SOLUTION: I'm having trouble with the following example problem and would appreciate if I could get a walkthrough of how to do it. Forces with magnitudes of v = 160 newtons and u = 280 n

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Question 1206728: I'm having trouble with the following example problem and would appreciate if I could get a walkthrough of how to do it.
Forces with magnitudes of v = 160 newtons and u = 280 newtons act on a hook. Find the magnitude of the resultant of this force.
Thank you.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
I'm having trouble with the following example problem and would appreciate if I could get a walkthrough
of how to do it.
Forces with magnitudes of v = 160 newtons and u = 280 newtons act on a hook.
The angle between the two forces is 45°. Find the magnitude of the resultant of this force.
Thank you.
~~~~~~~~~~~~~~~~~~~~~~~~~


        Do it exactly in accordance with the rule. 


The rule of adding forces (vectors) is the parallelogram rule.


In this case you have one vector with the magnitude 160 N
and another vector with the magnitude 280 N.

When you apply the parallelogram rule, the angle between the vectors is 135°.


To find the resultant, use the Law of Cosine

    R^2 = 160^2 + 280^2 - 2*160*280*cos(135°) = 160%5E2+%2B+280%5E2+-+2%2A160%2A280%2A%28-sqrt%282%29%2F2%29 = 167356.7676.


Hence, R = sqrt%28167356.7676%29 = 409.1 N  (rounded).

Solved.

-------------------

For introduction to vectors on a plane, see the lessons
    - Vectors in a plane
    - Sum of vectors that are coherently oriented sides of a convex closed polygon
    - Sum of vectors that are coherently oriented sides of an unclosed polygon
    - Sum of vectors that connect the center of a parallelogram with its vertices
    - Vectors in a coordinate plane
    - Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane
    - Summing vectors that are coherently oriented sides of a convex closed polygon
    - Summing vectors that are coherently oriented sides of an unclosed polygon
    - The Centroid of a triangle is the Intersection point of its medians
    - The Centroid of a parallelogram is the Intersection point of its diagonals
    - Sum of vectors connecting the center of mass of a triangle with its vertices
    - Sum of vectors connecting the center of mass of a quadrilateral with its vertices
    - Sum of vectors connecting the center of mass of a n-sided polygon with its vertices
    - Sum of vectors connecting the center of a regular n-sided polygon with its vertices
    - Solved problems on vectors in a plane
    - Solved problems on vectors in a coordinate plane
    - HOW TO find the length of the vector in a coordinate plane
in this site.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


given:
first force, F%5B1%5D+=+160N at 45⁰
second force, F%5B2%5D+=+280N at 0⁰
The vertical component of the forces is calculated as:
F%5By%5D=160%2Asin%2845%29%2B280%2Asin%280%29
F%5By%5D=160%2A%281%2Fsqrt%282%29%29%2B280%2A%280%29
F%5By%5D=160%2Fsqrt%282%29
F%5By%5D=113.14

The horizontal component of the forces is calculated as:
F%5Bx%5D=160%2Acos%2845%29%2B280%2Acos%280%29
F%5Bx%5D=160%2A%281%2Fsqrt%282%29%29%2B280%2A%281%29
F%5Bx%5D=160%2Fsqrt%282%29%2B280
F%5Bx%5D=393.14

The direction of the forces is:
theta=tan%5E-1%28F%5By%5D%2FF%5Bx%5D%29
theta=tan%5E-1%28113.14%2F393.14%29
theta=tan%5E-1%280.28778552169710536%29
theta=0.28021352584028169 radians
theta=16.06°

Magnitude of resultant force:
R=sqrt%28113.14%5E2%2B393.14%5E2%29
R=409.096