vector question in multivariable calculus

**Jenny20** · November 30th 2006, 01:14 AM

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.

The answer is false.

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

**topsquark** · November 30th 2006, 03:55 AM

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.

The answer is false.

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

Add the two forces vectorally.

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.

Note: The angle mentioned in the problem is correct. I leave that to you to show.

-Dan

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