Vector addition of three forces

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Name	Status	Author	Last Modified
Vector addition of three forces	Ready to use	William Haynes	16/01/2024 20:22
Timur's copy of Vector addition of three forces	draft	Timur Zaripov	03/04/2019 11:20
Vector addition of three forces	draft	Xiaodan Leng	10/07/2019 22:12

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Question statement

{geogebra_applet('cmq7dk74',[['A',A], ['B',B], ['C',C], ['O',O], ['MA',MA], ['MB',MB], ['MC',MC], ['units', '"' + units + '"']])}

Determine the resultant of the three forces shown.

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			Name	Type	Generated Value

O	vector	vector(0,0)
A	vector	vector(-4,-4)
B	vector	vector(-3,-4)
C	vector	vector(0,-4)
MA	integer	13
MB	integer	15
MC	integer	17
units	string	N

			Name	Type	Generated Value

F_A	vector	Vector with 2 components
F_B	vector	vector(-9,-12)
F_C	vector	vector(0,-17)
R	vector	Vector with 2 components
theta	number	-115.4701153943
R_mag	quantity	quantity(42.303918256023394, "N")
angle	number	64.5298846057

			Name	Type	Generated Value

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Name

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Value

xxxxxxxxxx
 
vector(0,0)

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Generated value: `vector`

vector(0,0)

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$R$ = Magnitude

$\theta_R$ = Angle measured Sign from the Reference.

Advice

Find the scalar components of the three forces.
Add the scalar components of the components to find the scalar components of the resultant.
$\begin{align}R_x &= \Sigma F_x & R_y &= \Sigma F_y \\R_x &= A_x + B_x + C_x & R_y &= A_y + B_y + C_y \\R_x &= (\var{fmt(F_A[0])}) +(\var{fmt(F_B[0])}) + (\var{fmt(F_C[0]) }) & R_y &=( \var{fmt(F_A[1])}) + (\var{fmt(F_B[1])} )+(\var{fmt(F_C[1])})\\R_x &= \var{qty(fmt(R[0]),units)} & R_y &=\var{qty(fmt(R[1]),units)}\end{align}$
Draw a triangle representing $\textbf{R}= \textbf{R}_x + \textbf{R}_y$,
Use the pythagorean theorem and inverse tangent to find the magnitude and direction of $\textbf{R}.$
$ \begin{align}R &= \sqrt{R_x^2 + R_y^2} = \var{qty(fmt(abs(R)),units)}& \theta&=\arctan{\left(\left|\dfrac{R_y}{R_x}\right|\right)} = \var{fmt(angle)}°\end{align}$

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William Haynes 4 years, 2 months ago

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William Haynes 4 years, 6 months ago

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William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

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Generated value: `vector`

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Vector addition of three forces

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

Error in variable testing condition

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Generated value: vector

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Generated value: `vector`