A force of 200n is inclined at an angle of 120° to another force P. The angle between the 200n force and the resultant force is 50°. Find th

Question

A force of 200n is inclined at an angle of 120° to another force P. The angle between the 200n force and the resultant force is 50°. Find the magnitude of the force P and the resultant of the two force.?​

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Delwyn 4 years 2021-07-28T21:50:16+00:00 1 Answers 47 views 0

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  1. Nem
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    2021-07-28T21:51:39+00:00
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    Answers:  

    Magnitude of force P = 163.041494

    Magnitude of resultant force = 184.320997

    Values are approximate. Units are in newtons.

    ====================================================

    Explanation:

    Let for P be pulled directly to the east. The vector for this force is <x, 0> where x is positive.

    The 200 newton force has the vector <200*cos(120), 200*sin(120)>

    The resultant vector is <x+200*cos(120),200*sin(120)>. Each component is the sum of the corresponding components of <x,0> and <200*cos(120), 200*sin(120)>

    The resultant vector is also <r*cos(70),r*sin(70)>. Note how 70+50 = 120. The 50 degree angle is known, so we effectively do 120-50 = 70 to find the angle of the resultant vector with the positive x axis.

    ——————————

    The resultant vector expressions we found were

    • <r*cos(70),r*sin(70)>
    • <x+200*cos(120),200*sin(120)>

    Equate the y components of each resultant vector expression. Solve for r

    r*sin(70) = 200*sin(120)

    r = 200*sin(120)/sin(70)

    r = 184.320997021376

    Make sure your calculator is in degree mode.

    Let’s round this r value to 6 decimal places to simplify things a bit

    r = 184.320997

    ——————————

    Now equate the x components of each resultant vector expression, plug in the r value we found, and solve for x

    x+200*cos(120) = r*cos(70)

    x+200*cos(120) = 184.320997*cos(70)

    x = 184.320997*cos(70) – 200*cos(120)

    x = 163.041494

    this value is approximate just like r is as well

    ——————————

    The magnitude of force P is

    magnitude = sqrt(x^2+y^2)

    magnitude = sqrt(x^2+0^2)

    magnitude = sqrt((163.041494)^2+0^2)

    magnitude = 163.041494

    Which is equal to the x value. This applies because y = 0.

    —————————–

    The magnitude of the resultant is r = 184.320997 which we found earlier

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