How solve this vector´s problem ?

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How solve this vector´s problem ?

The graph shows the vectors F and R that represent a pair of forces applied to the wheel of a toy, where the origin of the coordinate system corresponds to the position of the wheel axis.
Calculate the total force with operation 5 F+10R

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Answer 1 · 2017-11-29T19:36:27

$T = 5 | F | + 10 | R |$ $T = 5absF+10absR$

Explanation:

Assuming the question asks for the total torque due to the forces $F$ $F$ and $R$ $R$ we have

$T = d_{1} | F | + d_{2} | R |$ $T = d_1 absF + d_2 absR$

but

$d_{1} = \sqrt{3^{2} + 4^{2}} = 5$ $d_1 = sqrt(3^2+4^2)= 5$
$d_{2} = \sqrt{6^{2} + 8^{2}} = 10$ $d_2 =sqrt(6^2+8^2)=10$

then

$T = 5 | F | + 10 | R |$ $T = 5absF+10absR$

NOTE

If the forces are in a scale representation we have

$| F | = λ \sqrt{3^{2} + 4^{2}} = 5 λ$ $absF = lambda sqrt(3^2+4^2) = 5 lambda$
$| R | = λ \sqrt{3^{2} + 4^{2}} = 5 λ$ $absR = lambda sqrt(3^2+4^2) = 5 lambda$

and then

$T = (5 \times 5 + 10 \times 5) λ = 75 λ$ $T = (5 xx 5 + 10 xx 5)lambda = 75 lambda$

Here $λ$ $lambda$ is the scale factor for $F, R$ $F,R$

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How solve this vector´s problem ?

The graph shows the vectors F and R that represent a pair of forces applied to the wheel of a toy, where the origin of the coordinate system corresponds to the position of the wheel axis.
Calculate the total force with operation 5 F+10R

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How solve this vector´s problem ?

The graph shows the vectors F and R that represent a pair of forces applied to the wheel of a toy, where the origin of the coordinate system corresponds to the position of the wheel axis. Calculate the total force with operation 5 F+10R

1 Answer

Explanation:

Related questions

Impact of this question

The graph shows the vectors F and R that represent a pair of forces applied to the wheel of a toy, where the origin of the coordinate system corresponds to the position of the wheel axis.
Calculate the total force with operation 5 F+10R