-11.91637529=24.82597085\approx24.83N`