Question 1200093: The resultant of two forces p and q is 260N, if p is 80N and the angle between p and q is 150°. Find q Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52932) (Show Source):
You can put this solution on YOUR website! .
The resultant of two forces p and q is 260N, if p is 80N and the angle between p and q is 150°. Find q
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We are given two forces and as vectors.
We are given that the magnitude of is p = 80 N.
We are given that the angle between the vectors and is 150°.
We are given the resultant of forces and is equal to 260 N.
Apply the parallelogram rule of adding forces.
You will have a triangle with the sides p = 80N and q and the angle between them
of 180° - 150° = 30°.
The opposite side of this triangle is 260N (the resultant).
Apply the cosine law
= + - 2*80*q*cos(30°).
Transform to the standard form quadratic equation
q^2 - 2*80*q*(sqrt(3)/2}}} + = 0
q^2 - 138.56q - 61200 = 0.
Solve the quadratic equation using the quadratic formula.
You will get two roots 326.2 (rounded) and -187.6 (rounded).
Since we are looking for the magnitude, we select the positive root 326.2.
ANSWER. The magnitude of q is 326.2 N.
Solved.
Surely, you can work with any other precision you want - the methodology allows you to do it.
You can put this solution on YOUR website!
Draw out two vectors that have an angle of 150 degrees between them.
One vector has a magnitude of 80 newtons, and the other has magnitude q newtons.
Then draw in additional parallel lines to form a parallelogram.
For any parallelogram, the adjacent angles are supplementary.
150+x = 180
x = 180-150
x = 30
Next, draw a segment connecting the bottom left corner to the upper right corner. Erase the "150 degrees" label. This new line segment represents the resultant vector. We'll label it "260 N".
Focus on one of the triangles. Let's say we focused on the triangle on the right.
From here, use the steps the tutor @ikleyn had laid out to solve for q.
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