Question

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 200 N and b = 400 N. Round your answers to one decimal place.)

Answer 1

Answer: R = 346.4N and angle 30° to the horizontal negative axis

Explanation:

To find the resultant force, we need to sum up the forces on the vertical and horizontal axis.

For the horizontal axis;

Rx = -b + acos60

Rx = -400N +200cos60

Rx = -400N +100N

Rx = -300N

For the vertical axis;

Ry = asin60 = 200sin60

Ry = 173.2N

The resultant force R can be given as;

R = √(Rx^2 +Ry^2)

R = √((-300)^2 + 173.2^2)

R = 346.4N

Angle z can be written as

Tanz = Ry/Rx

z = taninverse (Ry/Rx)

z = taninverse (173.2/300)

z = 30°

Answer 2

The resultant force is the sum of the vertical and horizontal force. The magnitude resultant vector and the angle is 173.2 N and $30^o$ respectively.

   

To find the resultant force, sum up the vertical and horizontal force,

In the horizontal axis;  

$\rm Rx = -b + acos60^o$  

Put the values in the formula,

$\rm Rx = -400\ N +200\ cos60^o\\\\ Rx = -400\ N +100 \ N\\\\ Rx = -300\ N$

For the vertical axis;  

$\rm Ry = a\ sin60^o \\\\Ry= 200\ sin60^o\\\\Ry = 173.2\ N$

So, the resultant force R :  

$R = \sqrt {(Rx^2 +Ry^2)}\\\\R = \sqrt {((-300)^2 + 173.2^2)}\\\\R = 346.4\rm \ N$

The angle can be calculated by the formula,  

$\rm tan\theta = \dfrac {Ry}{Rx}$

Put the values and solve for $\theta$,  

$\theta = tan^{-1} \dfrac {Ry}{Rx}\\\\\theta = tan^{-1} \dfrac {173.2}{300}\\\\\theta = 30^o$

Therefore, the magnitude resultant vector and the angle is 173.2 N and $30^o$ respectively.

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