vector question in multivariable calculus

• Nov 30th 2006, 02:14 AM
Jenny20
vector question in multivariable calculus
Question
If two forces Fsub1 and Fsub2 each of magnitude 10N act on an object from perpendicular directions, then the effect is the same as that of a single force of 10N acting in a direction 45 degrees to each of the forces Fsub1 and Fsub2.

Could you explain to me why the answer is false? If possible , could you please show me the working step? Thank you very much.
• Nov 30th 2006, 04:55 AM
topsquark
Quote:

Originally Posted by Jenny20
Question
If two forces Fsub1 and Fsub2 each of magnitude 10N act on an object from perpendicular directions, then the effect is the same as that of a single force of 10N acting in a direction 45 degrees to each of the forces Fsub1 and Fsub2.

Could you explain to me why the answer is false? If possible , could you please show me the working step? Thank you very much.

Let $\vec{F}_1 = 10 \hat{i}$ N and $\vec{F}_2 = 10 \hat{j}$ N. Then
$\vec{F}_{tot} = \vec{F}_1 + \vec{F}_2$
$\vec{F}_{tot} = 10\hat{i} + 10\hat{j}$ N
which has a magnitude of $\left | \vec{F}_{tot} \right | = \sqrt{10^2 + 10^2} = 10\sqrt{2}$ N, not 10 N.