Question

Part A Determine the magnitude of the x component of F using scalar notation. Fx F x = nothing lb Request Answer Part B Determine the magnitude of the y component of F using scalar notation. Fy F y = nothing lb Request Answer Part C Determine the magnitude of the z component of F using scalar notation. Fz F z = nothing lb Request Answer Provide Feedback Figure1 of 1A force vector acting on a ring attached to the ground is shown in the xyz space together with its x, y, and z components lying on the corresponding positive axes. The ring is located at the origin. Force F is located in the first octant. F makes an angle of 60 degrees with its x component and an angle of 45 degrees with its y component. A force vector acting on a ring attached to the ground is shown in the xyz space together with its x, y, and z components lying on the corresponding positive axes. The ring is located at the origin. Force F is located in the first octant. F makes an angle of 60 degrees with its x component and an angle of 45 degrees with its y component.

Answer 1

As we know that force F makes an angle of 60 degree with X axis

so the X component is given as

$cos60 = \frac{F_x}{F}$

now we have

$F_x = F cos60$

$F_x = 0.50 F$

Similarly we know that force F makes an angle of 45 degree with Y axis

so the X component is given as

$cos45 = \frac{F_y}{F}$

now we have

$F_y = F cos45$

$F_y = 0.707 F$

Now for the component along z axis we know that

$F_x^2 + F_y^2 + F_z^2 = F^2$

now plug in all components

$(0.707 F)^2 + (0.50 F)^2 + F_z^2 = F^2$

$0.5 F^2 + 0.25 F^2 + F_z^2 = F^2$

$F_z^2 = F^2(1 - 0.75)$

$F_z^2 = 0.25 F^2$

$F_z = 0.5 F$