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

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 = √(F_x+F_y)= 9.54 u`

The direction is given by:
`\theta = \tan^(-1)(F_y)/(F_x)= 63.0 ^\circ`

See the graphical magnitude and direction below.

Step-by-step 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 = √(F_x+F_y)= 9.54 u`

The direction is given by:
`\theta = \tan^(-1)(F_y)/(F_x)= 63.0 ^\circ`