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

Answer:

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

$\alpha = 17.7\º$

$F = 29.67 N$

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:

$\alpha = \arctan(\frac{F_y}{F_x}) = \arctan(\frac{9.05}{28.26} = 17.7\º$

The magnitude is:

$F = \sqrt {F_x^2 + F_y^2}= \sqrt{798.6 + 81.9} = 29.67 N$