# 001 Horizontal and vertical componets of planar forces

**Problem 001**

Problem Determine the *x* and *y* components of the forces shown below in Fig P-001.

**Solution 001**

$F_{y1} = 58 \sin 30^\circ = 29 \, \text{ kN}$

$F_{x2} = -50 \cos 45^\circ = -35.36 \, \text{ kN}$

$F_{y2} = 50 \sin 45^\circ = 35.36 \, \text{ kN}$

$F_{x3} = -45(\frac{5}{13}) = -17.31 \, \text{ kN}$

$F_{y3} = -45(\frac{12}{13}) = -41.54 \, \text{ kN}$

$F_{x4} = 40 \, \text{ kN}$

$F_{y4} = 0$

**Rectangular Representation**

${\bf F} = F (\cos \theta_x {\bf i} + \sin \theta_x {\bf j})$

${\bf F_1} = 58 (\cos 30^\circ {\bf i} + \sin 30^\circ {\bf j}) = 50.23 {\bf i} + 29 {\bf j} \, \text{ kN}$

${\bf F_2} = 50 (-\cos 45^\circ {\bf i} + \sin 45^\circ {\bf j}) = -35.36 {\bf i} + 35.36 {\bf j} \, \text{ kN}$

${\bf F_3} = 45 (-\frac{5}{13} {\bf i} - \frac{12}{13} {\bf j}) = -17.31 {\bf i} - 41.54 {\bf j} \, \text{ kN}$

${\bf F_4} = 40 {\bf i} \, \text{ kN}$

From the above vector notations, *F _{x}* is the coefficient of

**i**and

*F*is the coefficient of

_{y}**j**.

**Calculator Techniques**

**Technique 1 -** Calculator in CMPLX mode: [MODE] → 2:CMPLX

For F_{1} = 58 kN:

To get the decimal display, input [S⇔D]

58 ∠ 30 = $50.23 + 29{\bf i}$

Thus,

$F_{x1} = 50.23 \, \text{kN}$

$F_{y1} = 29 \, \text{kN}$

Note: To enter the ∠ in the operation, input [SHIFT] → [(–)] and the calculator will display the symbol ∠. If not, that means, you are not yet in CMPLX mode.

For F_{2} = 50 kN:

Press [S⇔D] $-35.36 + 35.36{\bf i}$

Thus,

$F_{x2} = -35.36 \, \text{kN}$

$F_{y2} = 35.36 \, \text{kN}$

For F_{3} = 45 kN:

^{-1}(12/5)) = $-\frac{225}{13} - \frac{540}{13}{\bf i}$

Press [S⇔D] $-17.31 - 41.54{\bf i}$

Thus,

$F_{x3} = -17.31 \, \text{kN}$

$F_{y3} = -41.54 \, \text{kN}$

**Technique 2 -** Using Rec. Calculator in COMP mode: [MODE] → 1:COMP

To enter Rec input [SHIFT] → [–] and for comma " , " input [SHIFT] → [ ) ]

Note: For this method, the answer in *X* and *Y* are automatically stored to variable *X* and *Y*, replacing any stored values in those variables. To recall the new values, simply input [ALPHA] X or [ALPHA] Y

For F_{1} = 58 kN:

X = 50.23, Y = 29

For F_{2} = 50 kN:

X = -35.36, Y = 35.36

For F_{3} = 45 kN:

^{-1}(12/5))=

X = -17.31, Y = -41.54