Question

10. A force F S 1 of magnitude 6.00 units acts on an object at the ori- gin in a direction u 5 30.0° above the positive x axis (Fig. P3.10). A second force F S 2 of magnitude 5.00 units acts on the object in the direction of the positive y axis. Find graphically the mag- nitude and direction of the resul- tant force F S 1 1 F S

Answer 1

Answer:

The x component of the x axis is:   $F_x = F_1\cos(30)=5\cos(30)= 4.33 u$

The y component of the y axis is:  $F_y =F_2+ F_1\sin(30)=6.00+5\sin(30)= 8.50 u$

The magnitude is given by:  $F = \sqrt{F_x+F_y}= 9.54 u$

The direction is given by:  $\theta = \tan^{-1}\frac{F_y}{F_x}= 63.0 ^\circ$

See the graphical magnitude and direction below.

Explanation:

The x component of the x axis is:   $F_x = F_1\cos(30)=5\cos(30)= 4.33 u$

The y component of the y axis is:  $F_y =F_2+ F_1\sin(30)=6.00+5\sin(30)= 8.50 u$

The magnitude is given by:  $F = \sqrt{F_x+F_y}= 9.54 u$

The direction is given by:  $\theta = \tan^{-1}\frac{F_y}{F_x}= 63.0 ^\circ$