#$&*
Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Vector magnitude and angle
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What vector of magnitude 6.7 must be added to the force vector A = < -3.2 Newtons, 7.38 Newtons> in order to obtain a vertical vector R? Answer by giving the magnitude and angle of the vector to be added.
(Note on notation: stands for a vector whose x component is u and whose y component is v.)
Solution
If the resultant vector is to be vertical, then its x component will be 0.
So we must find a vector which when added to < -3.2 Newtons, 7.38 Newtons>, results in a vector whose x component is 0.
Clearly then the x component of the added vector will have to be - -3.2 Newtons, since this is the only way to cancel out the x component of the original vector and end up with x component 0.
The vector being added must have magnitude 6.7 Newtons.
We can use this fact to find its y component.
If y stands for the y component of the added vector, the Pythagorean Theorem tells us that
(- -3.2 Newtons) ^ 2+y ^ 2 = ( 6.7 Newtons) ^ 2, or 10.24 Newtons ^ 2 + y ^ 2 = 44.88 Newtons ^ 2.
We can solve this equation for y to obtain y = `sqrt( 44.88 Newtons ^ 2 - 10.24 Newtons ^ 2) = 44.88 Newtons.
The vector being added therefore has components - -3.2 Newtons and 44.88 Newtons, and is represented <--3.2 Newtons, 44.88 Newtons>
The magnitude and angle of this vector are easily found to be 6.7 Newtons, as required, and 85.92 degrees.
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I think there may be a typo here, but I still have an additional question.
I find that in the last step of the Pythagorean theorem, we get y = +-5.9.
Because y = `sqrt( 44.88 Newtons ^ 2 - 10.24 Newtons ^ 2) then
y = `sqrt(34.66 Newtons ^2)
y = +- 5.9
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The random number generator grabbed the wrong variable.
Your solution appears to be correct.
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In this case would we use both possible values for y to find the angle?
angle = tan^-1 (5.9/32) = 61.5 or degrees
angle = tan^-1 (-5.9/32) = - 61.5 degrees
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Your calculation of the angle also appears correct. The added vector can be back to the y axis either by being up and to the right, or down and to the right.
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