Question

Consider two force vectors in the xy-horizontal plane. Suppose a force of 12.7 N pointing along the +x-axis is added to a second force of 18.1 N directed at 30 degrees to the +x-axis , also in the horizontal plane. Find the resultant vector for this sum. magnitude direction degrees above the +x-axis in the horizontal plane

Answer 1

`F_1+F_2= (28.26, 9.05) N`

`\alpha = 17.7\º`

`F = 29.67 N`

Step-by-step explanation:

Hi!

In a (x, y) coordinate representation, the two forces are:

`F_1=(12.7N, 0)\\F_2=(18.1N\cos(30\º), 18.1N \sin(30\º) )\\\cos(\º30)=0.86\\\sin(\º30)= 0.5`

The sum of the two forces is:

`F_1 + F_2 = ( 12.7 + 0.86*18.1, 18.1*0.5) N`

`F_1+F_2= (28.26, 9.05) N`

The angle to x-axis is calculated using arctan:

`\alpha = \arctan((F_y)/(F_x)) = \arctan((9.05)/(28.26) = 17.7\º`

The magnitude is:

`F = \sqrt {F_x^2 + F_y^2}= √(798.6 + 81.9) = 29.67 N`